<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article">
  <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-14-369-2023</article-id><title-group><article-title>The influence of crustal strength on rift geometry and development –
insights from 3D numerical modelling</article-title><alt-title>The influence of crustal strength on rifting</alt-title>
      </title-group><?xmltex \runningtitle{The influence of crustal strength on rifting}?><?xmltex \runningauthor{T. B. Phillips et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Phillips</surname><given-names>Thomas B.</given-names></name>
          <email>tbphil13@gmail.com</email>
        <ext-link>https://orcid.org/0000-0002-6783-9092</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Naliboff</surname><given-names>John B.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>McCaffrey</surname><given-names>Ken J. W.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9882-1709</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Pan</surname><given-names>Sophie</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>van Hunen</surname><given-names>Jeroen</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3050-6753</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Froemchen</surname><given-names>Malte</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7159-477X</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Earth Science, Durham University, Science Labs,
Durham, DH13LE, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Earth and Environmental Science, New Mexico Institute of
Mining and Technology,<?xmltex \hack{\break}?> Socorro, New Mexico, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Basins Research Group (BRG), Imperial College, London, SW72BP, UK</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Thomas B. Phillips (tbphil13@gmail.com)</corresp></author-notes><pub-date><day>5</day><month>April</month><year>2023</year></pub-date>
      
      <volume>14</volume>
      <issue>4</issue>
      <fpage>369</fpage><lpage>388</lpage>
      <history>
        <date date-type="received"><day>16</day><month>November</month><year>2022</year></date>
           <date date-type="rev-request"><day>24</day><month>November</month><year>2022</year></date>
           <date date-type="rev-recd"><day>2</day><month>March</month><year>2023</year></date>
           <date date-type="accepted"><day>8</day><month>March</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 </copyright-statement>
        <copyright-year>2023</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="d1e142">The lateral distribution of strength within the crust is
non-uniform, dictated by crustal lithology and the presence and distribution
of heterogeneities within it. During continental extension, areas of crust
with distinct lithological and rheological properties manifest strain
differently, influencing the structural style, geometry, and evolution of the
developing rift system. Here, we use 3D thermo-mechanical models of
continental extension to explore how pre-rift upper-crustal strength
variations influence rift physiography. We model a <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> km volume
containing 125 km wide domains of mechanically “strong” and “weak” upper
crust along with two reference domains, based upon geological observations
of the Great South Basin, New Zealand, where extension occurs parallel to
the boundaries between distinct geological terranes. Crustal strength is
represented by varying the initial strength of 5 km<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> blocks. Extension
is oriented parallel to the domain boundaries such that each domain is
subject to the same 5 mm yr<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> extension rate. Our modelling results show that
strain initially localises in the weak domain, with faults initially
following the distribution of initial plastic strain before reorganising to
produce a well-established network, all occurring in the initial 100 kyr. In contrast, little to no localisation occurs in the strong
domain, which is characterised by uniform strain. We find that although
faults in the weak domain are initially inhibited at the terrane boundaries,
they eventually propagate through and “seed” faults in the relatively
strong adjacent domains. We show characteristic structural styles
associated with strong and weak crust and relate our observations to
rift systems developed across laterally heterogeneous crust worldwide, such
as the Great South Basin, New Zealand, and the Tanganyika Rift, East Africa.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Leverhulme Trust</funding-source>
<award-id>ECF-2018-645</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Natural Environment Research Council</funding-source>
<award-id>NE/S007431/1</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e191">The continental lithosphere is highly heterogeneous, with distinct areas of
relative strength and weakness ubiquitous across multiple scales of
observation (e.g. Thomas, 2006; Kirkpatrick et al., 2013). This non-uniform
distribution of strength and heterogeneity within the crust influences
strain localisation, exerting a great influence over the geometry and
development of rift systems developed during continental extension (e.g.
Holdsworth et al., 2001; Kirkpatrick et al., 2013; Brune et al., 2017;
Phillips et al., 2019; Howell et al., 2019; Wright et al., 2020; Gouiza and
Naliboff, 2021)</p>
      <p id="d1e194">Structures deep within the lithosphere and in the mantle have previously
been shown to focus deformation during tectonic events, for example,
controlling the locations of orogenic fronts (Heron et al., 2019). On
larger scales, areas of relatively undeformed cratonic lithosphere are
surrounded by relatively highly deformed mobile orogenic belts, which often
control the siting of rift systems (Daly et al., 1989; Schiffer et al.,
2020). Similarly, lithospheric thickness, and the vertical stratification of
strength within it, may influence the development of rift systems and
continental margins (Duretz et al., 2016; Brune et al., 2017; Schiffer et
al., 2020; Gouiza and Naliboff, 2021; Beniest et al., 2018). However, whilst
lithospheric-scale features may influence first-order rift<?pagebreak page370?> geometry and
evolution, we here focus on how the distribution of strength and
heterogeneity within the upper crust influences rift geometry and evolution,
particularly at the basin scale and during the early stages of rifting.</p>
      <p id="d1e197">The upper crust comprises a mosaic of geological bodies and units, each with
unique lithologies and tectonic histories. Typically strong crustal volumes
may include rheologically strong cratons or relatively homogeneous granitic
batholiths (e.g. Thomas, 2019; Howell et al., 2020), whilst weak areas may
include rheologically weaker sedimentary sequences. Large strength contrasts
exist between these different lithologies, often across short distances as
distinct areas of crust are created, deformed, and juxtaposed against one
another throughout multiple tectonic events (Thomas, 2006). In addition to
their rheology, heterogeneities associated with prior deformation, such as
shear zones within orogenic belts (Daly et al., 1989) or pre-existing faults
within older rift systems (Cowie et al., 2005; Henza et al., 2011; Naliboff
and Buiter, 2015), may also influence bulk crustal strength by acting as
focal points for deformation (e.g. Sutton and Watson, 1986; Holdsworth et
al., 2001). Such structures have been shown to reactivate during extension
or segment rift systems depending on their orientation with respect to the
regional stress field (Doré et al., 1997; Mortimer et al., 2002; Fossen
et al., 2017; Phillips et al., 2019; Vasconcelos et al., 2019). Whilst
rifting can occur in strong cratonic lithosphere (e.g. Larsen et al., 2008;
Tiberi et al., 2019), previous studies have demonstrated that, across
multiple scales, strain preferentially localises into relatively weak
areas with stronger bodies proving resistant to extension (e.g. Beniest et
al., 2018; Lang et al., 2020; Wright et al., 2020; Samsu et al., 2021).
However, less is known about how the characteristic geometry and development
of fault networks and rift systems vary across these relatively “strong”
and “weak” areas during extension.</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="d1e203"><bold>(a)</bold> Map showing the basement terranes present beneath the
South Island of New Zealand and their offshore projections beneath the Great
South Basin. Offshore terrane projections follow Ghisetti (2010)  and Mortimer
et al. (2002). MB stands for Median Batholith, and M stands for Murihiku Terrane. The main faults
shown follow Sahoo et al. (2020). <bold>(b)</bold> Two-way-time (TWT) structure map showing how faults
splay and rotate along internal strength contrasts following Phillips and
McCaffrey (2019). <bold>(c)</bold> Generalised crustal structure offshore of the eastern
coast of the South Island of New Zealand based on the South East South Island (SESI) seismic survey
following Mortimer et al. (2002). The southern end of the line is projected to
incorporate the Separation Point Batholith along the southern margin of the
Median Batholith Zone, and the hypothesised location of panel <bold>(b)</bold> is also
shown.</p></caption>
        <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f01.jpg"/>

