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  <front>
    <journal-meta><journal-id journal-id-type="publisher">SE</journal-id><journal-title-group>
    <journal-title>Solid Earth</journal-title>
    <abbrev-journal-title abbrev-type="publisher">SE</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Solid Earth</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1869-9529</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/se-12-187-2021</article-id><title-group><article-title>A systems-based approach to parameterise seismic hazard <?xmltex \hack{\break}?>in regions with
little historical or instrumental seismicity: <?xmltex \hack{\break}?>active fault and seismogenic
source databases for <?xmltex \hack{\break}?>southern Malawi</article-title><alt-title>A systems-based approach to parameterise seismic hazard</alt-title>
      </title-group><?xmltex \runningtitle{A systems-based approach to parameterise seismic hazard}?><?xmltex \runningauthor{J.~N.~Williams et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Williams</surname><given-names>Jack N.</given-names></name>
          <email>williamsj132@cardiff.ac.uk</email>
        <ext-link>https://orcid.org/0000-0001-6669-308X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Mdala</surname><given-names>Hassan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Fagereng</surname><given-names>Åke</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6335-8534</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Wedmore</surname><given-names>Luke N. J.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Biggs</surname><given-names>Juliet</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Dulanya</surname><given-names>Zuze</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Chindandali</surname><given-names>Patrick</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Mphepo</surname><given-names>Felix</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>School of Earth and Environmental Sciences, Cardiff University, Cardiff, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Geological Survey Department, Mzuzu Regional Office, Mzuzu, Malawi</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>School of Earth Sciences, University of Bristol, Bristol, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Geography and Earth Sciences Department, University of Malawi, Zomba, Malawi</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Geological Survey Department, Zomba, Malawi</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Jack N. Williams (williamsj132@cardiff.ac.uk)</corresp></author-notes><pub-date><day>27</day><month>January</month><year>2021</year></pub-date>
      
      <volume>12</volume>
      <issue>1</issue>
      <fpage>187</fpage><lpage>217</lpage>
      <history>
        <date date-type="received"><day>5</day><month>June</month><year>2020</year></date>
           <date date-type="rev-request"><day>14</day><month>July</month><year>2020</year></date>
           <date date-type="rev-recd"><day>19</day><month>October</month><year>2020</year></date>
           <date date-type="accepted"><day>18</day><month>November</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 </copyright-statement>
        <copyright-year>2021</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://se.copernicus.org/articles/.html">This article is available from https://se.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://se.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://se.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e177">Seismic hazard is commonly characterised using instrumental seismic records.
However, these records are short relative to earthquake repeat times, and
extrapolating to estimate seismic hazard can misrepresent the probable
location, magnitude, and frequency of future large earthquakes. Although
paleoseismology can address this challenge, this approach requires certain
geomorphic setting, is resource intensive, and can carry large inherent
uncertainties. Here, we outline how fault slip rates and recurrence
intervals can be estimated by combining fault geometry, earthquake-scaling
relationships, geodetically derived regional strain rates, and geological
constraints of regional strain distribution. We apply this approach to
southern Malawi, near the southern end of the East African Rift, and where,
although no on-fault slip rate measurements exist, there are constraints on
strain partitioning between border and intra-basin faults. This has led to
the development of the South Malawi Active Fault Database (SMAFD), a
geographical database of 23 active fault traces, and the South Malawi
Seismogenic Source Database (SMSSD), in which we apply our systems-based
approach to estimate earthquake magnitudes and recurrence intervals for the
faults compiled in the SMAFD. We estimate earthquake magnitudes of <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.4–7.2 for individual fault sections in the SMSSD and <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.6–7.8 for
whole-fault ruptures. However, low fault slip rates (intermediate estimates
<inline-formula><mml:math id="M3" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.05–0.8 mm/yr) imply long recurrence intervals between
events: 10<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>–10<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> years for border faults and 10<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>–10<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> years for intra-basin faults. Sensitivity analysis indicates that the large
range of these estimates can best be reduced with improved geodetic
constraints in southern Malawi. The SMAFD and SMSSD provide a framework for
using geological and geodetic information to characterise seismic hazard in
regions with few on-fault slip rate measurements, and they could be adapted for
use elsewhere in the East African Rift and globally.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e255">Earthquake ruptures tend to occur on pre-existing faults
(Brace and Byerlee, 1966; Jackson,
2001; Scholz, 2002; Sibson, 1989). Thus, the identification and systematic
mapping of active faults, which are then compiled with other fault
attributes (e.g. slip rate and slip sense) into a geospatial active fault
database, provide an important tool for assessing regional seismic hazard
(Christophersen
et al., 2015; Hart and Bryant, 1999; Langridge et al., 2016; Shyu et al.,
2016; Styron et al., 2020; Styron and Pagani, 2020; Taylor and Yin, 2009).
Not only can these databases provide information on<?pagebreak page188?> the surface rupture risk
(Hart and Bryant, 1999; Villamor
et al., 2012), they can also be converted into earthquake sources for
probabilistic seismic hazard analysis (PSHA) to forecast future levels of
ground shaking
(Beauval
et al., 2018; Cornell, 1968; Gerstenberger et al., 2020; Hodge et al., 2015;
Morell et al., 2020; Stirling et al., 2012). Furthermore, the data contained
in active fault databases are inherently useful for understanding regional
geological evolution
(Agostini
et al., 2011b; Basili et al., 2008; Taylor and Yin, 2009).</p>
      <p id="d1e258">Active fault databases with worldwide coverage have been compiled
(Christophersen et al., 2015; Yeats,
2012), including recent development of the Global Earthquake Model
Foundation Global Active Fault Database (Styron and
Pagani, 2020). However, in some regions, the fault mapping in these
databases has only been performed at a coarse scale, and the fault
attributes (e.g. slip rates, earthquake recurrence intervals) that are
required to use them as earthquake sources in PSHA have not been measured.
This partly reflects that obtaining these attributes from dating faulted
surfaces and/or paleoseismology is time-intensive, requires certain
geomorphic settings, and can involve large uncertainties
(Cowie
et al., 2012; McCalpin, 2009; Nicol et al., 2016b). Alternatively, decadal
timescale fault slip rates can be estimated using geodetic data and block
models where the crust is divided by mapped faults
(e.g. Field et al., 2014; Wallace et al., 2012; Zeng and Shen, 2014). However, not
all fault systems are covered by sufficiently dense geodetic networks to
perform this analysis, the resulting slip rates may be biased by the short
time over which these data have been collected relative to earthquake cycles,
and/or sometimes geodetic data cannot resolve how strain is distributed
(Calais et
al., 2016; Morell et al., 2020; Stein et al., 2012).</p>
      <p id="d1e261">In this study, we first describe the South Malawi Active Fault Database
(SMAFD), which is a systematic attempt to map active faults and collate their
geomorphic attributes in southern Malawi. Located within the East African
Rift System (EARS), southern Malawi lies in a region specifically
highlighted by Styron and Pagani (2020) as a
priority area for future active fault mapping; population growth in this region
as well as seismically vulnerable building stock is also driving an increased exposure
to seismic hazard
(Tectonic Shift RIFT2018 Report, 2019; Goda et al., 2016; Hodge et al., 2015; Kloukinas et al., 2020;
Ngoma et al., 2019; Novelli et al., 2019).</p>
      <p id="d1e264">Within southern Malawi itself, faults capable of hosting <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 7–8
earthquakes have been previously identified
(Hodge
et al., 2019, 2020; Jackson and Blenkinsop, 1997; Wedmore et al., 2020a).
However, there are currently no reports of historical surface-rupturing
earthquakes, on-fault slip rate measurements, or paleoseismic
investigations. Thus, in the second part of this study, we describe a new
systems-based approach for combining geodetic and geological information to
estimate slip rates and earthquake recurrence intervals. In particular, it
may be useful for low-slip-rate interplate regions (regional slip rates
<inline-formula><mml:math id="M9" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1–10 mm/yr; Scholz et al.,
1986) where the instrumental record is relatively short compared with fault
recurrence intervals and where earthquakes may be especially damaging
(England and Jackson, 2011). It would not, however, be
appropriate for low-strain intraplate settings where geodetic data cannot
resolve deformation rates (Calais et al.,
2016),</p>
      <p id="d1e286">By applying this approach to southern Malawi, we have developed the South
Malawi Seismogenic Source Database (SMSSD), which is a complementary database to the
SMAFD but where the attributes (e.g. fault segmentation, earthquake
recurrence intervals) are (1) targeted towards its inclusion in PSHA and
(2) derived from modelling (and are therefore mutable). Notably, previous PSHA in the
EARS has typically been conducted using the <inline-formula><mml:math id="M10" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 65-year-long
instrumental seismic record alone
(Ayele,
2017; Goitom et al., 2017; Midzi et al., 1999; Poggi et al., 2017). However,
fault-based earthquake sources, such as the SMSSD, may play an important
role in characterising the EARS's ever-increasing seismic risk
(Goda et al., 2016;
Hodge et al., 2015).</p>
      <p id="d1e296">We describe the SMAFD and SMSSD together here so that the assumptions and
uncertainties of our approach are clear, particularly for hazard modellers
who may wish to incorporate these databases into a PSHA. This study first
describes the seismotectonic setting of southern Malawi (Sect. 2), and the
approach used for mapping its active faults in the SMAFD (Sect. 3). In Sect. 4, we then describe the method used to estimate fault slip rates, earthquake
magnitudes, and recurrence intervals, and whose application to southern
Malawi has resulted in the development of the SMSSD. The SMAFD is described
in Sect. 5 along with an evaluation of fault slip rate estimates and
sensitivity analysis in the SMSSD. Finally, in Sect. 6, we discuss the
implication of these databases in terms of southern Malawi's seismic hazard,
and the strategies needed to reduce uncertainties in these databases.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Southern Malawi seismotectonics</title>
      <p id="d1e307">The SMAFD and SMSSD cover the geopolitical term “southern Malawi”; thus,
they include all active faults between the southern end of Lake Malawi and the
border between Mozambique and Malawi. Faults that lie close to or cross
this national boundary are also included. The extent of these databases
does not therefore correspond directly to the geological region of the
“southern Malawi Rift”, whose definition has varied in previous studies
(Chapola
and Kaphwiyo, 1992; Ebinger et al., 1987; Laõ-Dávila et al., 2015;
Williams et al., 2019). In this section, we briefly summarise the tectonic
history and seismic record in the region.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e312"><bold>(a)</bold> The location of Malawi in the context of major faults in the East
African Rift
(Daly
et al., 2020; Hodge et al., 2018a; Macgregor, 2015) and plate boundaries
proposed by Saria et al. (2013). LZR represents the Lower Zambezi Rift, LR represents the Luangwa Rift, and
RVP represents the Rungwe Volcanic Province. <bold>(b)</bold> A simplified geological map of Malawi, with
Proterozoic terranes after Fullgraf et al. (2017). The map is underlain by the Shuttle Radar Topography Mission (SRTM) 30 m
digital elevation model (DEM; Sandwell et
al., 2011). The extent of Fig. 2 is also shown. Active faults within this area are
those included in the South Malawi Active Fault Database (SMAFD). Active
faults outside this region are mapped as in panel <bold>(a)</bold>. Focal mechanisms collated from
Delvaux and Barth (2010),
Craig et al. (2011), and the
U.S. Department of the Interior U.S.
Geological Survey (2018). Minimum principal compressive stress (<inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) trend from focal mechanism stress inversion
(Williams et al., 2019). Plate motion
vector for central point of each basin in southern Malawi (Fig. S1) for the
Nubia–Rovuma Euler pole
(Saria et al., 2013),
modelled using methods described in
Robertson et al. (2016).</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f01.png"/>

      </fig>

<?xmltex \hack{\newpage}?>
<?pagebreak page189?><sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Southern Malawi tectonic setting</title>
      <p id="d1e350">Southern Malawi lies towards the southern incipient end of the EARS Western
Branch, where it channels the Shire River from Lake Malawi to its confluence
with the Zambezi River
(Dulanya, 2017; Ivory
et al., 2016). This portion of the EARS is typically considered to represent
the divergent boundary between the Rovuma and Nubia plates
(Fig. 1a; Saria et al., 2013; Stamps et al., 2008, 2018, 2020). However, recent
seismotectonic analysis suggests that the Nubia Plate can be further divided
by the Lower Zambezi and Luangwa rifts into the San and Angoni plates, with
the EARS in Malawi forming the Angoni–Rovuma plate boundary (Fig. 1a;
Daly et al., 2020). EARS
activity in southern Malawi is unlikely to have initiated prior to the
mid-Pliocene (<inline-formula><mml:math id="M12" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 4.5 Ma) onset of sediment accumulation in Lake
Malawi's south basin
(Delvaux,
1995; McCartney and Scholz, 2016; Scholz et al., 2020) and almost certainly
not before the Oligocene (23–25 Ma) age of the Rungwe Volcanic Province
(RVP) in southern Tanzania
(Mesko,
2020; Mortimer et al., 2016; Roberts et al., 2012). The RVP, 700 km to the north (Fig. 1a), marks the closest surface volcanism to southern Malawi; hence, this rift section is considered to be amagmatic.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e362"><bold>(a)</bold> Global Earthquake Model Global Active Fault Database map for
southern Malawi (GAF-DB;
Macgregor, 2015; Styron and Pagani, 2020). The sub-Saharan African Global
Earthquake Model (SSA-GEM; Poggi et al., 2017)
event locations are also shown. <bold>(b)</bold> Map of active fault traces compiled in the
South Malawi Active Fault Database (SMAFD) with field locations and TanDEM-X
coverage. Faults not interpreted to be active are also shown. <bold>(c)</bold> Aeromagnetic
image created from the vertical derivative, with foliation orientations
digitised from geological maps
(Bloomfield,
1958, 1965; Bloomfield and Garson, 1965; Habgood et al., 1973; Walshaw,
1965). SMAFD faults shown in white and the outline of lakes are shown by dashed
white lines. For full details of the acquisition of the aeromagnetic data,
see Laõ-Dávila et al. (2015). <bold>(d)</bold> Simplified geometry of faults in the South Malawi Seismogenic Source
Database (SMSSD), with faults sorted into border and intra-basin faults.
Ticks indicate fault hanging wall. The extent of all maps is equivalent and is
outlined in Fig. 1b. All maps are underlain by the SRTM 30 m digital elevation
model. “Mal” denotes Malawi, and “Moz” denotes Mozambique.</p></caption>
          <?xmltex \igopts{width=312.980315pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f02.png"/>

        </fig>

      <?pagebreak page191?><p id="d1e382">Like elsewhere in the Western Branch, the EARS in southern Malawi follows
Proterozoic orogenic belts and can be divided along strike into a number of
50–150 km long linked basins (Ebinger,
1989). Immediately south of Lake Malawi, the EARS bifurcates around the
Shire Horst within the NW–SE trending Makanjira Graben before following an
arcuate bend in regional Proterozoic fabrics to form the NNE–SSW trending
Zomba Graben
(Fig. 2; Dulanya, 2017; Fullgraf et al., 2017; Laõ-Dávila et al., 2015;
Wedmore et al., 2020a; Williams et al., 2019). Along strike to the south,
the EARS then intersects the Lower Shire Basin, a reactivated Karoo-age
(i.e. Permo-Triassic) basin
(Castaing,
1991; Chisenga et al., 2019; Habgood, 1963; Habgood et al., 1973; Wedmore et
al., 2020b), before bending around the Nsanje Horst to link up with the
Urema Graben in Mozambique
(Bloomfield,
1958; Steinbruch, 2010). Daly et al. (2020) proposed that the Lower Shire
Basin also extends to the west along the Mwanza Basin into Mozambique where
it links with the Lower Zambezi Rift and forms the San–Angoni plate boundary
(Fig. 1a).</p>
      <p id="d1e386">Prior to this study, the only systematic active fault mapping in southern
Malawi had been conducted by Chapola and Kaphwiyo (1992) and,
for the Lower Shire Basin, by Castaing (1991).
These maps were subsequently incorporated by
Macgregor (2015) into EARS-scale maps, and later
into the Global Earthquake Model Global Active Fault Database
(Styron and Pagani, 2020). However, the faults are
mapped at a coarse scale (Fig. 2a), and this database does not include
active faults traces identified in legacy geological maps
(Bloomfield,
1965; Bloomfield and Garson, 1965; Habgood et al., 1973; Walshaw, 1965) and
high-resolution digital elevation models
(Hodge
et al., 2019, 2020; Wedmore et al., 2020a, b).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Southern Malawi seismicity</title>
      <p id="d1e397">There are no known historical accounts of surface-rupturing earthquakes in
southern Malawi, although a continuous written record only extends to ca. 1870 (Pike, 1965; Stahl, 2010). However, in northern Malawi, the
previously unrecognised St Mary Fault exhibited surface rupture following
the 2009 Karonga earthquakes, a sequence consisting primarily of four
shallow (focal depths <inline-formula><mml:math id="M13" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 8 km) <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.5–5.9 events over a 13 d period
(Fig. 1b; Biggs et al., 2010; Gaherty et al., 2019; Hamiel et al., 2012; Kolawole
et al., 2018b; Macheyeki et al., 2015).</p>
      <p id="d1e418">The International Seismological Centre (ISC) record for Malawi is complete
from 1965 to present for events with <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">4.5</mml:mn></mml:mrow></mml:math></inline-formula>
(Figs. 1b, 2a; Hodge et al.,
2015), with the largest event in this record being the 1989 <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 6.3
Salima earthquake (Jackson and Blenkinsop,
1993). Notably, seismicity in Malawi is commonly observed to depths far
greater
(30–35 km; Craig et al., 2011; Delvaux and Barth, 2010; Jackson and Blenkinsop,
1993) than would be expected for continental crust of typical composition
and geothermal gradient (10–15 km). Thick cold anhydrous lower crust
(Craig
et al., 2011; Jackson and Blenkinsop, 1997; Njinju et al., 2019; Nyblade and
Langston, 1995), localised weak viscous zones embedded within strong lower
crust (Fagereng, 2013), and/or volumes
of mafic material in the lower crust (Shudofsky et al.,
1987) that are velocity weakening at temperatures <inline-formula><mml:math id="M17" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 700 <inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (Hellebrekers et al., 2019) have been
proposed as explanations for this unusually deep seismicity.</p>
      <p id="d1e463">Earthquake focal mechanism stress inversions that encompass events from
across Malawi indicate a normal fault stress state (i.e. vertical maximum
principal compressive stress) with an ENE–WSW to E–W trending minimum
principal compressive stress
(<inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, Fig. 1b; Delvaux and Barth, 2010; Ebinger et al., 2019; Williams et
al., 2019). This <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> orientation is comparable to the <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> direction inferred from regional joint orientations
(Williams et al., 2019) and the
geodetically derived extension direction between the Nubia and Rovuma plates
(Fig. 1b; Saria et al., 2014; Stamps et al., 2018, 2020).</p>
      <p id="d1e499">Using instrumental catalogues, probabilistic seismic hazard analysis (PSHA)
finds that there is a 10 % probability of exceeding 0.15 g peak ground
acceleration in the next 50 years in southern Malawi
(Midzi et
al., 1999; Poggi et al., 2017). Through the SMAFD and SMSSD, we outline how
geological and geodetic data can be collated and assessed so that they may
also be incorporated into PSHA in southern Malawi.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Mapping and describing active faults in the South Malawi Active Fault
Database (SMAFD)</title>
      <p id="d1e511">An active fault database consists of an active fault map, where for each
fault, attributes are added that detail geomorphic, kinematic, geometric,
and geological information about the fault
(Christophersen et al.,
2015; Styron and Pagani, 2020). Typically, an active fault database is
stored in a geographic information system (GIS) environment, in which the
fault attributes are assigned to a linear feature that represents the
fault's geomorphic trace
(e.g. Langridge et al., 2016; Machette et al., 2004; Styron et al., 2020). In this
section, we describe how active faults were mapped in the South Malawi
Active Fault Database (SMAFD) as well as the geomorphic attributes that were
assigned to them. Estimates of associated earthquake source parameters,
which are collated separately in the South Malawi Seismogenic Source
Database (SMSSD), are described in Sect. 4.</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Identifying active and inactive faults in southern Malawi</title>
      <p id="d1e521">There are many inherent limitations in mapping active faults. Even in
countries with well-developed databases, such as Italy and New Zealand, their
success in accurately predicting the locations of future surface-rupturing
earthquakes is, at best, mixed
(Basili
et al., 2008; Nicol et al., 2016a). An active fault might not be recognised
because evidence of previous surface rupture is subsequently buried, eroded
(Wallace, 1980), or the fault itself is blind
(e.g. Quigley et al., 2012), which in turn depends on earthquake magnitude, focal
depth, thickness of the seismogenic crust, and the local<?pagebreak page192?> geology.
Furthermore, although active and inactive faults are typically
differentiated by the age of the most recent earthquake, the precise maximum
age that is used to define “active” varies between different active fault
databases depending on the regional strain rate (i.e. plate boundary vs. stable craton) and the prevalence of youthful sediments
(Clark
et al., 2012; Jomard et al., 2017; Langridge et al., 2016; Machette et al.,
2004). Indeed, it may not always be possible to reliably determine if an
exposed fault has been recently active or not
(Cox
et al., 2012; Nicol et al., 2016a).</p>
      <p id="d1e524">Each of these issues has relevance to mapping active faults in southern
Malawi. Firstly, active faults may be buried by sediments deposited due to
tectonic subsidence (Gawthorpe and Leeder, 2000)
and/or by regular (10–100 ka) climate-driven <inline-formula><mml:math id="M22" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 m scale
fluctuations in the level of Lake Malawi, which would likely flood the Zomba
and Makanjira basins
(Ivory
et al., 2016; Lyons et al., 2015; Wedmore et al., 2020a). Alternatively, the
relatively thick (30–35 km) seismogenic crust in southern Malawi means that
even moderate–large earthquakes (<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula>) do not necessarily
result in surface rupture, as illustrated by the <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 6.3 Salima
earthquake (Gupta, 1992; Jackson and
Blenkinsop, 1993). Finally, except for studies around Lake Malombe
(Van Bocxlaer et al.,
2012), there is no chronostratigraphic control for this section of the EARS
to help differentiate between inactive and active faults
(Dulanya, 2017;
Wedmore et al., 2020a).</p>
      <p id="d1e560">Thus, for the SMAFD, we define active faults based on evidence of
activity within the current tectonic regime. Such an approach has been
advocated elsewhere in the EARS
(Delvaux et al., 2017) and in
other areas with low levels of seismicity, few paleoseismic studies, and/or
where there are faults that are favourably oriented for failure in the
current stress regime but that have no definitive evidence of recent
activity
(Nicol
et al., 2016a; De Pascale et al., 2017; Villamor et al., 2018). In practice,
this means that faults will be included in the SMAFD if they can be
demonstrated to have been active during East African rifting. This evidence
can vary from the accumulation of post-Miocene hanging-wall sediments to the
presence of a steep fault scarp, offset alluvial fans, and/or knickpoints in
rivers that have migrated only a short vertical distance (<inline-formula><mml:math id="M25" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 100 m)
upstream
(Hodge
et al., 2019, 2020; Jackson and Blenkinsop, 1997; Wedmore et al., 2020a). We
note that the absence of post-Miocene sediments in the hanging wall of a
normal fault does not necessarily imply that it is inactive, if, for example,
faults are closely spaced across strike so that sediments are eroded during
subsequent footwall uplift of an interior normal fault
(e.g. Chirobwe–Ncheu Fault, Fig. 3c; see also Mortimer et al., 2016; Muirhead et
al., 2016). In these cases, if there is other evidence of recent activity
(e.g. scarp, triangular facets), these faults are still included.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e573">Field examples of border and intra-basin faults in southern Malawi.
Unmanned aerial vehicle (UAV) images of scarps (dashed red line) along the <bold>(a)</bold> intra-basin Mlungusi Fault in the Zomba Graben as well as <bold>(b)</bold> the Thyolo Fault – the
border fault for the Lower Shire Basin. <bold>(c)</bold> View across the western edge of
the Makanjira Graben showing the Chirobwe–Ncheu and Bilila–Mtakataka faults
as well as Proterozoic syenite intrusions
(Walshaw,
1965). <bold>(d)</bold> Minor step in the scarp along the intra-basin Chingale Step fault,
with the escarpment of the Zomba border fault behind.</p></caption>
          <?xmltex \igopts{width=275.991732pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f03.jpg"/>