      </fig>

      <p id="d1e223">Our study is primarily influenced by geological observations from the Great
South Basin, offshore of New Zealand, where rifting occurred roughly
perpendicular to the boundaries between multiple elongate basement terranes
of varying lithology (Phillips and McCaffrey, 2020; Sahoo et al., 2020;
Tulloch et al., 2019; Barrier et al., 2020), including the dominantly
granitic Median Batholith and the dominantly sedimentary Murihiku Terrane, a
relict forearc basin (Fig. 1a) (Campbell et al., 2003,
2019). Due to this geometry, where terrane boundaries are oriented parallel
to regional extension, each terrane is subject to the same stress, offering
insights into how strain is accommodated across areas of differing strength
and the effect of this on rift geometry and development. As well as the bulk
strength of the various terranes, the boundaries between them form
prominent upper-crustal structures that may be exploited during later
tectonic events (Fig. 1c) (Mortimer et al., 2002; Tarling et al., 2019;
Phillips and McCaffrey, 2019; Phillips and Magee, 2020). The structural
style and evolution of rift systems reflects the geologically and
rheologically complex crustal substrate beneath them, but how strain is
manifested across and within these areas of differing strength and lithology
remains relatively unknown.</p>
      <p id="d1e226">In this study, we use 3D thermo-mechanical simulations of continental
rifting to investigate how rift physiography varies across crustal units of
varying initial strength and their respective boundaries. We extend a
<inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> km region consisting of four 125 km wide domains that are each
assigned different crustal strengths and oriented parallel to the extension
direction (Fig. 1c). The relative strengths of each domain is represented
by randomly varying the initial brittle strength (parameterised through
plastic strain softening) between 5 km<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> “unit blocks”, with weaker
domains containing weaker unit blocks and a greater contrast between blocks.
We explore a range of different parameters representing the strength of our
various domains, varying the degree of strain weakening and the amount of
initial plastic strain within the models. Our modelling results highlight
how crustal strength and heterogeneities related to prior deformation
control strain localisation and rift physiography. We document
characteristic structural styles associated with strong and weak crust,
examine how faults behave at the boundaries between different domains, and
highlight how faults developed in weaker domains influence those developing
in adjacent, relatively strong material. We compare our 3D observations
and analyses to previous analogue and numerical modelling studies, relate our
findings to the Great South Basin and other rift systems globally, and apply
our observations to general continental rifting concepts.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Numerical approach</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Modelling design and geometry</title>
      <p id="d1e269">We model the 3D thermo-mechanical evolution of extending continental
lithosphere using the mantle convection and lithospheric dynamics ASPECT
(Kronbichler et al., 2012; Heister et al., 2017; Glerum et al., 2018; Naliboff
et al., 2020; Pan et al., 2022). The simulations span <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> km, and
fixed outward velocities of 2.5 mm yr<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> on the lateral boundaries drive
extension at a constant total rate of 5 mm yr<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Fig. 2a). As insufficient data
exist to assess the rift velocities, we selected this extension rate as an
intermediate value commonly used in studies of continental extension (e.g.
Naliboff et al., 2020). Inflow along the lower boundary balances outflow,
while a stress-free upper boundary allows the development of topography
(Rose et al., 2017). Diffusion of the free surface at each time step
minimises solver instabilities arising from localised deformation along
faults and acts as a coarse approximation of landscape evolution.</p>
      <p id="d1e312">The initial lithospheric structure contains distinct lithologies with
thermodynamic and rheological properties characteristic of unstretched upper
crust (0–20 km depth), lower crust (20–40 km depth), and mantle lithosphere
(40–100 km<?pagebreak page371?> depth) (Fig. 2a). The rheological structure follows a
visco-plastic constitutive relationship, which captures both brittle
(plastic) and ductile (viscous) deformation processes observed within rifts
and rifted margins. Coupling brittle strain softening of cohesion and the
internal angle of friction with randomised initial plastic strain (IPS)
enables the formation of distributed normal fault networks (Naliboff et al.,
2017, 2020; Duclaux et al., 2020; Pan et al., 2022). We use
variable distributions of the IPS along the model length to define upper-crustal volumes of differing strength (e.g. distinct geologic terranes),
with the cohesion and angle of internal friction decreasing linearly between
defined IPS values (e.g. strain softening interval). Aside from the initial
variations in IPS, the crustal structure and rheological parameters are
identical between distinct model domains.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e317"><bold>(a)</bold> Diagram showing the map view and cross-sectional setups
for the model. Strain is applied across a 500 km wide and 100 km deep area,
with a 150 km wide “damage zone” extending to 40 km depth across the centre
of the model where IPS is assigned to unit blocks. <bold>(b)</bold> Images of the IPS
distribution applied to each model prior to extension at 0 Myr. Variations in
IPS values between 5 km<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> unit blocks define various strength terranes.</p></caption>
          <?xmltex \igopts{width=412.564961pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f02.png"/>

        </fig>

      <p id="d1e341">The initial resolution throughout the model is set to 5 km and refined to
1.25 km in the upper 20 km (i.e. upper crust) across the central 150 km of
the model. This approach enables a relatively high resolution in the region
of interest (upper crust), while producing “natural” boundary conditions at
its base. The full details of the model design and numerical methods are
provided in Appendix A, including the underlying governing equations.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Exploring upper-crustal strength</title>
      <p id="d1e352">We assign IPS values to 5 km<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> blocks, termed unit blocks, in the upper
crust across the central 150 km of the model, termed the damage zone. IPS
values were randomly assigned to unit blocks in a binary fashion, such that
a block has either the minimum or maximum value specific to that strength.
We define four 125 km wide upper-crustal domains of varying strength,
oriented parallel to the extension direction (Fig. 2a). From north to
south, the domains are assigned “reference (north)”, “weak”, “strong”, and
“reference (south)” strengths (Fig. 2a). The 5 km<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> block size corresponds to
4<inline-formula><mml:math id="M12" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> the numerical resolution of 1.25 km; Pan et al. (2022) show that these
values sufficiently localise deformation at the onset of extension.</p>
      <p id="d1e380">We generated four models with varying values and combinations of IPS in each
of the domains. The initial cohesion (20 MPa) and internal angle of friction
(30<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) decrease by a factor of 4 between plastic strain values of
0.5–1.5. For each of our models we assign specified IPS values to unit
blocks within the damage zone, with zero IPS outside of the zone. The
assigned IPS values vary between unit blocks in the strong, weak, or
reference domains (Fig. 2). The greater the value of IPS, and the greater
the contrast in IPS between adjacent unit blocks, the weaker the domain.
Unit blocks in the weak domain have values of 0.5 or 1.5 across all<?pagebreak page372?> models.
In models 1 and 2, we characterise the strong domain as having zero IPS and
the reference domains as having IPS values of 0.5 or 0.75 (model 1) and 0.5
or 1.0 (model 2). In model 3, the strong domain is characterised by a
constant IPS of 0.5 across all unit blocks within the domain, whilst IPS values for
unit blocks in the reference domains are either 0.5 or 0.75. In model 4, the
strong domain is characterised by IPS of either 0.5 or 0.6 between different
unit blocks and a reference domain that varies between 0.5 and 1.0. In
addition, we performed two runs of model 4 using different randomised
distributions of IPS between unit blocks, highlighting that whilst the
randomised IPS may influence individual fault geometries, they do not affect
the first-order patterns identified in each domain.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Exploring strength parameter space</title>
      <p id="d1e401">Each of our models is subject to the same 5 mm yr<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> extension rate. How strain
localises across each model varies markedly between models and each of the
domains. For each model, we now describe the overall fault geometries
(defined by strain rates, IPS, or viscosity) across the weak, strong, and
north and south reference domains (Fig. 2a). Notably, all descriptions of
fault geometries by strain strictly refer to strain accumulated through
brittle (plastic) deformation (i.e. non-initial plastic strain).</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Model 1</title>
      <p id="d1e423">Model 1 consists of a strong domain with no initial strain perturbations and
a relatively strong reference domain. Strain rapidly localises into the weak
domain, producing a well-defined fault network from early in the model run
(Fig. 3a). These high-strain zones represent faults and interact with one
another laterally, forming linkages and abandoned splays (Fig. 3a).
Outside of this developed high-strain fault network the background strain is
relatively low, forming strain shadows between the highly localised faults.
As the initial strain parameters for the weak domain remain the same for
each model, this domain is not discussed for the other models but will be
examined in greater detail later.</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="d1e428">Map view images of each model <bold>(a–d)</bold> showing the
non-initial plastic strain <bold>(a, c)</bold> and strain-rate-invariant <bold>(b, d)</bold>
attributes at 10 Myr.</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f03.png"/>

        </fig>

      <p id="d1e446">The strong domain in model 1 is characterised by zero strain weakening. At
10 Myr strain is distributed uniformly across the model, with little
localisation occurring. Some higher strain is observed at the edge of the
strong domain in this model, potentially representing edge effects at the
edge of the damage zone as the entire domain forms a rigid, strong body that
does not extend.</p>
      <p id="d1e450">The reference domains in model 1 are relatively strong compared to the
reference domain in the other models. After 10 Myr some localisation appears
to have occurred in both reference domains, with increased localisation
occurring in the north reference domain (adjacent to the weak domain)
compared to the south reference domain, located adjacent to the strong
domain. In the north reference domain increased localisation occurs close to
the boundary with the weak domain. No clear differentiation can be
identified from north to south within the south reference domain.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Model 2</title>
      <p id="d1e461">As with model 1, no strain weakening occurs in the strong domain of model 2.
Accordingly, this produces similar patterns of deformation to model 1, with
little localisation across the entire domain, and some increased strain
observed at the boundaries of the damage zone.</p>
      <p id="d1e464">The reference domain in this model is weaker than that of model 1, with unit
blocks assigned IPS values of 0.5 or 1.0. Accordingly, the reference domain
in model 2 shows increased localisation compared to model 1 (Fig. 3b). A
similar differentiation can be identified between the north and<?pagebreak page373?> south
reference domains, with the former showing increased strain localisation and
better developed faults. Localisation does begin to occur in the south
reference domain, with some increased localisation seemingly occurring at
the southern edge of the domain (and the model) compared to the boundary
with the strong domain at the northern edge of the domain (Fig. 3b).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Model 3</title>
      <p id="d1e475">In model 3, the reference domain is characterised by the same IPS range as
that in model 1 (0.5–0.75), producing similar strain patterns. In contrast
to models 1 and 2, the strong domain in model 3 is assigned a constant IPS value
of 0.5, with no variation between adjacent unit blocks. Although strain
weakening is permitted in the strong domain of this model, we still do not
identify any strain localisation. As with models 1 and 2, where no strain
weakening was present, the strong domain undergoes relatively uniform
strain, with some increased localisation at the edge of the domain where
there is a contrast in IPS between the outside of the model, where no IPS is
present, and the damage zone where IPS is prescribed (Fig. 3c).</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Model 4</title>
      <p id="d1e487">Model 4 is characterised by varying IPS values in the strong, reference and
weak domains (Fig. 2b). IPS varies between 0.5 and 1.5 in the weak domain,
0.5–1.0 in the normal domain (as in model 2), and (in contrast to the
previous models) varying IPS of 0.5–0.6 in the strong domain. We performed
two runs of this model, keeping the same values but<?pagebreak page374?> changing how they were
distributed across the unit blocks prior to extension.</p>
      <p id="d1e490">As in model 2, strain localisation varies between the north and south
reference domains, with increased localisation occurring in the north
reference domain, located adjacent to the weak domain (Fig. 3d). At the
end of the model run, we begin to see some strain localisation within the
strong domain with broad zones of increased strain beginning to develop
(Fig. 3d). We now analyse this model in detail, examining the localisation
of strain through time and in three dimensions.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Strain accommodation through time (model 4)</title>
      <p id="d1e502">Model 4 shows the greatest variation within each domain across the 10 Myr
model run. We qualitatively and quantitatively analyse the results of this
model in three dimensions at 2.5 Myr intervals (Fig. 4).</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="d1e507"><bold>(a)</bold> Map view images highlighting the fault evolution
across the model using the non-initial plastic strain attribute at 2.5, 5, 7.5, and 10 Myr. The black box shown for the 10 Myr model time step shows
the location of Fig. 6. <bold>(b)</bold> Cross-sectional views across the centre of the
weak domain (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> km), the boundary between the north
reference and weak domains (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">375</mml:mn></mml:mrow></mml:math></inline-formula> km), and within the strong
domain 10 km from the weak domain boundary (<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">240</mml:mn></mml:mrow></mml:math></inline-formula> km). Cross
sections shown at 2.5<inline-formula><mml:math id="M18" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> vertical exaggeration. <bold>(c)</bold> Map and cross-sectional
views of the strain rate attribute highlighting the fault network at 10 Myr.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f04.png"/>