        </fig>

      <p id="d1e594">For the sake of completeness, major faults that control modern-day
topography but that do not fit the criteria of being active (e.g. Karoo
faults) were mapped separately (Fig. 2a). However, this map is not
necessarily complete for all other faults in southern Malawi, and we also
cannot definitively exclude the possibility that some of these faults are
still active although they display no evidence for it. The relatively broad
definition of an active fault may also mean that some inactive faults are
included in the SMAFD. However, in applying the opposite approach (i.e. requiring an absolute age for the most recent activity on a fault) there is
a greater risk that faults mistakenly interpreted to be inactive
subsequently rupture in a future earthquake
(Litchfield
et al., 2018; Nicol et al., 2016a).</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Datasets for mapping faults in southern Malawi</title>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Legacy geological maps</title>
      <p id="d1e612">Between the 1950s and 1970s, the geology of southern Malawi was
systematically mapped at a <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> 000 scale. These studies noted evidence of
recent displacement on the Thyolo (Habgood et al.,
1973), Bilila–Mtakataka, Tsikulamowa
(Walshaw,
1965), and Mankanjira faults (King and Dawson, 1976). However,
they did not systematically distinguish between active and inactive faults.
Furthermore, these studies are in places ambiguous with equivalent
structures in the Zomba Graben being variably described as “terrace
features” (Bloomfield, 1965), active fault scarps
(Dixey, 1926), and Late Jurassic–Early Cretaceous faults
(Dixey, 1938).</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Geophysical datasets</title>
      <p id="d1e635">Regional-scale aeromagnetic data were acquired across Malawi in 2013 by the
Geological Survey Department of Malawi
(Fig. 2c;
Kolawole et al., 2018a; Laõ-Dávila et al., 2015). These survey data
were used to refine fault mapping in cases where features interpreted as
faults in the aeromagnetic survey extended beyond their surface expression.
Gravity surveys have also been used to map blind faults in the Lower Shire
Basin (Chisenga et al., 2019), and these have
been incorporated into the SMAFD.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e640">Fault segmentation along the Chingale Step fault,
modified after Wedmore et al. (2020a). <bold>(a)</bold> Along-strike variation in stream knickpoint (blue points) and
fault scarp height (black line), with the gap due to erosion by the
Lisanjala River. Grey shading represents 1 standard deviation error in
scarp height measurements (Wedmore et
al., 2020a). <bold>(b)</bold> A map of the Chingale Step fault underlain by TanDEM-X DEM, with the
extent of the area shown in Fig. 2b. The dashed red line shows the surface trace
of the fault as per the South Malawi Active Fault Database (SMAFD). The
solid red line shows the simplified geometry of the fault in the South
Malawi Seismogenic Source Database (SMSSD), where it is defined by straight
lines between section end points (blue triangles). Ticks indicate fault
hanging wall. An along-strike scarp height minima at the boundary between
the northern and central section occurs at a bend in the fault scarp;
however, there is no obvious geometrical complexity at the along-strike
scarp height minima between the southern and central sections. Topography
associated with the Proterozoic Chingale Ring Structure and Chilwa Alkaline
Province (Bloomfield, 1965; Manda et
al., 2019) is also indicated. For full details on panel <bold>(a)</bold>, see
Wedmore et al. (2020a).</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f04.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS2.SSS3">
  <label>3.2.3</label><title>Digital elevation models</title>
      <p id="d1e666">The topography of southern Malawi is primarily controlled by EARS faulting
(Dulanya,
2017; Laõ-Dávila et al., 2015; Wedmore et al., 2020a) except in the
case of the Kirk Range (Fig. 2b) as well as readily identifiable igneous
intrusions and Karoo faults (Figs. 3c, 4b). To exploit this interaction
between topography and active faulting, TanDEM-X digital elevation models
(DEMs) with a 12.5 m horizontal resolution and an absolute vertical mean
error of <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> m (Wessel et al., 2018) were acquired for
southern Malawi (Fig. 2b). This small error means that the TanDEM-X data
perform better at identifying the metre-scale scarps common in southern
Malawi
(Hodge
et al., 2019; Wedmore et al., 2020a) than the more widely used but lower-resolution Shuttle Radar Topography Mission (SRTM) 30 m DEMs
(Sandwell et al.,<?pagebreak page193?> 2011). Furthermore, TanDEM-X
data can be used to assess variations in along-strike scarp height
(Hodge
et al., 2018a, 2019; Wedmore et al., 2020a, b) and the
interactions between footwall uplift and fluvial incision
(Fig. 4a; Wedmore et al., 2020a).
The Mwanza and Nsanje faults partly extended out of the region of TanDEM-X
coverage, and these sections were mapped using the SRTM 30 m resolution DEM
(Fig. 2b).</p>
</sec>
<sec id="Ch1.S3.SS2.SSS4">
  <label>3.2.4</label><title>Fieldwork</title>
      <p id="d1e687">To corroborate evidence of recent faulting recognised in DEMs and geological
reports, fieldwork was conducted on several faults (Fig. 2b). This ranged
from documenting features indicative of recent displacement on the faults,
such as scarps, triangular facets, and displaced Quaternary–recent
sediments, to comprehensively sampling the fault and surveying it with an
unmanned aerial vehicle
(Fig. 3; see also: Hodge et al., 2018a; Wedmore et al., 2020a, b; Williams et
al., 2019).</p><?xmltex \hack{\newpage}?>
</sec>
</sec>
<?pagebreak page194?><sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Strategy for mapping and describing active faults in the SMAFD</title>
      <p id="d1e700">Following the active fault definition and synthesis of the datasets
described above, faults in southern Malawi are mapped following the approach
outlined for the Global Earthquake Model Global Active Fault Database
(GAF-DB) where each fault constitutes a single continuous GIS feature
(Styron and Pagani, 2020). Therefore, the SMAFD
differs from other active fault databases where each distinct geomorphic
(i.e. traces) or geometric (i.e. sections) part of a fault is mapped as a
separate GIS feature
(Christophersen et al., 2015;
Machette et al., 2004).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Table}?><label>Table 1</label><caption><p id="d1e706">List and brief description of attributes in the SMAFD. Attributes
are based on the Global Earthquake Model Global Active Faults Database
(Styron and Pagani, 2020).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="4cm"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="4cm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Attribute</oasis:entry>
         <oasis:entry colname="col2">Type</oasis:entry>
         <oasis:entry colname="col3">Description</oasis:entry>
         <oasis:entry colname="col4">Notes</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SMAFD-ID</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">Unique two-digit numerical <?xmltex \hack{\hfill\break}?>reference ID for each trace</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Assigned based on previous <?xmltex \hack{\hfill\break}?>mapping or local geographic <?xmltex \hack{\hfill\break}?>feature.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Geomorphic expression</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Geomorphological feature used to identify and map fault trace.</oasis:entry>
         <oasis:entry colname="col4">For example, scarp and escarpment</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Location method</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Dataset used to map trace.</oasis:entry>
         <oasis:entry colname="col4">For example, type of digital elevation <?xmltex \hack{\hfill\break}?>model</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Accuracy</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">Coarsest scale at which trace <?xmltex \hack{\hfill\break}?>can be mapped; expressed as <?xmltex \hack{\hfill\break}?>denominator of map scale.</oasis:entry>
         <oasis:entry colname="col4">Reflects the prominence of the fault's geomorphic expression.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">activity_confidence</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">Certainty of neotectonic <?xmltex \hack{\hfill\break}?>activity</oasis:entry>
         <oasis:entry colname="col4">1 if certain, 2 if uncertain</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">exposure_quality</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">Fault exposure quality</oasis:entry>
         <oasis:entry colname="col4">1 if high, 2 if low</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">epistemic_quality</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">Certainty that fault exists there</oasis:entry>
         <oasis:entry colname="col4">1 if high, 2 if low</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">last_movement</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Currently this is unknown for <?xmltex \hack{\hfill\break}?>all faults in southern Malawi <?xmltex \hack{\hfill\break}?>but can be updated when new <?xmltex \hack{\hfill\break}?>information becomes available.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">References</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Relevant geological maps/<?xmltex \hack{\hfill\break}?>literature where fault has <?xmltex \hack{\hfill\break}?>been previously described.</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMSSD ID</oasis:entry>
         <oasis:entry colname="col2">Numeric, assigned</oasis:entry>
         <oasis:entry colname="col3">ID of equivalent structure in <?xmltex \hack{\hfill\break}?>South Malawi Seismogenic <?xmltex \hack{\hfill\break}?>Source Database</oasis:entry>
         <oasis:entry colname="col4">Will be multiple IDs for multi-segment faults, as these consist of multiple potential earthquake sources</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e934">The attributes associated with each fault in the SMAFD are listed and
briefly described in Table 1. These resemble the attributes in the GEM
GAF-DB that describe a fault's geomorphic attributes and confidence that it
is still active (Styron and Pagani, 2020). To
incorporate the multidisciplinary approach that we have used to map faults in
southern Malawi, we also include a “Location method” attribute, which
details how the fault was mapped (Table 1). Some fault attributes used in
the GEM GAF-DB, such as slip rates, are not included in the SMAFD, as these
data have not been collected in southern Malawi. We instead derive these
attributes as outlined in Sect. 4 and incorporate them separately into the
SMSSD (Table 2). However, within each database, a numerical ID system is
used make the two databases compatible (Tables 1, 2).</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>A systems-based approach to estimating seismic source parameters:
application to southern Malawi</title>
      <p id="d1e946">Typically, estimates of fault slip rate, earthquake magnitudes, and
recurrence intervals are derived from paleoseismology, geodesy, historical
records of past earthquakes, or considerations of the seismic moment rate
(Basili
et al., 2008; Field et al., 2014; Langridge et al., 2016; McCalpin, 2009;
Molnar, 1979; Youngs and Coppersmith, 1985). However, as noted in Sect. 1, these types of data have not been collected in southern
Malawi. Indeed, very few such records currently<?pagebreak page195?> exist across the entire EARS
(Delvaux
et al., 2017; Muirhead et al., 2016; Siegburg et al., 2020; Zielke and
Strecker, 2009), and even in regions with well-developed active fault
databases, such as California and New Zealand, only a small number of faults
have directly measured slip rates and paleoseismic information
(Field
et al., 2014; Langridge et al., 2016).</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Table}?><label>Table 2</label><caption><p id="d1e952">List and brief description of fault geometry, slip rate estimates, and earthquake source attributes in the SMSSD.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="87pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="50pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="150pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="6cm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Attribute</oasis:entry>
         <oasis:entry colname="col2">Type</oasis:entry>
         <oasis:entry colname="col3">Description</oasis:entry>
         <oasis:entry colname="col4">Notes</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SMSSD-ID</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">Unique numerical reference ID for <?xmltex \hack{\hfill\break}?>each seismic source</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault name</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Fault that section belongs to</oasis:entry>
         <oasis:entry colname="col4">Assigned based on previous mapping or local <?xmltex \hack{\hfill\break}?>geographic feature.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section name</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Assigned based on previous mapping, local <?xmltex \hack{\hfill\break}?>geographic feature, or location along fault.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Basin</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Basin that fault is located within.</oasis:entry>
         <oasis:entry colname="col4">Used in slip rate calculations.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault type</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Intra-basin or border fault</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section length <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">Straight-line distance between <?xmltex \hack{\hfill\break}?>section tips.</oasis:entry>
         <oasis:entry colname="col4">Measured in kilometres. Except for linking sections, must be <inline-formula><mml:math id="M29" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 5 km.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section strike</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">Measured from section tips, using <?xmltex \hack{\hfill\break}?>bearing that is <inline-formula><mml:math id="M30" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 180<inline-formula><mml:math id="M31" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>.</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault length <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">Straight-line distance between fault <?xmltex \hack{\hfill\break}?>tips or sum of <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for segmented faults.</oasis:entry>
         <oasis:entry colname="col4">Measured in kilometres.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault strike</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">Measured from fault tips using <?xmltex \hack{\hfill\break}?>bearing <inline-formula><mml:math id="M34" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 180<inline-formula><mml:math id="M35" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>.</oasis:entry>
         <oasis:entry colname="col4">For segmented (i.e. non-planar) this is an “averaged” value of fault geometry, which is required for slip rate estimates (Eq. 3).</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Dip (<inline-formula><mml:math id="M36" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Attribute parameterised by a set of representative values (40, 53, 65<inline-formula><mml:math id="M37" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>).</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Dip direction</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Compass quadrant that fault dips in.</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault width (<inline-formula><mml:math id="M38" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Eq. (2)  from <?xmltex \hack{\hfill\break}?>Leonard (2010) scaling  <?xmltex \hack{\hfill\break}?>relationship using <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</oasis:entry>
         <oasis:entry colname="col4">Not equivalent to rupture width for individual-section earthquakes.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Slip type</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Fault kinematics</oasis:entry>
         <oasis:entry colname="col4">All faults in the SMSSD assumed to be normal</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section net slip <?xmltex \hack{\hfill\break}?>rate</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Eq. (3).</oasis:entry>
         <oasis:entry colname="col4">In millimetres per year. All faults in the SMSSD assumed to be normal, so is equivalent to dip-slip rate.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault net slip rate</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Eq. (3).</oasis:entry>
         <oasis:entry colname="col4">In millimetres per year. All faults in the SMSSD assumed to be normal, so is equivalent to dip-slip rate. Different from section net slip rate where fault strike <inline-formula><mml:math id="M40" display="inline"><mml:mo>≠</mml:mo></mml:math></inline-formula> section strike.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section earthquake<?xmltex \hack{\hfill\break}?>magnitude</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Leonard (2010) scaling <?xmltex \hack{\hfill\break}?>relationship using Eq. (4) and <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</oasis:entry>
         <oasis:entry colname="col4">Lower, intermediate, and upper values<?xmltex \hack{\hfill\break}?>calculated.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault earthquake<?xmltex \hack{\hfill\break}?>magnitude</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Leonard (2010) scaling <?xmltex \hack{\hfill\break}?>relationship using Eq. (4) and <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</oasis:entry>
         <oasis:entry colname="col4">Lower, intermediate, and upper values <?xmltex \hack{\hfill\break}?>calculated.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Section earthquake <?xmltex \hack{\hfill\break}?>recurrence interval (<inline-formula><mml:math id="M43" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Eq. (6) and using <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>to calculate average single-event <?xmltex \hack{\hfill\break}?>displacement in Eq. (5).</oasis:entry>
         <oasis:entry colname="col4">Lower, intermediate, and upper values <?xmltex \hack{\hfill\break}?>calculated.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault earthquake <?xmltex \hack{\hfill\break}?>recurrence interval (<inline-formula><mml:math id="M45" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Numeric, <?xmltex \hack{\hfill\break}?>calculated</oasis:entry>
         <oasis:entry colname="col3">Calculated from Eq. (6) and using <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?>to calculate average single-event <?xmltex \hack{\hfill\break}?>displacement in Eq. (5).</oasis:entry>
         <oasis:entry colname="col4">Lower, intermediate, and upper values <?xmltex \hack{\hfill\break}?>calculated.</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault notes</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Remaining miscellaneous information<?xmltex \hack{\hfill\break}?>about fault.</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">References</oasis:entry>
         <oasis:entry colname="col2">Text</oasis:entry>
         <oasis:entry colname="col3">Relevant geological maps/literature <?xmltex \hack{\hfill\break}?>where fault has been <?xmltex \hack{\hfill\break}?>previously described.</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMAFD-ID</oasis:entry>
         <oasis:entry colname="col2">Numeric,<?xmltex \hack{\hfill\break}?>assigned</oasis:entry>
         <oasis:entry colname="col3">ID of equivalent structure in South <?xmltex \hack{\hfill\break}?>Malawi Active Fault Database</oasis:entry>
         <oasis:entry colname="col4"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <p id="d1e1573">In the absence of direct on-fault slip rate estimates, we suggest that they
can be estimated through a systems-level approach in which geodetically
derived plate motion rates are partitioned across faults in a manner
consistent with their geomorphology and regional tectonic regime. Although
such an approach has been used before over small regions
(Cox et al., 2012;
Litchfield et al., 2014), it has not been applied to an entire fault system.
In addition, we outline how the uncertainties and alternative hypotheses
that are inherent to this approach can, in common with seismic hazard
practice elsewhere, be explored with a logic tree approach (Fig. 6;
Field et al., 2014;
Vallage and Bollinger, 2019; Villamor et al., 2018). We use the South Malawi
Seismogenic Source Database (SMSSD) as an example of how this approach can
be applied to narrow (<inline-formula><mml:math id="M47" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 100 km width;
Buck, 1991) amagmatic continental rifts,
where the distribution of regional strain between border faults and
intra-basin faults is well constrained by previous studies
(Agostini
et al., 2011a; Corti, 2012; Gupta et al., 1998; Morley, 1988; Muirhead et
al., 2016, 2019; Nicol et al., 1997; Shillington et al., 2020; Wedmore et
al., 2020a; Wright et al., 2020).</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Earthquake source geometry</title>
      <?pagebreak page197?><p id="d1e1591">Faults may rupture both along their entire length and in smaller individual-section ruptures that are often bounded by changes in fault geometry
(DuRoss
et al., 2016; Goda et al., 2018; Gómez-Vasconcelos et al., 2018; Hodge
et al., 2015; Iezzi et al., 2019; Valentini et al., 2020). Therefore, the
basic GIS feature in the SMSSD is a fault section, where individual faults
from the SMAFD may be divided into multiple sections by bends in their fault
trace
(Fig. 2d; DuRoss et al., 2016; Jackson and White, 1989; Wesnousky, 2008; Zhang et
al., 1991). Along-strike minima in fault displacement (e.g. scarp or
knickpoint height) may also be indicative of segmentation
(Willemse, 1997), but these do not always coincide with
geometrical complexities in southern Malawi
(Fig. 4; Hodge et al., 2018a, 2019; Wedmore et al., 2020a, b). This may
indicate that deeper structures, not visible in the surficial fault
geometry, are also influencing fault segmentation
(Wedmore et al., 2020b). Therefore, where
along-strike scarp height measurements exist, these local minima are also
used to define fault sections (Figs. 2d, 4).</p>
      <p id="d1e1594">Faults that are closely spaced across strike but are not physically connected
may also rupture together through “soft linkages”
(Childs et
al., 1995; Wesnousky, 2008; Willemse, 1997; Zhang et al., 1991). In the
SMSSD, we follow empirical observations and Coulomb stress modelling that
suggests that normal fault earthquakes may rupture across steps whose width
is <inline-formula><mml:math id="M48" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 20 % of the combined length of the interacting sections, up
to a maximum separation of 10 km (Biasi and Wesnousky,
2016; Hodge et al., 2018b), and we use this as a criteria to assign whether
two en echelon faults in the SMSSD may rupture together.</p>
      <p id="d1e1604">A number of geometrical attributes are then assigned to both individual
sections and whole faults in the SMSSD (Table 2). Section length
(<inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) is defined as the straight-line distance between section end
points (Fig. 4b). This approach avoids the difficulty of measuring the
length of fractal features, and it accounts for the hypothesis that small-scale
(less than kilometre-scale) variations in fault geometry in southern Malawi may
represent only near-surface complexity (depths <inline-formula><mml:math id="M50" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 5 km) and that the
faults are relatively planar at depth (Hodge et
al., 2018a). However, it only provides a minimum estimate of section length.
For segmented faults in the SMSSD, fault length (<inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) is the sum of
<inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, otherwise <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the distance between its tips (Fig. 4b).
As each GIS feature in the SMSSD represents a distinct earthquake source,
we consider that <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and/or <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> must be <inline-formula><mml:math id="M56" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M57" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 km, except in the case of linking sections that rupture
only in whole-fault ruptures.
(Christophersen et al., 2015).</p>
      <p id="d1e1695">In southern Malawi, fault dip is either unknown or uncertain, because fault
planes are rarely exposed, surface processes affect scarp angle
(Hodge et
al., 2020), and/or dip at depth is not constrained. This difficulty in
measuring fault dip is common, and dip has been parameterised
using a range of reasonable values in these cases
(Christophersen
et al., 2015; Langridge et al., 2016; Styron et al., 2020). Thus, we assign minimum, intermediate, and maximum dip values in the SMSSD of
40, 53, and 65<inline-formula><mml:math id="M58" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> respectively, which encapsulate dip
estimates from field data in southern Malawi
(Hodge et al., 2018a;
Williams et al., 2019), and earthquake focal mechanisms
(Biggs
et al., 2010; Ebinger et al., 2019), seismic reflection data
(Mortimer
et al., 2007; Wheeler and Rosendahl, 1994), and aeromagnetic surveys
(Kolawole et al., 2018a) elsewhere in
Malawi.</p>
      <p id="d1e1708">It is typically assumed that fault width (<inline-formula><mml:math id="M59" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>) can be estimated by projecting
the difference in lower and upper seismogenic depth into fault dip (<inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>), with the assumption that faults are equidimensional up to the point
where <inline-formula><mml:math id="M61" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> is limited by the thickness of the seismogenic crust
(Christophersen et al., 2015):
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M62" display="block"><mml:mrow><mml:mi>W</mml:mi><mml:mo>=</mml:mo><mml:mfenced open="{" close=""><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>where</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>≤</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>z</mml:mi><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>z</mml:mi><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>where</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>z</mml:mi><mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1820">In southern Malawi, both seismogenic thickness, <inline-formula><mml:math id="M63" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>
(30–35 km;
Jackson and Blenkinsop, 1993; Craig et al., 2011), and <inline-formula><mml:math id="M64" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>
(40–65<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, as justified above) are poorly constrained, so
a range of <inline-formula><mml:math id="M66" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> values must be considered. Furthermore, ruptures unlimited by <inline-formula><mml:math id="M67" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>
are not necessarily equidimensional
(Leonard, 2010;
Wesnousky, 2008). Therefore, in the SMSSD, we estimate <inline-formula><mml:math id="M68" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> from an empirical
scaling relationship between fault length and <inline-formula><mml:math id="M69" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>
(Leonard, 2010):
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M70" display="block"><mml:mrow><mml:mi>W</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:msubsup><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext><mml:mi mathvariant="italic">β</mml:mi></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> km, and <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M73" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> are
empirically derived constants that are equal to 17.5 and 0.66 respectively for
interplate dip-slip earthquakes
(Leonard, 2010). As shown in Fig. 5c, when applying Eq. (2), estimates of <inline-formula><mml:math id="M74" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> in the SMSSD are consistent
with (1) observations of <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> length-to-width ratios for dip-slip
earthquakes (Fig. 5c) and (2) the thick seismogenic crust in East Africa
(i.e. <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mi>W</mml:mi><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> km, Fig. 5c; Craig et al., 2011; Ebinger et al., 2019;
Jackson and Blenkinsop, 1993; Lavayssière et al., 2019; Nyblade and
Langston, 1995).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1964">Assessment of fault geometry in the SMSSD. <bold>(a)</bold> Histograms showing the
distribution of <bold>(a)</bold> fault (<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and section (<inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) lengths in the
SMSSD. <bold>(b)</bold> Histogram of fault widths in the SMSSD as derived from the
Leonard (2010) scaling
relationship (Eq. 2); in panel <bold>(c)</bold>, the predicted aspect ratio of faults
following this relationship (dashed grey line) in comparison to an
alternative method to estimate <inline-formula><mml:math id="M79" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> using Eq. (1) (white circles). <bold>(d)</bold> A
comparison of empirical scaling relationships used to estimate earthquake
magnitudes (<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) from fault geometry in the SMSSD.
Leonard (2010) magnitudes
estimated using Eq. (4), with error bars representing range of <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values derived for interplate dip-slip faults. <inline-formula><mml:math id="M83" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> is the fault area
calculated from <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M85" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> using Eq. (1), WC94 is from
Wells and Coppersmith (1994), and W08 is from
Wesnousky (2008).</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f05.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Estimating fault slip rates</title>
      <p id="d1e2085">For a narrow amagmatic continental rift such as the EARS in southern Malawi,
the first step to estimate slip rates is to divide the rift along its axis
into its basins (Fig. 2b); within each basin, the mapped
faults are then divided into border and intra-basin faults. We define border faults
geometrically, as a fault located at the edge of the rift with the implicit
assumption that all other mapped active faults are intra-basin faults
(Fig. 2d; Ebinger, 1989; Gawthorpe and Leeder, 2000; Muirhead et al., 2019;
Wedmore et al., 2020b). These geometric definitions have no direct
implications for how displacement is partitioned among border and intra-basin
faults.</p>
      <?pagebreak page198?><p id="d1e2088">The slip rate for each fault or fault section <inline-formula><mml:math id="M86" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> is then estimated using the following
equation:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M87" display="block"><mml:mrow><mml:mtext>Slip</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>rate</mml:mtext><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced open="(" close=")"><mml:mi>i</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mfenced open="{" close=""><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub><mml:mi>v</mml:mi><mml:mi>cos⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>bf</mml:mtext></mml:msub><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mtext>for border faults</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mi>v</mml:mi><mml:mi>cos⁡</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>for intra-basin faults</mml:mtext></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
          Here, <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula>) is the fault or fault section slip azimuth, <inline-formula><mml:math id="M89" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> and  <inline-formula><mml:math id="M90" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>
are the respective horizontal rift extension rate and azimuth, <inline-formula><mml:math id="M91" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> is a weighting
applied to each fault depending on whether it is a border (<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)
or intra-basin (<inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) fault, and it is divided by the number of
mapped border faults (<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) or intra-basin faults (<inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) in each basin
(Fig. 6). Although Eq. (3) is specific for rifts, it could be adapted in other
tectonic settings where there is an a priori understanding of the rate and
distribution of regional strain – for example, to distribute regional strain
between the basal detachment and thrust ramps in a fold and thrust belt
(Poblet and Lisle, 2011), to distribute regional strain between multiple
subparallel faults in a strike-slip system, or to assess more complex strain
partitioning between kinematically distinct fault populations in
transtensional or transpressional systems (Braun and
Beaumont, 1995).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e2290">Logic tree for calculating lower, intermediate, and upper
estimates of fault slip rates and earthquake magnitudes and recurrence
intervals in the SMSSD; <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the rift
extension weighting assigned to border faults (BF) and intra-basin faults
(IF) respectively; <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the number of border or
intra-basin faults in a basin respectively; and <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the respective
whole-fault and individual-section slip azimuth values.</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f06.png"/>