      </fig>

<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Qualitative observations</title>
      <p id="d1e575">The weak domain is characterised by a network of widely spaced (10–15 km),
high-strain localised zones, separated by low-strain shadows (Fig. 4).
Faults are sub-perpendicular to the extension direction, although some
variation occurs, particularly at fault tips (Fig. 4a). In cross section
these faults form conjugate sets that join at the top of the ductile lower
crust (Fig. 4b). Fault location and geometry, including the interactions
and linkages between adjacent faults, are established within 100 kyr of the
simulation. Strain continues to be accommodated along this fixed network
throughout the model run, as evidenced by the fixed areas of high strain
rate and non-initial plastic strain (Fig. 4a; see Appendix B for images of
the entire model run).</p>
      <p id="d1e578">Throughout the model run, the strong domain is characterised by uniform
strain with little to no localisation onto faults. Strain rate across the
model is highly variable, as evidenced by the strain-rate-invariant attributes (Fig. 4a). Bands of high instantaneous strain rate continually migrate across the
model throughout the run; accordingly, plastic strain does not accumulate in
any area, resulting in no strain localisation (Fig. 4a). Broad zones of
elevated non-initial plastic strain start to develop towards the end of the
run, extending outwards from the boundaries of the strong domain with the
adjacent weak and reference domains (Fig. 4b).</p>
      <p id="d1e581">Both reference domains display some evidence of strain localisation,
intermediate between the complete localisation in the weak domain and the
lack thereof in the strong domain. Faults are typically sub-linear in plan
view with limited interaction occurring between adjacent structures. Looking
at the strain rate, high-strain-rate structures display some transient
properties throughout the model run as faults move, and strain does not fully
localise onto established structures (Fig. 4). Strain localisation occurs
diachronously between the north and south reference domains, with different
degrees of localisation occurring in each domain (Fig. 4a). Increased
strain localisation occurs in the north reference domain, with localisation
in the latter also occurring earlier in the model run. The north reference
domain is adjacent to the highly localised weak domain, whereas the south
reference domain is adjacent to the strong domain, which experiences little
strain localisation.</p>
      <p id="d1e584">In map view, strain appears greatest in the centre of the faults in the
reference and weak domains, decreasing towards the fault tips (Fig. 4a).
High strain values are also identified along faults in the weak domain close
to its boundaries. The faults are typically retarded at the domain boundary,
and strain rapidly decreases to background levels. In some instances,
particularly along the boundary between the weak and north reference domain,
faults may extend across the boundary, with lower amounts of strain
accommodated in the north reference compared to the weak domain. In
cross section, faults typically dip at around 45–50<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and display a
high-strain, highly localised core, which decreases to background levels
away from the fault (Fig. 4b). Faults appear more well defined in the
centre of the weak domain compared to the boundaries and other domains.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Quantitative strain analyses</title>
      <p id="d1e605">To quantitatively analyse our model results we measured the accumulated
non-initial plastic strain along a series of transects through model 4.
Cumulative strain was measured across the centre of each of the domains and
also at 2.5 km intervals covering the boundary between the strong and weak
domains (Fig. 5). Large vertical jumps in the cumulative strain show the
location of faults, with the gap between these jumps representing the fault
spacing. A line displaying a constant gradient represents uniform strain
across the model. Individual faults may be difficult to distinguish,
particularly those with less localised structures. As such, measurements of
individual per-fault strain and fault spacing are approximate, although we
can identify first-order differences between domains.</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="d1e610"><bold>(a)</bold> Map view image of non-initial plastic strain at 10 Myr
across the central 250 km of the model. <bold>(b)</bold> Strain analysis of multiple
transects across the centre of each domain of the model; see <bold>(a)</bold> for the location.
The grey-shaded area represents the location of the damage zone initially
across the central 150 km of the model. Note how fault spacing and per-fault
strain are greatest in the weak domain, whilst the strong domain approximates
uniform strain. <bold>(c)</bold> Strain analysis of a series of model transects spanning
the boundary between the strong and weak domains. Fault spacing and
per-fault strain decrease across the boundary into the strong domain.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f05.png"/>