        </fig>

      <p id="d1e2367">The distribution of <inline-formula><mml:math id="M102" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> between border (<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and intra-basin faults
(<inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) in an amagmatic narrow rift depends on factors such as
total rift extension
(Ebinger,
2005; Muirhead et al., 2016, 2019), rift obliquity
(Agostini et al., 2011b),
hanging-wall flexure
(Muirhead
et al., 2016; Shillington et al., 2020), lower crustal rheology (Heimpel and Olson, 1996;
Wedmore et al., 2020a), and whether border faults have attained their
maximum theoretical displacement
(Accardo
et al., 2018; Olive et al., 2014; Scholz and Contreras, 1998). In some
incipient rifts like southern Malawi, extensional strain is observed to be
localised (<inline-formula><mml:math id="M105" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 80 %–90 %) on its border faults
(Muirhead et
al., 2019; Wright et al., 2020). Furthermore, evidence from boreholes and
topography indicates that border faults in southern Malawi have relatively
small throws (<inline-formula><mml:math id="M106" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 1000 m, Fig. S1), which combined with its thick
seismogenic crust indicates that the flexural extensional strain on its
intra-basin faults is likely to be negligible
(Billings
and Kattenhorn, 2005; Muirhead et al., 2016; Wedmore et al., 2020a).
However, detailed analysis of fault scarp heights across the Zomba Graben
indicates that <inline-formula><mml:math id="M107" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 50 % of<?pagebreak page199?> extensional strain is currently
distributed onto its intra-basin faults
(Wedmore et al., 2020a). To account
for this uncertainty in the SMSSD, lower, intermediate, and upper estimates
of <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are set to 0.5, 0.7, and 0.9 respectively (Fig. 6).
As <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, respective lower, intermediate, and
upper estimates are 0.1, 0.3, and 0.5 (Fig. 6).</p>
      <p id="d1e2454">Where distinct intra-basin faults kinematically interact across steps, we
consider these as one fault in Eq. (3), as this equation accounts for strain
across, not along, the rift. For the Mwanza and Nsanje basins, no intra-basin
faults are identified (Fig. 2b), so all the extension strain is assigned to
their border faults (i.e. <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>). In the case of the Nsanje
Basin, however, this is extension is divided into increments of 30 %, 50 %, and
70 % between the Nsanje Fault and a border fault identified 25 km along
strike in Mozambique (Fig. S1; Macgregor, 2015)
to estimate its lower, intermediate, and upper slip rate.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Table}?><label>Table 3</label><caption><p id="d1e2475">Coordinates from which the Nubia–Rovuma plate motion vector for
different basins in southern Malawi was derived (Fig. 1b). The velocity,
azimuth, and uncertainties of each vector are also reported given the
Nubia–Rovuma Euler poles in
Saria et al. (2013) (S13)
or in Stamps et al. (2008) (S08; Fig. A1)
and where the uncertainties associated with the Euler pole are derived from
the methods presented in Robertson et al. (2016). For justification of basin centre locations, see Fig. S1.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Basin</oasis:entry>
         <oasis:entry colname="col2">Centre of basin</oasis:entry>
         <oasis:entry colname="col3">Centre of basin</oasis:entry>
         <oasis:entry colname="col4">Geodetic</oasis:entry>
         <oasis:entry colname="col5">Velocity and velocity</oasis:entry>
         <oasis:entry colname="col6">Azimuth, and azi-</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">latitude (S)</oasis:entry>
         <oasis:entry colname="col3">longitude (E)</oasis:entry>
         <oasis:entry colname="col4">model</oasis:entry>
         <oasis:entry colname="col5">uncertainty of plate</oasis:entry>
         <oasis:entry colname="col6">muthal uncertainty</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">motion (mm/yr)</oasis:entry>
         <oasis:entry colname="col6">of plate motion</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Makanjira</oasis:entry>
         <oasis:entry colname="col2">14.51</oasis:entry>
         <oasis:entry colname="col3">34.88</oasis:entry>
         <oasis:entry colname="col4">S13</oasis:entry>
         <oasis:entry colname="col5">1.08 <inline-formula><mml:math id="M111" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.66</oasis:entry>
         <oasis:entry colname="col6">075<inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M113" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 089<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">S08</oasis:entry>
         <oasis:entry colname="col5">3.01 <inline-formula><mml:math id="M115" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.28</oasis:entry>
         <oasis:entry colname="col6">085<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M117" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 002<inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Zomba</oasis:entry>
         <oasis:entry colname="col2">15.42</oasis:entry>
         <oasis:entry colname="col3">34.93</oasis:entry>
         <oasis:entry colname="col4">S13</oasis:entry>
         <oasis:entry colname="col5">0.88 <inline-formula><mml:math id="M119" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.65</oasis:entry>
         <oasis:entry colname="col6">072<inline-formula><mml:math id="M120" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M121" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 110<inline-formula><mml:math id="M122" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">S08</oasis:entry>
         <oasis:entry colname="col5">2.84 <inline-formula><mml:math id="M123" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.28</oasis:entry>
         <oasis:entry colname="col6">085<inline-formula><mml:math id="M124" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M125" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 002<inline-formula><mml:math id="M126" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Lower Shire</oasis:entry>
         <oasis:entry colname="col2">16.26</oasis:entry>
         <oasis:entry colname="col3">35.08</oasis:entry>
         <oasis:entry colname="col4">S13</oasis:entry>
         <oasis:entry colname="col5">0.69 <inline-formula><mml:math id="M127" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.65</oasis:entry>
         <oasis:entry colname="col6">069<inline-formula><mml:math id="M128" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M129" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 141<inline-formula><mml:math id="M130" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">S08</oasis:entry>
         <oasis:entry colname="col5">2.69 <inline-formula><mml:math id="M131" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.28</oasis:entry>
         <oasis:entry colname="col6">086<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M133" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 002<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Nsanje</oasis:entry>
         <oasis:entry colname="col2">17.28</oasis:entry>
         <oasis:entry colname="col3">35.23</oasis:entry>
         <oasis:entry colname="col4">S13</oasis:entry>
         <oasis:entry colname="col5">0.46 <inline-formula><mml:math id="M135" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.63</oasis:entry>
         <oasis:entry colname="col6">063<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M137" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 212<inline-formula><mml:math id="M138" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">S08</oasis:entry>
         <oasis:entry colname="col5">2.49 <inline-formula><mml:math id="M139" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.27</oasis:entry>
         <oasis:entry colname="col6">086<inline-formula><mml:math id="M140" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M141" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 002<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mwanza</oasis:entry>
         <oasis:entry colname="col2">n/a</oasis:entry>
         <oasis:entry colname="col3">n/a</oasis:entry>
         <oasis:entry colname="col4">n/a</oasis:entry>
         <oasis:entry colname="col5">0.6 <inline-formula><mml:math id="M143" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.4</oasis:entry>
         <oasis:entry colname="col6">n/a</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e2478">n/a: “not applicable”.</p></table-wrap-foot></table-wrap>

      <p id="d1e3008">In the SMSSD, the horizontal extension rate, <inline-formula><mml:math id="M144" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>, is taken from the plate
motion vector between the Rovuma and Nubia plates at the centre of each
individual basin (Table 3, Figs. 1b, S1) using the Euler poles reported by
Saria et al. (2013).
We use the Euler pole (as defined by a location and rotation rate) and the
uncertainties associated with the Euler pole (defined by an error ellipse;
Fig. A1) to calculate the plate motion and the plate motion uncertainty
between the Rovuma and Nubia plates for each basin (Table 3, Fig. 1b) following
the methods<?pagebreak page200?> outlined in Robertson et al. (2016). With this approach, the lower bound of <inline-formula><mml:math id="M145" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> is negative (i.e. the
plate motion is contractional; Table 3). However, the topography and
seismicity of southern Malawi clearly indicate that it is not a contractional
regime nor is it a stable craton. Therefore, a lower bound of 0.2 mm/yr horizontal
extension is assigned in the SMSSD, which is considered the
minimum strain accrual that is measurable using geodesy
(Calais et al., 2016). There are no geodetic
constraints for the extension rate across the Mwanza Basin as it lies along
the poorly defined Angoni–San plate boundary
(Daly et al., 2020). Therefore, we
assign this basin an extension rate of 0.2–1 mm/yr. This reflects the
smaller escarpment height along its border fault (250 m vs. <inline-formula><mml:math id="M146" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 750 m; Fig. 2b) relative to the Lower Shire Basin, which indicates a slower
average extension rate over geological time.</p>
      <p id="d1e3032">The rift extension azimuth (<inline-formula><mml:math id="M147" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>) in southern Malawi is derived from a
regional focal mechanism stress
(<inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:mn mathvariant="normal">073</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mo>±</mml:mo><mml:mn mathvariant="normal">012</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, Fig. 1b; Delvaux and Barth, 2010; Ebinger et al.,
2019; Williams et al., 2019), as there is considerable uncertainty in this
parameter from geodesy
(Table 3; Saria et al.,
2013). Faults in southern Malawi are considered to be normal
(Delvaux
and Barth, 2010; Hodge et al., 2015; Williams et al., 2019). Therefore, the
slip azimuth (<inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) is the dip direction of each fault or fault
section, where it is then projected into <inline-formula><mml:math id="M150" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> in Eq. (3). Although this
sets up an apparent inconsistency in which variably striking faults
accommodate normal dip-slip under a uniform extension direction, this
phenomena that can be explained by lateral heterogeneity in the lower crust
in southern Malawi
(Corti
et al., 2013; Philippon et al., 2015; Wedmore et al., 2020a; Williams et
al., 2019). To account for the uncertainty in <inline-formula><mml:math id="M151" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>, upper and lower
extension rates are obtained by varying <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>±</mml:mo><mml:mn mathvariant="normal">012</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>
depending on the fault's dip direction (e.g. upper slip rate estimates for
NE and NW dipping fault are estimated with <inline-formula><mml:math id="M153" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> set to 061
and 085<inline-formula><mml:math id="M154" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> respectively). An example of these slip rate calculations
for the central section of the Chingale Step fault is provided in Fig. 7.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Earthquake magnitudes and recurrence intervals</title>
      <p id="d1e3131">We estimate earthquake magnitudes in the SMSSD by applying empirically
derived scaling relationships between fault length and earthquake magnitude.
Scaling relationships between fault length and average single-event
displacement (<inline-formula><mml:math id="M155" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula>) can then be combined with slip rate estimates to
calculate earthquake recurrence intervals (<inline-formula><mml:math id="M156" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) through the relationship
<inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M158" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> slip rate (Wallace,
1970). To select an appropriate set of earthquake-scaling relationships for
the SMSSD, we consider three previously reported regressions and apply them
to its mapped faults: (1) between normal fault length and <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Wesnousky, 2008), (2) interplate dip-slip fault length
and <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Leonard, 2010), and
(3) fault area and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Wells and
Coppersmith, 1994) where <inline-formula><mml:math id="M162" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> is calculated using <inline-formula><mml:math id="M163" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> derived from Eq. (1).</p>
      <?pagebreak page201?><p id="d1e3221">We find that although generally comparable for <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn></mml:mrow></mml:math></inline-formula>, the
Wells and Coppersmith (1994)
regression overestimates magnitudes relative to
Leonard (2010) (Fig. 5d). This
likely reflects the discrepancy in <inline-formula><mml:math id="M165" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula> between applying Eq. (1) and the
Leonard (2010) regression (Eq. 2; Fig. 5c; Sect. 4.1). The Wesnousky (2008)
regression overestimates magnitudes for <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">6.9</mml:mn></mml:mrow></mml:math></inline-formula> relative to
Leonard (2010) equations and
underestimates them at larger magnitudes (Fig. 5d). This may reflect that
the Wesnousky (2008) regression is derived from only six
events, and these events show a poor correlation between length and <inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Pearson's regression coefficient <inline-formula><mml:math id="M168" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.36). Given these considerations, the
Leonard (2010) regressions are
used in the SMSSD. Furthermore, these regressions are used to estimate <inline-formula><mml:math id="M169" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>
(Sect. 4.1) and are self-consistent when estimating <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M171" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula>
from <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, which is not necessarily true for the other cases.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e3321">Example of the calculations in the SMSSD logic tree (Fig. 6),
performed for the central section of the Chingale Step Fault (Fig. 4b). This
is an intra-basin fault in the Zomba Graben, where the number of intra-basin
faults (<inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) is five. A multiparameter sensitivity analysis for these
calculations is documented in Appendix A.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f07.png"/>

        </fig>

      <p id="d1e3342">Thus, <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M175" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> are estimated in the SMSSD by

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M176" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E4"><mml:mtd><mml:mtext>4</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtable rowspacing="0.2ex" columnspacing="1em" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced close="" open="{"><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="italic">μ</mml:mi></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mn mathvariant="normal">9.09</mml:mn></mml:mrow><mml:mn mathvariant="normal">1.5</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><?xmltex \hack{\hbox\bgroup\fontsize{6.0}{6.0}\selectfont$\displaystyle}?><mml:mtext mathvariant="normal">for individual-section ruptures and</mml:mtext><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="italic">μ</mml:mi></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mn mathvariant="normal">9.09</mml:mn></mml:mrow><mml:mn mathvariant="normal">1.5</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><?xmltex \hack{\hbox\bgroup\fontsize{7.0}{7.0}\selectfont$\displaystyle}?><mml:mtext mathvariant="normal">for whole-fault ruptures, and</mml:mtext><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtable class="split" columnspacing="1em" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="normal">log</mml:mi><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="{" close=""><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><?xmltex \hack{\hbox\bgroup\fontsize{6.0}{6.0}\selectfont$\displaystyle}?><mml:mtext mathvariant="normal">for individual-section ruptures and</mml:mtext><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><?xmltex \hack{\hbox\bgroup\fontsize{7.0}{7.0}\selectfont$\displaystyle}?><mml:mtext mathvariant="normal">for whole-fault ruptures,</mml:mtext><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M177" display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula> is the shear modulus (<inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> Pa), <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is as defined
for Eq. (2), and <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is another constant derived by
Leonard (2010). Both constants
are varied between the full range of values derived in a least square
analysis (Leonard, 2010) to obtain
lower, intermediate, and upper estimates of <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M182" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> (Figs. 6, 7). Following Eq. (5), recurrence intervals <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:math></inline-formula>) can be calculated
as follows:
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M184" display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>Slip rate</mml:mtext><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where upper estimates of <inline-formula><mml:math id="M185" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are calculated by dividing the upper estimate of
<inline-formula><mml:math id="M186" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> by the lowest estimate of fault or section slip rate and vice versa (Fig. 6).
An example of these earthquake source calculations for the central section
of the Chingale Step fault is provided in Fig. 7.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Key features of the SMAFD and SMSSD</title>
      <p id="d1e3795">In this section, we briefly describe the fault mapping collated in the
SMAFD and then the present fault slip rates, earthquake magnitudes, and
recurrence intervals in the SMSSD as estimated by our systems-based
approach.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e3800"><bold>(a–e)</bold> Cross sections through each basin in southern Malawi.
Topography from the TanDEM-X 12 m digital elevation model (DEM) except for panel <bold>(d)</bold> which
is from the SRTM 30 m DEM. Tectonic terranes are from
Fullgraf et al. (2017), except for
Proterozoic intrusions
(Bloomfield,
1965; Walshaw, 1965). All normal faults in cross sections inferred to dip at
60<inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Post-Miocene deposits in panels <bold>(a)</bold> and <bold>(b)</bold> are shown to be 50–100 m
thick, as estimated by borehole data (Fig. S1). <bold>(f)</bold> A simplified geological
map for southern Malawi showing extent of cross sections that is underlain by the SRTM
30 m DEM.</p></caption>
        <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f08.png"/>