        </fig>

      <p id="d1e630">The total accumulated strain across the strong domain is less
(<inline-formula><mml:math id="M20" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 18) than that of the weak domain (<inline-formula><mml:math id="M21" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 22)
(Fig. 5b). Although both domains are subject to the same strain and
experience the same amount of total extension (5 km across the full model
run), varying amounts of extension are focussed into the central damage zone
depending on the domain. We find that relatively high strain is focussed
into the damage zone in the weak domain compared to the strong domain; strain is
more distributed between the 125 km wide damage zone and the rest of the
model (375 km) in the strong domain compared to the weak domain.</p>
      <?pagebreak page375?><p id="d1e648">The fault network maintains its overall pattern and topology in the weak
domain throughout the model run, with individual faults displaying some
advection outwards as the model extends. These faults are spaced at 10–15 km
intervals with each fault accommodating strain of <inline-formula><mml:math id="M22" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.5–1. The
areas between the faults are characterised by low-to-zero strain of a
magnitude similar to the model areas outside the damage zone. In the
reference domains, some strain transfer and interactions occur between fault
tips, as identified using the strain rate parameter. Isolated faults appear
to progressively link with adjacent structures at various points throughout
the model run, forming larger continuous structures (Fig. 4c).</p>
      <p id="d1e658">Faults within the reference domains are more closely spaced and accommodate
less strain than those in the weak domain. In the south reference domain,
per-fault strain is <inline-formula><mml:math id="M23" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.25–0.5 with spacing of around 25 km.
Values in the north reference domain are relatively similar, with per-fault
strains of 0.5–0.75 and spacing of 10–15 km. There are often less-developed
faults between the more localised structures in the reference domains. We
note a slight change in fault density across the north reference domain,
with more well-developed and localised structures, producing larger steps in
the transects, present to the left side of the model (Fig. 5). This may in
part reflect the distribution of the initial plastic strain within the north
reference domain or the prevalence of faults extending across the boundary
from the adjacent weak domain.</p>
      <p id="d1e668">A key point is that fault spacing and per-fault strain, and therefore strain
localisation, are highest in the weak domain, decreasing into the north
reference domain and the south reference domain. No localisation is
identified in the centre of the strong domain, with no clear steps
identified in the transect (Fig. 5), which appears to approximate uniform
strain (Fig. 5b). Some localisation is identified towards the northern
boundary of the domain, as faults from the weak domain begin to extend into
the strong domain as broad zones of elevated strain (Fig. 4).</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Strain accommodation across domain boundaries</title>
      <p id="d1e679">We analyse fault geometry across the reference–weak and weak–strong domain
boundaries (Fig. 4). Strain is more localised in the weak compared to the
reference domain, with the latter having a higher background strain (i.e.
more distributed) (Fig. 4a). The weak–reference boundary is characterised
by a <inline-formula><mml:math id="M24" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10 km zone of diffuse strain (Fig. 4a). To the south,
highly localised faults in the weak domain are inhibited at and dissipate
towards the strong domain boundary (Fig. 4b). Broad zones of elevated
strain characterise the boundary-proximal strong domain and persist up to 25 km away from the boundary (Fig. 5c).</p>
      <p id="d1e689">This transition from localised to diffuse strain across domain boundaries
demonstrates a “seeding” effect of faults in stronger domains by those in
weaker domains (Fig. 4).<?pagebreak page376?> Established faults propagate into adjacent
stronger domains, initially as broad zones of elevated strain that become
increasingly localised. This may account for the lateral variation in fault
density across the north reference domain; this reflects the density of
faults in the weak domain, with more seeding occurring to the left of the
model (Fig. 5a). Faults in the north reference domain are partially
seeded by those in the adjacent weak domain. However, as the south
reference domain is weaker than the adjacent strong domain, faults here are
not seeded and initiate independently, accounting for the differences
between the reference domains (Fig. 3). In turn, faults in the south
reference domain may, along with faults in the weak domain, seed faults in
the strong domain (Fig. 4b).</p>
</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Fault geometry</title>
      <p id="d1e700">The fault network in the weak domain is established in the first 100 kyr of the model run. Faults within the network display a range of
orientations and overall strain (Figs. 5a, 6). Numerous relay ramps,
lateral fault linkages, and abandoned fault splays are present across the
domain, with the larger faults associated with numerous synthetic and
antithetic splays (Fig. 6b). Further faults are also present at lower
strain values, cross-cutting the main fault and oriented at a relatively high angle(Fig. 6a, b). These high-angle structures appear to roughly
follow the distribution of initial plastic strain within the model (Fig. 6b) and are cross-cut by the main fault in map and cross-sectional view
(Fig. 6c). In some instances it seems that the cross-cut structures may
also form antithetic or synthetic splays to the main structure (Fig. 6b).
This suggests the higher-angle faults formed initially before being
cross-cut by the main structure. This complex multi-generational faulting
occurred within the first 100 kyr of the model run (Fig. 6).</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="d1e705"><bold>(a)</bold> Close-up map view image of a fault within the weak
domain; see Fig. 4a for the location. The locations of cross sections and key
faults are shown. <bold>(b)</bold> Interpretation of fault geometries within and
immediately adjacent to the weak domain. The interpretation and the
distribution of initial plastic strain between unit blocks are shown with
the interpretation. <bold>(c)</bold> Cross sections across the model, showing the
cross-cutting fault systems. Cross sections shown at 1<inline-formula><mml:math id="M25" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> vertical
exaggeration. See <bold>(a)</bold> for the location.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f06.png"/>

        </fig>

      <p id="d1e732">At domain boundaries, faults are typically inhibited or greatly reduced in
per-fault strain (Fig. 6a). At the boundary between the north reference
and weak domains the main fault<?pagebreak page377?> extends into the reference domain, albeit
with lower overall strain (Fig. 6a, c). In contrast, the main fault
terminates at the strong–weak domain boundary. Strain is much more
distributed within the strong domain, although a wide zone of elevated
strain associated with the fault can be identified (Fig. 6a, c).</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion</title>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Comparisons to previous numerical and analogue modelling studies</title>
      <p id="d1e752">In this study we present a series of 3D thermo-mechanical numerical models
examining the influence of crustal strength on rift development. Previous
analogue modelling studies highlight the influence and interplay between
discrete structures throughout the upper crust and lithosphere. Zwaan et
al. (2021) show how arrays of intersecting discrete structures may produce
complex fault geometries. Similarly, Samsu et al. (2021) use analogue models
to show how discrete basement structures can influence the location of
faults that formed later without reactivation, whilst Schmid et al. (2022)  demonstrate
how discrete structures may locally reorient the regional stress field. In
our models we do not prescribe discrete individual heterogeneities, instead
modelling a diffuse zone of randomised weakness; thus, our heterogeneities
display no overall preferred orientation (Fig. 2). This is more
representative of a pervasive weak rheology, similar to the analogue models
presented in Samsu et al. (2021). A benefit of our numerical modelling
approach is that we can assign weakness without relying upon discrete
heterogeneities or a weak seed. By altering the contrast between adjacent
unit blocks, we are able to effectively assign varying bulk strengths to
different domains.</p>
      <?pagebreak page378?><p id="d1e755">Beniest et al. (2018) use analogue modelling to investigate how lateral
strength variations in the lithosphere influence rift style, showing that
strain preferentially localises into weaker areas, with strong areas being
resistant to strain and acting as rigid blocks. Whilst our model supports
the findings of Beniest et al. (2018), a key difference is that it is
oriented at 90<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, with each domain subject to strain rather than
localised into one area. As a result of this we see some limited
localisation within the strong domain, particularly where faults begin to
propagate across the domain boundary from adjacent domains (Fig. 6). Where
either no strain weakening (models 1 and 2, Fig. 4) or no variation in
strain weakening (model 3, Fig. 4) was incorporated into the strong
domain, it acts as a rigid block with strain localising around its margins
(Fig. 4), in agreement with the observations of Beniest et al. (2018). We
are able to identify along-strike changes in the rift physiography and
examine how the faults behave at boundaries between domains (Figs. 5, 6).
Both models are highly applicable to different geological areas, depending
on the initial crustal configuration and orientation of rifting (e.g. Brune
et al., 2017).</p>
      <p id="d1e767">Previously, numerical modelling studies have often examined first-order
controls on the geometry and development of rifts and rifted margins (e.g.
Duretz et al., 2016; Naliboff and Buiter, 2015), rather than the
three-dimensional upper-crustal-scale observations presented here. Some
studies have attempted to replicate the complexity present within the crust
and lithosphere (e.g. Duretz et al., 2016), although these are typically
limited to two dimensions. One of the key tenets of our study is the ability
to analyse rift development in 3D and to examine how rift physiography
changes in the along-strike direction atop varying upper-crustal properties. Numerous studies
have also focussed on how deeper lithospheric-scale heterogeneities
influence tectonic processes (e.g. Heron et al., 2019; Schiffer et al.,
2020). Gouiza and Naliboff (2021) use 3D numerical modelling to investigate
how lithospheric strength and thickness affect continental rifting and
breakup in the Labrador Sea, although this focuses on the first-order rift
margin geometry, rather than rift-scale faults and features identified in
our models. Whilst we do not incorporate any heterogeneities in the mantle
lithosphere in our models, the 150 km wide damage zone controls the
first-order rift location, perhaps fulfilling a similar role to mantle
heterogeneities during rifting (Fig. 1c). Nevertheless, whilst deeper
lithospheric-scale structures may govern first-order rift location, we
suggest that rift structural style and physiography is primarily controlled
by upper-crustal properties and structures.</p>
      <p id="d1e770">Recently, a series of high-resolution 3D numerical investigations have
explored fault network evolution and crustal-scale rifting processes
(Duclaux et al., 2020; Naliboff et al., 2020; Jourdon et al., 2021; Pan et
al., 2022). The models of Duclaux et al. (2020) and Jourdon et al. (2021)
demonstrate the dynamics of normal fault network evolution during oblique
rifting. Our models of orthogonal extension here share a similar setup to
those of Pan et al. (2022) and build upon those of Naliboff et al. (2020),
using a randomised distribution of initial plastic strain across a broad
area rather than a single weak seed. These studies highlight how complex
fault geometries may arise through fault interactions rather than individual
heterogeneities. In contrast to these previous studies, our models highlight
how fault geometries and rift physiographies vary across crust of varying
strength. The cross-cutting fault networks developed during the initial
100 kyr of our models resemble transient fault networks generated in
previous modelling studies that focus on fault evolution across smaller
timescales (e.g. Cowie et al., 2000; Pan et al., 2022). We suggest that
during the initial stages of extension faults exploit the weaknesses between
the unit blocks, forming a complex fault network displaying a range of
orientations. As extension progresses and strain increases during this
initial 100 kyr, strain begins to localise onto larger faults oriented
perpendicular to the regional stress (Fig. 6). Similar observations have
been made in nature; fractures that initially exploit non-optimally oriented
fabrics at low strains may join to form larger throughgoing structures, as
identified in shear zones in East Africa (Daly et al., 1989). In addition,
the Ekitale Basin along the East African Rift initially exploits low
basement structures during low-strain extension, before being overprinted by
more optimally oriented structures (Ragon et al., 2019).</p>
</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>Comparison to natural systems and implications for rifting processes</title>
      <p id="d1e781">Our models showcase an idealised scenario where rifting occurs parallel to
crustal terranes of varying strength separated by vertical boundaries. Here,
we relate key first-order observations from our models to other rift systems
globally, including the Great South Basin, New Zealand. In addition, we draw
upon our model observations to inform our understanding of rifting processes
generally.</p>
      <p id="d1e784">Rift structural style varies markedly between different domains; the weak
domain is characterised by a highly localised and widely spaced fault
network that is established in the model within 100 kyr (Supplement
animation S1), whereas the strong domain is characterised by a lack of
localisation and relatively distributed strain (Fig. 7). Beneath the Great
South Basin, the Murihiku Terrane is a dominantly sedimentary
terrane sourced from a fore-arc setting (Tulloch et al., 2019; Sahoo et al.,
2020) and is taken as an analogue for the weak domain in our models. The
sedimentary nature of this terrane may cause it to be relatively weak, and it
also may contain a multitude of pre-existing weaknesses such as bedding
planes and pre-existing faults (Tulloch et al., 2019). Similarly, the Brook
Street Terrane is primarily composed of volcaniclastic material. In
contrast, the Median Batholith is predominantly granitic and relatively
homogeneous; this is taken to represent an analogue for the strong domain in
our models. Weaknesses are also likely present in the strong<?pagebreak page379?> Median
Batholith terrane, for example, internal shear zones or the boundaries
between individual granitic plutons (Allibone and Tulloch, 2004; Phillips
and McCaffrey, 2019). However, we suggest these heterogeneities are less
pervasive and may display a lower difference in relative strength than
heterogeneities in weak areas such as the Murihiku Terrane. Strong bodies,
such as granites, typically resist strain localisation, as exemplified by
their role as “blocks” in the “block and basin” geometry of UK Carboniferous
rift systems (Fraser and Gawthorpe, 1990; Howell et al., 2020) and the
Sierra Nevada Batholith in the USA, which buffers extension in the basin and
range (Ryan et al., 2020).</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="d1e789">The characteristic structural styles
associated with each domain and the key concepts demonstrated in our model.
Cones of increased strain extend into the strong domain. As extension
progresses, faults would eventually propagate into the strong domain, forming
throughgoing structures that localise strain and relatively undeformed
islands of strength.</p></caption>
          <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f07.png"/>