      </fig>

<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Border and intra-basin faults in southern Malawi</title>
      <p id="d1e3839">The SMAFD contains 23 active faults across five EARS basins. The
northernmost faults lie in the NW–SE trending Makanjira Graben, a full
graben where two border faults, the Makanjira and Chirobwe–Ncheu, clearly
define either side of the rift (Fig. 8a). Four intra-basin faults are
identified, with, two of them, the Bilila–Mtakataka and Malombe faults,
exhibiting steep scarps
(Hodge et al.,
2018a, 2019). In particular, one-dimensional diffusional models of scarp
degradation suggest that the Bilila–Mtakataka Fault scarp formed within the past
10 000 years
(Hodge et
al., 2020). The Malombe Fault forms a <inline-formula><mml:math id="M188" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 500 m high escarpment
that bounds the Shire Horst and divides post-Miocene deposits in the
Makanjira Graben across strike
(Fig. 8a; Hodge et al., 2019; Laõ-Dávila et al., 2015).</p>
      <p id="d1e3849">Along strike to the south, the NNE–SSW trending Zomba Graben contains a
prominent border fault, the Zomba Fault, on its eastern edge, and three well-defined intra-basin fault scarps in its interior
(Fig. 8b; Bloomfield, 1965;
Wedmore et al., 2020a). The western edge of the Zomba Graben grades onto the
Kirk Plateau where there are several deeply incised N–S trending valleys
that have been previously mapped as “rift valley faults”
(Fig. 8b; Bloomfield and Garson, 1965). However, only one of
these faults has an active scarp and accumulated post-Miocene sediments (the
Lisungwe Fault; Wedmore et al.,
2020a). In addition, the Wamkurumadzi Fault, which lies to the west of the
Lisungwe, is also included in the SMAFD – albeit with low confidence – as
evidence of recent activity is noted by Bloomfield and
Garson (1965), and any recent sediments may have been eroded by the
Wamkurumadzi River that flows along its base. Given the complex topography
and ambiguity on fault activity, we tentatively interpret these faults as
intra-basin faults in the SMSSD and note that the western Zomba Graben should
be a priority area for future fault mapping.</p>
      <p id="d1e3852">The floor of the NW–SE trending Lower Shire Basin lies at an elevation 350 m
lower than the floor of the Zomba Graben. Between these two EARS sections
basement is exposed, and there is no evidence of tectonic activity that
falls within the SMAFD definition of an active fault. Gravity surveys and
topographic data indicate that the Lower Shire Basin exhibits a half-graben
structure, with the Thyolo Fault bounding it to the northeast
(Fig. 8d; Chisenga
et al., 2019; Wedmore et al., 2020b). A number of intra-basin faults have
been identified in the hanging wall of the Thyolo Fault
(Chisenga et al., 2019), although none are
identified in the Nsanje and Mwanza basins (Fig. 8d, e).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Table}?><label>Table 4</label><caption><p id="d1e3859">Range of selected numeric attributes across all faults and sections in the SMSSD. To demonstrate how calculated attributes vary across different faults in the
SMSSD, as opposed to variation from the set of parameters used to calculate
them, the values shown are for the intermediate branches in the SMSSD logic
tree (Fig. 6).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Attribute</oasis:entry>
         <oasis:entry colname="col2">Minimum</oasis:entry>
         <oasis:entry colname="col3">Median</oasis:entry>
         <oasis:entry colname="col4">Maximum</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Section length (<inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, km)</oasis:entry>
         <oasis:entry colname="col2">0.7</oasis:entry>
         <oasis:entry colname="col3">13.4</oasis:entry>
         <oasis:entry colname="col4">62.4</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fault length (<inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, km)</oasis:entry>
         <oasis:entry colname="col2">6.2</oasis:entry>
         <oasis:entry colname="col3">33.2</oasis:entry>
         <oasis:entry colname="col4">144.0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fault width (<inline-formula><mml:math id="M191" display="inline"><mml:mi>W</mml:mi></mml:math></inline-formula>, km)</oasis:entry>
         <oasis:entry colname="col2">5.9</oasis:entry>
         <oasis:entry colname="col3">18.1</oasis:entry>
         <oasis:entry colname="col4">48.0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Section net slip rate (mm/yr)</oasis:entry>
         <oasis:entry colname="col2">0.05</oasis:entry>
         <oasis:entry colname="col3">0.13</oasis:entry>
         <oasis:entry colname="col4">0.90</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fault net slip rate (mm/yr)</oasis:entry>
         <oasis:entry colname="col2">0.05</oasis:entry>
         <oasis:entry colname="col3">0.08</oasis:entry>
         <oasis:entry colname="col4">0.81</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Section earthquake magnitude (<inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">5.4</oasis:entry>
         <oasis:entry colname="col3">6.3</oasis:entry>
         <oasis:entry colname="col4">7.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fault earthquake magnitude (<inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">5.6</oasis:entry>
         <oasis:entry colname="col3">6.8</oasis:entry>
         <oasis:entry colname="col4">7.8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Section earthquake recurrence interval (<inline-formula><mml:math id="M194" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>, years)</oasis:entry>
         <oasis:entry colname="col2">380</oasis:entry>
         <oasis:entry colname="col3">2814</oasis:entry>
         <oasis:entry colname="col4">14 600</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fault earthquake recurrence interval (<inline-formula><mml:math id="M195" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>, years)</oasis:entry>
         <oasis:entry colname="col2">2020</oasis:entry>
         <oasis:entry colname="col3">7870</oasis:entry>
         <oasis:entry colname="col4">23 690</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>Fault slip rates, and earthquake magnitudes and recurrence intervals in
the SMSSD</title>
      <p id="d1e4107">By implementing a logic tree approach to assess uncertainty in the SMSSD,
three values (lower, intermediate, and upper) are derived for each
calculated attribute (Table 2, Fig. 6). However, it is implicit that the
upper and lower values have a low probability as they require a unique, and
possibly unrealistic, combination of parameters. Therefore, we primarily
report values obtained from applying the intermediate branches in the logic
tree but discuss the uncertainties in Sect. 5.4.</p>
      <?pagebreak page202?><p id="d1e4110">Although the SMAFD contains 23 active faults, these are further
subdivided into 74 sections in the SMSSD – of which 13 are linking sections. Section
lengths (<inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) range between 0.7 and 62 km, whereas fault lengths
(<inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) vary from 6.2 to 144 km (Fig. 5a, Table 4). The highest slip
rates are estimated to be on the Thyolo and Zomba faults (intermediate
estimates of 0.6–0.8 mm/yr). On intra-basin faults in the SMSSD, intermediate
slip rate estimates are 0.05–0.1 mm/yr (Fig. 9). Slip rates tend to be
relatively fast in the Makanjira Graben (Fig. 9c), as the extension rate is
higher (Table 3), and its NNW–SSE striking faults are more optimally
oriented to the regional extension direction (Fig. 2). The difference
between upper and lower slip rate estimates in the SMSSD logic tree is 2 orders of magnitude: <inline-formula><mml:math id="M198" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.05–5 mm/yr for the border faults and
<inline-formula><mml:math id="M199" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.005–0.5 mm/yr on the intra-basin faults (Fig. 9).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e4151">Fault slip rate estimates in the SMSSD, calculated following
the approach outlined in Fig. 6 and sorted into different basins in southern
Malawi.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f09.png"/>

        </fig>

      <p id="d1e4161">For whole-fault ruptures along border faults, intermediate estimates of
earthquake recurrence intervals (<inline-formula><mml:math id="M200" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>)  are between 2000 and 5000 years, whereas they are between 10 000 and 30 000 years for
intra-basin whole-fault ruptures (Fig. 10a–c).
Considerable uncertainty exists in these values, with the upper and lower
estimates for <inline-formula><mml:math id="M201" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> varying from 10<inline-formula><mml:math id="M202" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> to 10<inline-formula><mml:math id="M203" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> years and from <inline-formula><mml:math id="M204" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M205" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> to 10<inline-formula><mml:math id="M206" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> years for border and intra-basin whole-fault ruptures
respectively (Fig. 10a–c). Furthermore, if these faults rupture in
individual sections, <inline-formula><mml:math id="M207" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> may be reduced by up to an order of magnitude (Fig. 10d–f). Intermediate estimates of earthquake magnitudes range from <inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.4 to <inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 7.2 for individual-section ruptures and from <inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.6 to
<inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 7.8 for faults that rupture their entire length (Table 4, Fig. 11b).
The SMSSD also includes one example where multiple en echelon faults, the Panga Fault
system (Fig. 2d), could rupture together given the constraints outlined in
Sect. 4.1.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e4276">Recurrence interval (<inline-formula><mml:math id="M212" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) estimates in the SMSSD for <bold>(a–c)</bold> whole-fault ruptures and <bold>(d–f)</bold> individual-section ruptures. Note, <inline-formula><mml:math id="M213" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates
for each Panga Fault are included in panel <bold>(d)</bold>, and a multi-fault rupture is shown
in panel <bold>(a)</bold>.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f10.png"/>

        </fig>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Table}?><label>Table 5</label><caption><p id="d1e4315">Parameters and their associated upper and lower levels used in the
sensitivity analysis for recurrence interval (<inline-formula><mml:math id="M214" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) calculations for the
Chingale Step fault central section using the
Stamps et al. (2008) (S08) and
Saria et al. (2013) (S13)
Nubia–Rovuma Euler poles (Fig. A1). The main effect of each parameter (<inline-formula><mml:math id="M215" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>) for
each geodetic model is then also reported. See Appendix A for full details
of this analysis.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="145pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="65pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="65pt"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Parameter</oasis:entry>
         <oasis:entry colname="col2">Lower</oasis:entry>
         <oasis:entry colname="col3">Upper</oasis:entry>
         <oasis:entry colname="col4">S08 parameter</oasis:entry>
         <oasis:entry colname="col5">S13 parameter</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">level</oasis:entry>
         <oasis:entry colname="col3">level</oasis:entry>
         <oasis:entry colname="col4">main effect (<inline-formula><mml:math id="M216" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">main effect (<inline-formula><mml:math id="M217" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Component of regional <?xmltex \hack{\hfill\break}?>extensional strain (<inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">0.1</oasis:entry>
         <oasis:entry colname="col3">0.02</oasis:entry>
         <oasis:entry colname="col4">1.88</oasis:entry>
         <oasis:entry colname="col5">3.05</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Rift extension rate <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M219" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>, mm/yr)</oasis:entry>
         <oasis:entry colname="col2">2.56 (S08) <?xmltex \hack{\hfill\break}?>0.2 (S13)</oasis:entry>
         <oasis:entry colname="col3">3.12 (S08) <?xmltex \hack{\hfill\break}?>2.53 (S13)</oasis:entry>
         <oasis:entry colname="col4">0.20</oasis:entry>
         <oasis:entry colname="col5">2.54</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Rift extension azimuth (<inline-formula><mml:math id="M220" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">085<inline-formula><mml:math id="M221" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">061<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.32</oasis:entry>
         <oasis:entry colname="col5">0.32</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Fault dip (<inline-formula><mml:math id="M223" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">65<inline-formula><mml:math id="M224" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">40<inline-formula><mml:math id="M225" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.59</oasis:entry>
         <oasis:entry colname="col5">0.59</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Leonard (2010) empirically <?xmltex \hack{\hfill\break}?>derived scaling parameter  <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (m<inline-formula><mml:math id="M227" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">12</oasis:entry>
         <oasis:entry colname="col3">25</oasis:entry>
         <oasis:entry colname="col4">0.37</oasis:entry>
         <oasis:entry colname="col5">0.37</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Leonard (2010) empirically <?xmltex \hack{\hfill\break}?>derived scaling parameter  <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">1.5</oasis:entry>
         <oasis:entry colname="col3">12</oasis:entry>
         <oasis:entry colname="col4">2.08</oasis:entry>
         <oasis:entry colname="col5">2.08</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Rupture length (<inline-formula><mml:math id="M229" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula>, km)</oasis:entry>
         <oasis:entry colname="col2">9.6 (individual <?xmltex \hack{\hfill\break}?>section, <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3">38.0 (whole fault, <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">1.15</oasis:entry>
         <oasis:entry colname="col5">1.15</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S5.SS3">
  <label>5.3</label><title>Robustness of fault slip rate estimates</title>
      <p id="d1e4689">It is possible that slip rate estimates in the SMSSD are effectively upper
bounds, as some proportion of the geodetically<?pagebreak page203?> derived rift extension may be
accommodated by aseismic creep or along unrecognised faults. With regards to
aseismic creep, the discrepancy between geodetic and seismic moment rates in
Malawi implies that its faults are strongly coupled
(Ebinger
et al., 2019; Hodge et al., 2015). This is also consistent with the
velocity-weakening behaviour of some samples from the rift in deformation
experiments at lower crustal pressure–temperature conditions
(Hellebrekers et al., 2019).</p>
      <p id="d1e4692">Conversely, the possible inclusion of inactive faults in the SMAFD and SMSSD
would mean that individual fault slip rates may be lower bounds. Without
paleoseismic investigations and dating of offset surfaces in southern
Malawi, it is difficult to test this point. Nevertheless, reactivation
analysis that encompasses the range of fault orientations in southern Malawi
indicates that these faults are favourably oriented in the current stress
field (Williams et al., 2019).
Therefore, even faults that have been inactive for a considerable time (up
to the entire age of the EARS) could still theoretically be reactivated. We
also note that slip rates of intra-basin faults in the North Basin of Lake
Malawi over the last 75 ka (0.15–0.7 mm/yr;
Shillington et al.,
2020) are within the range of estimates of intra-basin faults in the SMSSD
(Fig. 9).</p>
</sec>
<?pagebreak page204?><sec id="Ch1.S5.SS4">
  <label>5.4</label><title>Sensitivity analysis</title>
      <p id="d1e4703">Upper and lower estimates of <inline-formula><mml:math id="M232" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> differ by up to 3 orders of magnitude in
the SMSSD (Fig. 10). To investigate these uncertainties, we performed a
multiparameter sensitivity analysis following the methods presented in
Box et al. (1978) and Rabinowitz and
Steinberg (1991). Full details of this analysis are given in Appendix A. In
summary, seven parameters that contribute to uncertainty in <inline-formula><mml:math id="M233" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> for the central
section of the Chingale Step fault are considered (Table 5). By exploring
all possible combinations in which these seven parameters are set at their upper
or lower estimates, 128 (i.e. 2<inline-formula><mml:math id="M234" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula>) different values of <inline-formula><mml:math id="M235" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> can be
calculated. However, we instead considered 64 parameter combinations that
were chosen following a fractional factorial design (Table S1; Box et al., 1978). In this way, parameter combinations that offer little
insight into how a system works are omitted, thereby increasing the
efficiency of this analysis at minimal cost to its validity
(Rabinowitz and Steinberg, 1991). From these combinations,
the natural log of the average value of <inline-formula><mml:math id="M236" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> when a parameter (<inline-formula><mml:math id="M237" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>) is set at its
upper (<inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) and lower (<inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:math></inline-formula>)) value is calculated and
the difference between these values defines the parameter effect
(<inline-formula><mml:math id="M240" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>; Rabinowitz and Steinberg, 1991):
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M241" display="block"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e4839">This analysis indicates that <inline-formula><mml:math id="M242" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is most sensitive to uncertainties in the
partitioning of strain between border and intra-basin faults in the rift
(i.e. <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), the rift extension rate (<inline-formula><mml:math id="M244" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>), and the
<inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter in Eq. (5), and it is least sensitive to uncertainties in the
rift's extension azimuth and the <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter in Eq. (5)  (Table 5). If,
however, <inline-formula><mml:math id="M247" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> and its associated uncertainties were estimated using a different
Nubia–Rovuma Euler pole solution (Fig. A1; Table 3;
Stamps et al., 2008), <inline-formula><mml:math id="M248" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates are least
sensitive to <inline-formula><mml:math id="M249" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> and most sensitive to <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Table 5). There are no
interaction effects between two separate parameters that may influence their
effect on <inline-formula><mml:math id="M251" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> (Table S2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e4938"><bold>(a)</bold> Faults in the SMAFD with lines weighted by intermediate
estimates of fault slip rate in the SMSSD. The fault map is underlain by
population density, where the pixel size is 3 arcsec (approximately 1 ha),
as derived from WorldPop predicted 2020 datasets for Malawi
(WorldPop, 2018) with major population centres also
highlighted. Note that the population density in these places may exceed 100 people per hectare. The area shown is the same as in Fig. 2. Histograms show the range of <bold>(b)</bold> earthquake magnitudes and <bold>(c)</bold> recurrence interval estimates in the SMSSD
from intermediate branches in Fig. 6.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f11.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Discussion</title>
<sec id="Ch1.S6.SS1">
  <label>6.1</label><title>Implications for seismic hazard in southern Malawi</title>
      <p id="d1e4971">The existence of active faults within southern Malawi poses a significant
risk to the 7.75 million people living in this region (Malawi
National Statistics Office, 2018) as well as those living adjacent to the rift in northern
Mozambique (Fig. 11a). Furthermore, with population growth at an annual rate
of 2.7 % in southern Malawi (Malawi National Statistics
Office, 2018), this risk will increase over the coming decades. The rapidly
growing city of Blantyre (population of 800 000; Malawi National Statistics
Office, 2018), which is in the footwall of both the relatively fast slipping
(intermediate estimates <inline-formula><mml:math id="M252" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.8 mm/yr) Zomba and Thyolo faults
is at a particularly high risk (Fig. 11a).</p>
      <p id="d1e4981">Intermediate estimates in the SMSSD for <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 5.4–7.8 earthquakes and
fault recurrence intervals (<inline-formula><mml:math id="M254" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) of 10<inline-formula><mml:math id="M255" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>–10<inline-formula><mml:math id="M256" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> years (Fig. 11) imply
that southern Malawi's seismic hazard is characterised by infrequent large-magnitude events. Indeed, faults in this region may host earthquakes
comparable to the largest historical continental normal fault earthquakes
(<inline-formula><mml:math id="M257" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 7.5; Valentini et al., 2020); although relatively rare, <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> km long normal faults have been mapped elsewhere, and these would be capable of
even larger events (Styron and Pagani, 2020).</p>
</sec>
<sec id="Ch1.S6.SS2">
  <label>6.2</label><title>Improving earthquake source estimates in the SMSSD</title>
      <?pagebreak page206?><p id="d1e5057">One of the purposes of collating the SMSSD was to identify current knowledge
gaps in our understanding of active faulting and seismic hazard in southern
Malawi. Our sensitivity analysis (Sect. 5.4) indicates that the two biggest
factors contributing to uncertainty in <inline-formula><mml:math id="M260" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> in the SMSSD is related to our
understanding of the distribution and rate of extension (<inline-formula><mml:math id="M261" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>) in southern
Malawi (Table 5). In particular, there is considerable uncertainty in the
position of the Nubia–Rovuma Euler pole
(Fig. A1; Saria et al.,
2013), and we would not expect such large differences between upper and
lower fault slip rate estimates by following our systems-based approach
elsewhere. Although the uncertainties associated with <inline-formula><mml:math id="M262" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> in the SMSSD could be
reduced if an alternative solution for the Nubia–Rovuma Euler pole was
applied (Fig. A1, Tables 5, S2; Stamps
et al., 2008), this solution uses fewer Global Positioning System (GPS)
sites and a shorter position time series
(Saria et al., 2013).
Therefore, in the short term, the best refinements to <inline-formula><mml:math id="M263" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates may come
from new regional geodetic data and further high-resolution topographic
analysis
(e.g. Daly et al., 2020; Stamps et al., 2020; Wedmore et al., 2020a).</p>
      <p id="d1e5088">Directly measuring on-fault slip rates and paleoseismicity would provide
more robust <inline-formula><mml:math id="M264" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates than the model-derived estimates in SMSSD.
However, careful site selection would be required for these analyses in
southern Malawi because of its potential for large (<inline-formula><mml:math id="M265" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 10 m)
single-event displacements
(Hodge et
al., 2020). Furthermore, these investigations carry large inherent
uncertainties in low-strain-rate regions like southern Malawi if only a few
earthquakes are sampled, as these events may be temporally clustered
(Nicol
et al., 2006, 2016b; Pérouse and Wernicke, 2017; Taylor-Silva et al.,
2020).</p>
      <p id="d1e5105">When considering how different rupture magnitude estimates in the SMSSD
influence <inline-formula><mml:math id="M266" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>, the main source of uncertainty  is the <inline-formula><mml:math id="M267" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter from the
Leonard (2010) regressions (Table 5). This factor controls the amount of displacement for a given rupture area
(Leonard, 2010). It is therefore
likely related to earthquake stress drops, and uncertainty in <inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in
southern Malawi will only be reduced by recording more events here or in
similar tectonic environments – i.e. normal fault earthquakes in regions with
low (<inline-formula><mml:math id="M269" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 1–10 mm/yr) extension rates and thick (20–35 km)
seismogenic crust.</p>
</sec>
</sec>
<?pagebreak page207?><sec id="Ch1.S7">
  <label>7</label><title>Incorporation of the SMSSD into probabilistic seismic hazard analysis</title>
      <p id="d1e5153">The SMSSD contains the attributes (earthquake magnitudes and <inline-formula><mml:math id="M270" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates)
that allow it to be used as a source model for future PSHA in southern
Malawi. However, in common with other low-strain-rate regions with limited
paleoseismic information
(e.g. Cox et al.,
2012; Villamor et al., 2018), there are various aleatory (i.e. the
uncertainty related to unpredictable nature of future event) and epistemic
(i.e. the uncertainty due to incomplete knowledge and data) uncertainties.
Firstly, as noted in Sect. 5.2, it is unrealistic that the intermediate,
lower, and upper value of each attribute in the SMSSD logic tree has an
equal probability (Fig. 6). This could be formalised by treating these
attributes as continuous variables and assigning probability distribution
functions to them.</p>
      <p id="d1e5163">Implicit in the <inline-formula><mml:math id="M271" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> estimates in the SMSSD is that each earthquake source can
only host events of two sizes: “individual sections” and “whole faults”.
Therefore, it does not consider multi-segment ruptures that do not rupture the
entire fault. Although not strictly the same, the SMSSD therefore follows
many aspects of the characteristic earthquake model (i.e. each earthquake
source only hosts event of one size) whose applicability remains contentious
(Kagan et al., 2012; Page and
Felzer, 2015; Stirling and Gerstenberger, 2018). An alternative approach to
model <inline-formula><mml:math id="M272" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> in southern Malawi would be to allow each fault to host a range of
earthquake sizes that follow a frequency–magnitude distribution that is
consistent with its moment rate (Youngs and Coppersmith, 1985),
with this moment rate derived from the instrumental record and data
incorporated into the SMSSD.</p>
      <p id="d1e5180">Finally, there are likely active faults in Malawi that are not included in
the SMAFD and SMSSD. Thus, we recommend that future PSHA in southern
Malawi should also consider “off-fault” areal seismic sources by using the
instrumental record
(e.g. Field et al., 2014; Gerstenberger et al., 2020; Hodge et al., 2015; Morell
et al., 2020; Stirling et al., 2012). Many of the challenges discussed above
can be addressed through the creation of synthetic seismic catalogues, which
are then used as a PSHA source (Hodge
et al., 2015).</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S8" sec-type="conclusions">
  <label>8</label><title>Conclusions</title>
      <p id="d1e5192">We describe a new systems-based approach that combines geologic and geodetic
data to estimate fault slip rates and earthquake recurrence intervals in
regions with little historical or paleoseismic earthquake data. This
approach is used to develop the South Malawi Active Fault Database (SMAFD)
and South Malawi Seismogenic Source Database (SMSSD), geospatial databases
designed to direct future research and aid seismic hazard analysis and
planning.</p>
      <p id="d1e5195">In the SMAFD, we document 23 active faults that have accumulated
displacement during East African rifting in southern Malawi. In the SMSSD,
fault slip rates, earthquake magnitudes, and recurrence intervals are
estimated for the active faults compiled in the SMAFD. The SMSSD indicates
the potential for <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> 6.5–7.8 earthquakes throughout southern Malawi.
However, slow geodetically derived extension rates (<inline-formula><mml:math id="M274" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 1 mm/yr)
imply low fault slip rates (0.001–5 mm/yr), and so the recurrence intervals
of <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>W</mml:mtext></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula> events are estimated to be 10<inline-formula><mml:math id="M276" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>–10<inline-formula><mml:math id="M277" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> years. The large range of these estimated recurrence times reflects aleatory
uncertainty on fault rupture scenarios and epistemic uncertainties in
fault-scaling relationships, fault slip rates, and fault geometry.
Sensitivity analysis suggests the biggest reduction in uncertainties would
come from improved knowledge of fault slip rates through paleoseismic
investigations or geodetic studies. Nevertheless, the combination of long,
highly coupled, low-slip-rate faults and a short (<inline-formula><mml:math id="M278" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 65 years)
instrumental record imply that the SMAFD and SMSSD are important sources of
information for future seismic hazard analyses in the region. In this
respect, the development of SMSSD is timely as the seismic risk of southern
Malawi is growing due to rapid population growth, urbanisation, and
seismically vulnerable building stock. Similar challenges exist elsewhere
along the EARS, which may also be partially addressed by following the
framework provided by the SMAFD and SMSSD.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<?pagebreak page208?><app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>A multiparameter sensitivity analysis for recurrence interval
estimates in the South Malawi Active Fault Database</title>
      <p id="d1e5269">Recurrence interval estimates in the South Malawi Seismogenic Database
(SMSSD) vary by over 3 orders of magnitude (Fig. 10). These
uncertainties are not unexpected in a region like Malawi with no
paleoseismic data and an incomplete instrumental seismic record
(Cox et al., 2012;
Villamor et al., 2018), and they can be accounted for in probabilistic seismic
hazard analysis (PSHA) using synthetic seismicity catalogues
(Hodge et al., 2015). Nevertheless,
by conducting a sensitivity analysis on the logic tree approach used to
calculate these recurrence intervals (Fig. 6), it is possible to determine
which parameters contribute most to this uncertainty and, in turn, guide
future research directions that will help constrain them in future
iterations of the SMSSD. This analysis is briefly described in the main text
(Sect. 5.4, Table 5) and is documented fully below.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S1.F12"><?xmltex \currentcnt{A1}?><?xmltex \def\figurename{Figure}?><label>Figure A1</label><caption><p id="d1e5274">Plate boundaries in East Africa with location and uncertainty of
the Nubia–Rovuma Euler pole derived by
Saria et al. (2013) and
Stamps et al. (2008). “Vic.” denotes Victoria, and “Rov.” denotes
Rovuma. Modified after
Saria et al. (2013).</p></caption>
        <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f12.png"/>

      </fig>

      <p id="d1e5283">Here, we follow the multiparameter sensitivity analysis presented by
Rabinowitz and Steinberg (1991). This study conducted
sensitivity analysis for the parameters that feed into PSHA, where the
output metric is the probability of exceedance of a given level of ground
shaken. For the SMSSD, we adapt this method to test the sensitivity of seven
parameters that are used to calculate earthquake recurrence intervals (<inline-formula><mml:math id="M279" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>; Eq. A1; Table 5). This metric is chosen as it fully incorporates the aleatory
uncertainties in rupture length as well as epistemic uncertainties in fault slip
rates and the Leonard (2010)
scaling relationships (Fig. 6). This analysis is performed for the Chingale
Step fault central section (Fig. 4), where like all intra-basin faults in the
SMSSD, <inline-formula><mml:math id="M280" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is calculated by
          <disp-formula id="App1.Ch1.S1.E8" content-type="numbered"><label>A1</label><mml:math id="M281" display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">5</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">δ</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mi>v</mml:mi><mml:mi>cos⁡</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>
        Here, <inline-formula><mml:math id="M282" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> is rupture length and depends on whether an individual-section
(<inline-formula><mml:math id="M283" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>sec</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) or whole-fault (<inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mtext>fault</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) rupture is considered, <inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are empirically derived constants from
Leonard (2010), <inline-formula><mml:math id="M287" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> is
fault dip, <inline-formula><mml:math id="M288" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> is the fault slip azimuth, <inline-formula><mml:math id="M289" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> and  <inline-formula><mml:math id="M290" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> are the rift
extension rate and azimuth respectively, <inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is a weighting of rift extension
for intra-basin faults, and <inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the number of mapped intra-basin faults
(<inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) in the basin.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S1.F13" specific-use="star"><?xmltex \currentcnt{A2}?><?xmltex \def\figurename{Figure}?><label>Figure A2</label><caption><p id="d1e5495"><bold>(a)</bold> Cumulative distribution function (CDF) of the natural log of
the recurrence intervals calculated for the Chingale Step fault central
section using the various parameter combinations listed in Table S1 (blue
line). This CDF is compared to a standard normal CDF (red line) with the
same mean value and standard deviation as the values in Table S1. <bold>(b)</bold> A normal
probability plot of the parameter effects assessed in the sensitivity
analysis and reported in Table 5. The most important effects are those that
plot above a standard normal distribution (red line). The line is solid when
within the first and third quartiles of data and is dashed when outside of this region.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://se.copernicus.org/articles/12/187/2021/se-12-187-2021-f13.png"/>

      </fig>

      <p id="d1e5509">Equation (A1) is essentially a combination of Eqs. (3), (5), and (6) in the main text, and its application with the SMSSD logic tree to calculate <inline-formula><mml:math id="M294" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> for the Chingale
Step fault central section is shown in Fig. 7. There are five intra-basin faults
in the Zomba Graben where the Chingale Step fault is situated (Fig. 2), and this parameter is not treated as an uncertainty in this analysis. However,
for simplicity, it is combined with <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> to give the “component
of rift extensional strain” parameter, which is defined by <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>if</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mtext>if</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Table 5). Assuming that the Chingale Step fault is a
normal fault
(Wedmore
et al., 2020a; Williams et al., 2019), <inline-formula><mml:math id="M297" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> is the fault dip direction,
and differs by only 4<inline-formula><mml:math id="M298" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> depending on whether the whole fault
ruptures or just the central section (Fig. 7). Hence, uncertainty in this
parameter is not considered here, and it is set at 290<inline-formula><mml:math id="M299" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, which is
the average value for these two rupture scenarios. When assessing the
influence of <inline-formula><mml:math id="M300" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>, we consider two geodetic models
(Fig. A1; Saria et al., 2013; Stamps et al., 2008) and perform this sensitivity
analysis for both.</p>
      <p id="d1e5581">The method presented by Rabinowitz and Steinberg (1991)
involves a two-level fractional factorial multiparameter design, where each
parameter is restricted to the two levels which will give lower or upper
estimates of <inline-formula><mml:math id="M301" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> (Table 5). Ideally, these levels would be symmetric about the
intermediate case; however, in the SMSSD this is not possible for the <inline-formula><mml:math id="M302" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M303" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula>,
and <inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Compared with a “one-at-a-time (OAT)” parameter analysis, a
multiparameter analysis allows us to assess how different parameters
interact with each other and, thus, more fully explore the parameter space
(Rabinowitz and Steinberg, 1991). This is achieved through a
factorial design, which for the seven parameters (<inline-formula><mml:math id="M305" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>) tested here would
generate 128 (i.e. 2<inline-formula><mml:math id="M306" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula>) possible combinations in a full two-level
factorial approach. However, in a fractional factorial design, just a subset
of these combinations is assessed. This approach recognises that many of the
combinations in a full factorial design offer little insight into how a
system works and that<?pagebreak page209?> this can instead be achieved at minimal cost to the
results by considering a carefully selected subset of these combinations
(Box et al., 1978; Rabinowitz and Steinberg, 1991). In this analysis,
2<inline-formula><mml:math id="M307" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> combinations are assessed, where <inline-formula><mml:math id="M308" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is the number of generators and
is set at one. This results in the assessment of 64 combinations (Table S1)
and a “resolution” of five, which means it is possible to estimate the main
effects of each parameter (Eq. A2), interactions between two parameters (Eq. A3), but not interactions between three parameters (Box et al.,
1978).</p>
      <p id="d1e5654">The main effect (<inline-formula><mml:math id="M309" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>) of one parameter (e.g. fault dip, <inline-formula><mml:math id="M310" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>) is
quantified from the difference between the average of the natural log of
recurrence interval (<inline-formula><mml:math id="M311" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula>) for the 32 combinations in Table S1 when a
parameter was at its upper level (i.e. <inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>+</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">40</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) and
<inline-formula><mml:math id="M313" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> for the 32 combinations when the parameter was at its low level
(i.e. <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>-</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">65</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>):
          <disp-formula id="App1.Ch1.S1.E9" content-type="numbered"><label>A2</label><mml:math id="M315" display="block"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>+</mml:mo></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e5774">By applying a multiparameter approach it is also possible to quantify the
parameter–parameter interaction effects – for example, if the effect of
<inline-formula><mml:math id="M316" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> depends on the choice of rift extension azimuth (<inline-formula><mml:math id="M317" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>). To
do this, the results in Table S1 can be divided into two sets with
2<inline-formula><mml:math id="M318" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> combinations each depending on which level of <inline-formula><mml:math id="M319" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> was
applied. Following the table designs developed by Box et al. (1978), each set of 32 combinations will have 16 combinations when <inline-formula><mml:math id="M320" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> was at is upper level (<inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>+</mml:mo></mml:mrow></mml:math></inline-formula>) and 16 combinations when <inline-formula><mml:math id="M322" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>
was at its lower level (<inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:math></inline-formula>). The effect of <inline-formula><mml:math id="M324" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> on each level
of <inline-formula><mml:math id="M325" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> (i.e. <inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="italic">φ</mml:mi></mml:mrow></mml:math></inline-formula>) is then calculated from the
corresponding differences in <inline-formula><mml:math id="M327" display="inline"><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> (Rabinowitz and
Steinberg, 1991):
          <disp-formula id="App1.Ch1.S1.E10" content-type="numbered"><label>A3</label><mml:math id="M328" display="block"><mml:mtable columnspacing="1em" rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>+</mml:mo></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>+</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mover accent="true"><mml:mi>R</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e5989">If there is no interaction effect between these two parameters, <inline-formula><mml:math id="M329" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="italic">φ</mml:mi></mml:mrow></mml:math></inline-formula> is zero; otherwise, the size of the effect is proportional to the
magnitude of <inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi mathvariant="italic">φ</mml:mi></mml:mrow></mml:math></inline-formula>. In addition, we demonstrate our results in
terms of an empirical cumulative distribution function for the values of
ln<inline-formula><mml:math id="M331" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> reported in Table 1 (Fig. A2a) and, following
Rabinowitz and Steinberg (1991), values of <inline-formula><mml:math id="M332" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> in a normal
probability plot (Fig. A2b).</p>
      <p id="d1e6027">If the Saria et al. (2013) model is used to provide estimates of <inline-formula><mml:math id="M333" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> in this
sensitivity analysis, the parameter that contributes most to uncertainties
of <inline-formula><mml:math id="M334" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> in the SMSSD is the component of regional extensional strain that each
fault accommodates (<inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.05</mml:mn></mml:mrow></mml:math></inline-formula>, Table 5). This essentially means that ln<inline-formula><mml:math id="M336" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is
higher by 3.05 when this component is set at its high value compared with its lower value, or, in other words, that <inline-formula><mml:math id="M337" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is <inline-formula><mml:math id="M338" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 21 times (<inline-formula><mml:math id="M339" display="inline"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mn mathvariant="normal">3.05</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) higher when 10 %
of regional extensional strain is assigned to the Chingale Step fault as
opposed to 2 %. The importance of this parameter is also demonstrated by
the fact that it does not plot close to the normal distribution line in Fig. A2b. The parameters with the next highest main effect on <inline-formula><mml:math id="M340" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are <inline-formula><mml:math id="M341" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> and
<inline-formula><mml:math id="M342" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, whereas estimates of <inline-formula><mml:math id="M343" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are least sensitive to uncertainties in
<inline-formula><mml:math id="M344" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> (Table 5). If, however, estimates of <inline-formula><mml:math id="M345" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> are provided by the Stamps
et al. (2008) model (Fig. A1), estimates of <inline-formula><mml:math id="M346" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> are considerably less sensitive
to uncertainties in rift extension rates, and the <inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter has the
biggest influence on <inline-formula><mml:math id="M348" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> (Table 5). Multiparameter effects are all equal<?pagebreak page210?> to zero
(Table S2) regardless of geodetic model; thus, the sensitivity of each of
these parameters is independent of changes in other parameters.</p>
      <?pagebreak page211?><p id="d1e6161">The results of the sensitivity analysis reported here are specific to
estimates of <inline-formula><mml:math id="M349" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> for the Chingale Step fault central section; however, results
should be broadly applicable to all other faults in the SMSSD, as <inline-formula><mml:math id="M350" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> was
calculated following the same steps. Nevertheless, there will be differences for
faults that are not segmented (where <inline-formula><mml:math id="M351" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> is not an uncertainty) or that have
more than the three sections mapped along the Chingale Step fault (e.g. the
seven-section Bilila–Mtakataka Fault). The uncertainty in the weighting of
rift extension may also be different for border faults, as
the weighting factor (<inline-formula><mml:math id="M352" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>bf</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) is varied between 0.5 and 0.9 in these cases. The
results of this analysis are discussed further in Sect. 5.4 and 6.2 in the
main text.
<?xmltex \hack{\clearpage}?></p>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e6201">The South Malawi Active Fault Database (SMAFD), South Malawi Seismogenic
Source Database (SMSSD), and a GIS file for all other faults in Malawi are
available in the Supplement as shapefiles. In addition, an Excel file is
included for the SMSSD where the earthquake source parameters were
performed. All files are available under Creative Commons Attribution-ShareAlike (CC-BY-SA 4.0) licence 4.0.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e6204">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/se-12-187-2021-supplement" xlink:title="zip">https://doi.org/10.5194/se-12-187-2021-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e6214">JNW and LNJW led the fault mapping from TanDEM-X data, and HM led the fault
mapping using aeromagnetic data. All authors participated in the fieldwork.
LNJW conducted the analysis of geodetic data. JNW designed the method to obtain
fault slip rates and earthquake source parameters with input from all
co-authors. JB and ÅF secured the funding for this project. All authors
contributed to paper preparation, but JNW had the primary responsibility.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e6220">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e6226">This work is supported by the EPSRC Global Challenges Research Fund PREPARE
project (grant no. EP/P028233/1). TanDEM-X data were provided through DLR proposal
DEM_GEOL0686. The Geological Survey Department of Malawi
kindly gave us access to the 2013 aeromagnetic surveys across Malawi. We
gratefully acknowledge thoughtful and constructive reviews from Richard Styron and Folarin Kolawole. We also thank Katsu Goda and Mark Stirling for
useful discussions on developing this database as well as Mike Floyd for his
assistance with calculating geodetic extension rates from Euler poles.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e6231">This research has been supported by the Engineering and Physical Sciences Research Council (grant no. EP/P028233/1).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e6237">This paper was edited by Zoe Mildon and reviewed by Richard Styron and Folarin Kolawole.</p>
  </notes><ref-list>
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    <!--<article-title-html>A systems-based approach to parameterise seismic hazard in regions with little historical or instrumental seismicity: active fault and seismogenic source databases for southern Malawi</article-title-html>
<abstract-html><p>Seismic hazard is commonly characterised using instrumental seismic records.
However, these records are short relative to earthquake repeat times, and
extrapolating to estimate seismic hazard can misrepresent the probable
location, magnitude, and frequency of future large earthquakes. Although
paleoseismology can address this challenge, this approach requires certain
geomorphic setting, is resource intensive, and can carry large inherent
uncertainties. Here, we outline how fault slip rates and recurrence
intervals can be estimated by combining fault geometry, earthquake-scaling
relationships, geodetically derived regional strain rates, and geological
constraints of regional strain distribution. We apply this approach to
southern Malawi, near the southern end of the East African Rift, and where,
although no on-fault slip rate measurements exist, there are constraints on
strain partitioning between border and intra-basin faults. This has led to
the development of the South Malawi Active Fault Database (SMAFD), a
geographical database of 23 active fault traces, and the South Malawi
Seismogenic Source Database (SMSSD), in which we apply our systems-based
approach to estimate earthquake magnitudes and recurrence intervals for the
faults compiled in the SMAFD. We estimate earthquake magnitudes of <i>M</i><sub>W</sub> 5.4–7.2 for individual fault sections in the SMSSD and <i>M</i><sub>W</sub> 5.6–7.8 for
whole-fault ruptures. However, low fault slip rates (intermediate estimates
 ∼ &thinsp;0.05–0.8&thinsp;mm/yr) imply long recurrence intervals between
events: 10<sup>2</sup>–10<sup>5</sup> years for border faults and 10<sup>3</sup>–10<sup>6</sup> years for intra-basin faults. Sensitivity analysis indicates that the large
range of these estimates can best be reduced with improved geodetic
constraints in southern Malawi. The SMAFD and SMSSD provide a framework for
using geological and geodetic information to characterise seismic hazard in
regions with few on-fault slip rate measurements, and they could be adapted for
use elsewhere in the East African Rift and globally.</p></abstract-html>
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