        </fig>

      <p id="d1e799">Strain localisation occurs diachronously across our model, first in the weak
domain and last in the strong domain (Fig. 5a). This agrees with our
assumptions of terrane strength from the Great South Basin, where rifting
has been shown to initiate in the weak sedimentary and volcaniclastic Murihiku
and Brook Street terranes prior to the strong granitic Median Batholith
(Fig. 1a) (Sahoo et al., 2020). Similarly, extension in the Tanganyika
Rift of the East African Rift system rapidly localises onto border faults
where the rift traverses Proterozoic mobile belts but remains distributed
across the cratonic Bangwelu Block (Fig. 1b) (Wright et al., 2020). Here,
the mobile belts host prominent fabrics, forming weaknesses and acting
similarly to the large IPS contrasts in the weak domain (Fig. 2a),
thereby causing strain to preferentially localise. In contrast, the cratonic
Bangwelu Block hosts only weakly developed fabrics, analogous to the small
IPS contrasts present between unit blocks in the strong domain, inhibiting
strain localisation (Wright et al., 2020). Similar observations have been
made from analogue modelling studies, which show more distributed (uniform)
deformation in areas of stronger basement (Samsu et al., 2021).</p>
      <p id="d1e802">Gouiza and Naliboff (2021) show how continental rifting and breakup in the
Labrador Sea first occurred in the strong North Atlantic Craton before
proceeding to relatively weak adjacent basement terranes. The timing and
style of breakup between these regions is directly linked to the
lithospheric structure, where the geothermal gradient and crustal thickness
and rheology control rapid localisation in the stronger (colder, thinner
crust) northern regions. Upon first consideration, this would appear to
contradict our model results and the geological observations described
above, with continental rifting and breakup proceeding rapidly in the
relatively stronger areas of crust and suppressed in weaker areas (Gouiza
and Naliboff, 2021; Peace et al., 2018). However, these simulations
contained randomised brittle heterogeneities of equivalent magnitudes (i.e.
degree of initial plastic strain perturbations) within the crust and mantle
lithosphere of the northern, central, and southern cratonic domains. As a
result, rifting was able to initiate simultaneously across the distinct
domains defined by variations in lithospheric structure, rather than
randomised brittle strength heterogeneities as done in this study. The model
design of Gouiza and Naliboff (2021) was based on the observations that rift
initiation in the Labrador Sea was not significantly offset between distinct
domains, and numerous heterogeneities are identified onshore in the strong
North Atlantic Craton that extend beneath the Labrador Sea (Peace et al.,
2018; Wilson et al., 2006) that could have reactivated to accommodate the
initial rift fault networks. We suggest that the presence of these sparse
weaknesses partition the strong, homogeneous body into multiple isolated
“islands of strength” separated by numerous weaker heterogeneities (Fig. 7). Whilst the strong “islands” resist extension, as in our model's strong
domain (Fig. 2), strain may rapidly localise along the surrounding weaker
heterogeneities. Due to large differences in relative strength between the
strong areas and intervening weaknesses, these areas may rapidly localise
strain. At the rift scale, strong bodies such as the Median Batholith
beneath the Great South Basin or the North Atlantic Craton beneath the
Labrador Sea may resemble homogeneous areas similar to the strong domain in
our models (Fig. 7). However, examining these areas in more detail
highlights internal weaknesses that may localise strain and allow rift
systems to propagate through these strong areas. Based on this, we suggest
that the strong domain in our models may be more representative of these
islands of strength within the rift.</p>
      <p id="d1e805">At terrane boundaries, we find that faults are inhibited at boundaries with
adjacent, stronger domains, before potentially propagating through them (Fig. 4). No faults are present in the strong domain, with faults arrested at its
boundaries. However, faults do traverse the boundary between the weak and
reference domains, albeit displaying lower strain in the relatively strong
domain (Fig. 6). In the Great South Basin, we observe that faults commonly
rotate into alignment with the boundary or segment and terminate against the
stronger areas (Fig. 1a) (Phillips and McCaffrey, 2019; Sahoo et al.,
2020). Our model observations show that as faults are initially arrested at
the boundaries, diffuse areas of strain form in the stronger area,
potentially analogous to damage zones in nature (Fig. 3b). We suggest that
as extension progresses strain may continue to build up at the terrane
boundaries, accommodated by localised structures in the weaker domains and
diffuse strain in the stronger domains. These broad areas of elevated strain weaken
the stronger domain, and once it is sufficiently weakened, faults from adjacent
domains may propagate through the domain boundary and seed faults in the
stronger domains (Fig. 3a). These faults are then able to propagate
through the stronger area. With further extension, the seeded faults in the
strong domain may lead to the development of the islands of strength and
intervening weaknesses (Fig. 7). Strain continues to further weaken the
established weaknesses, leading to a greater relative strength difference
between them and the low-strain strong island. This creates a positive
feedback cycle where strain is preferentially focussed into the weaker area
(Fig. 7).</p>
</sec>
</sec>
<?pagebreak page380?><sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e817">We document characteristic structural styles associated with strong and weak
crust and examine how strain is manifested across boundaries between areas of
different strength. We relate our findings to multiple rift systems
globally, offering insights into their evolution and to fundamental
continental rifting processes.</p>
      <p id="d1e820">We demonstrate that well-developed fault networks develop in weaker areas
containing numerous heterogeneities, whilst localisation is inhibited in
relatively homogeneous, stronger areas. We find that strain initially
localises in these weaker areas before eventually propagating into and
traversing stronger areas (Fig. 7), similar to observations from rift
systems globally.</p>
      <p id="d1e823">Within the weak domain, multiple generations of cross-cutting faults develop
in the first 100 kyr, in agreement with other studies examining fault
evolution across shorter time intervals. We show how the faults that developed first
initially form at non-optimal orientations and follow the weaknesses
present within the initial model setup. With continued extension, the fault
system reorganises, with new faults aligning perpendicular to the extension
direction and cross-cutting the older structures (Fig. 6).</p>
      <p id="d1e826">We also highlight how strain localisation and fault development is inhibited
within the strong domain of our models. We find that faults are initially
inhibited at the boundaries between different domains in our model, as they
are at terrane boundaries in nature. Our models offer a temporal perspective,
however, showing that broad areas of elevated strain develop in the stronger
areas adjacent to fault tips before the barrier is eventually breached and
the fault can continue to propagate. The presence of faults within
relatively weak domains is able to seed the development of those in
adjacent, stronger areas.</p>
      <p id="d1e830">We are also able to highlight key differences between our idealised model
observations and observations from geological examples. Whilst the strong
domain in our models<?pagebreak page381?> represents a large relatively homogeneous body with
only little relative strength differences, similar examples in nature
contain some weaknesses at the basin scale that localise strain and may lead
to rapid fault development. We suggest that these weaknesses traverse the
otherwise strong bodies, creating a series of isolated “islands of strength”
that are resistant to extension and more resemble the strong domain in our
models.</p>
      <p id="d1e833">Our modelling highlights how upper-crustal strength distributions influence
rift geometry and physiography. We relate our findings to other modelling
studies and rift systems globally and highlight key implications for our
understanding of continental rifting processes, particularly during early
stages of rifting across a geologically complex crustal substrate.</p>
</sec>

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

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title/>
      <p id="d1e846">We use the open-source, mantle convection and lithospheric dynamics code
ASPECT (Kronbichler et al., 2012; Heister et al., 2017) to model 3D
continental extension (Fig. 1a) following an approach modified from Naliboff
et al. (2020) and Pan et al. (2022). The Stokes equations follow the
incompressible Boussinesq approximation:

              <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M27" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S1.E1"><mml:mtd><mml:mtext>A1</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">∇</mml:mi><mml:mo>⋅</mml:mo><mml:mi>u</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S1.E2"><mml:mtd><mml:mtext>A2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>-</mml:mo><mml:mi mathvariant="normal">∇</mml:mi><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">μ</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mfenced close=")" open="("><mml:mi>u</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">∇</mml:mi><mml:mi>p</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          where <inline-formula><mml:math id="M28" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> is the velocity, <inline-formula><mml:math id="M29" display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula> is the viscosity, <inline-formula><mml:math id="M30" display="inline"><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover></mml:math></inline-formula> is
the second invariant of the deviatoric strain rate tensor, <inline-formula><mml:math id="M31" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is the pressure,
<inline-formula><mml:math id="M32" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> is the density, and <inline-formula><mml:math id="M33" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the gravitational acceleration.</p>
      <p id="d1e971">Temperature evolves through a combination of advection, heat conduction, and
internal heating as follows:
          <disp-formula id="App1.Ch1.S1.E3" content-type="numbered"><label>A3</label><mml:math id="M34" display="block"><mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">∇</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mi mathvariant="normal">∇</mml:mi><mml:mo>⋅</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="italic">κ</mml:mi><mml:mi mathvariant="italic">ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">∇</mml:mi><mml:mi>T</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>H</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the heat capacity, <inline-formula><mml:math id="M36" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the temperature, <inline-formula><mml:math id="M37" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> is the time, <inline-formula><mml:math id="M38" display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula> is the thermal diffusivity, <inline-formula><mml:math id="M39" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> is the linear thermal expansion
coefficient, and <inline-formula><mml:math id="M40" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> is the rate of internal heating.</p>

<?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.S1.T1" specific-use="star"><?xmltex \currentcnt{A1}?><label>Table A1</label><caption><p id="d1e1094">Material properties for distinct compositional layers.</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="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Upper crust</oasis:entry>
         <oasis:entry colname="col3">Lower crust</oasis:entry>
         <oasis:entry colname="col4">Mantle lithosphere</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Reference density</oasis:entry>
         <oasis:entry colname="col2">2800 kg m<inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">2900 kg m<inline-formula><mml:math id="M42" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">3300 kg m<inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Viscosity prefactor (<inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">8.57 <inline-formula><mml:math id="M45" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M46" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">28</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> Pa<inline-formula><mml:math id="M47" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M48" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M49" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">7.13 <inline-formula><mml:math id="M50" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> Pa<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M53" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">6.52 <inline-formula><mml:math id="M55" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M56" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> Pa<inline-formula><mml:math id="M57" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M58" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M59" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M60" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> (stress exponent)</oasis:entry>
         <oasis:entry colname="col2">4</oasis:entry>
         <oasis:entry colname="col3">3</oasis:entry>
         <oasis:entry colname="col4">3.5</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M61" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> (grain size exponent)</oasis:entry>
         <oasis:entry colname="col2">0</oasis:entry>
         <oasis:entry colname="col3">0</oasis:entry>
         <oasis:entry colname="col4">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Activation energy (<inline-formula><mml:math id="M62" display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">223 kJ mol<inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">345 kJ mol<inline-formula><mml:math id="M64" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">530 kJ mol<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Activation volume (<inline-formula><mml:math id="M66" display="inline"><mml:mi>V</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">–</oasis:entry>
         <oasis:entry colname="col3">–</oasis:entry>
         <oasis:entry colname="col4">18 <inline-formula><mml:math id="M67" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M68" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M69" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> mol<inline-formula><mml:math id="M70" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Specific heat (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">750 J kg<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> k<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">750 J kg<inline-formula><mml:math id="M74" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> k<inline-formula><mml:math id="M75" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">750 J kg<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> k<inline-formula><mml:math id="M77" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Thermal conductivity   (K)</oasis:entry>
         <oasis:entry colname="col2">2.5 W m<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">2.5 W m<inline-formula><mml:math id="M80" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">2.5 W m<inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Thermal expansivity (<inline-formula><mml:math id="M84" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">2.5 <inline-formula><mml:math id="M85" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M86" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">2.5 <inline-formula><mml:math id="M88" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">2.5 <inline-formula><mml:math id="M91" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Heat production (<inline-formula><mml:math id="M94" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">1 <inline-formula><mml:math id="M95" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> W m<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">0.25 <inline-formula><mml:math id="M98" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M99" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> W m<inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Friction angle (<inline-formula><mml:math id="M101" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">30<inline-formula><mml:math id="M102" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">30<inline-formula><mml:math id="M103" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">30<inline-formula><mml:math id="M104" 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">Cohesion angle (<inline-formula><mml:math id="M105" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">20 MPa</oasis:entry>
         <oasis:entry colname="col3">20 MPa</oasis:entry>
         <oasis:entry colname="col4">20 MPa</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{A1}?></table-wrap>

      <p id="d1e1967">Density varies linearly as a function of the reference density (<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), linear thermal expansion coefficient (<inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, reference
temperature (<inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), and temperature.
          <disp-formula id="App1.Ch1.S1.E4" content-type="numbered"><label>A4</label><mml:math id="M109" display="block"><mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></disp-formula>
        The model domain spans 500 by 500 km across the horizontal plane (<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula>) and
100 km in the depth (<inline-formula><mml:math id="M111" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>) direction (Fig. 1a). The grids are coarsest (5 km)
on the sides and base of the model domain and are successively reduced using
adaptive-mesh refinement, increasing the resolution to 1.25 km over a
central region measuring <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:mn mathvariant="normal">190</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> km (Fig. 1a). Aside from mesh
deformation related to free surface evolution, the numerical resolution
otherwise stays constant through time with no further adaptive refinement
steps. Broadly, this approach provides “natural” boundary conditions for the
formation of a distributed fault network within the upper crust. Deformation
is driven by prescribed velocities on the model sides to give a total
extension rate of 5 mm yr<inline-formula><mml:math id="M113" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>  (2.5 mm yr<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> on the left and right walls), which is balanced by inflow at the base of the model.</p>
      <p id="d1e2100">The model domain contains three distinct compositional layers, representing
the upper crust (0–20 km depth), lower crust (20–40 km depth), and
lithospheric mantle (40–100 km depth). Distinct reference densities (2800,
2900, 3300 kg m<inline-formula><mml:math id="M115" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and viscous flow laws for dislocation creep (wet
quartzite, Gleason and Tullis, 1995; wet anorthite, Rybacki et al., 2006;
dry olivine, Hirth and Kohlstedt, 2003) distinguish these three layers,
which deform through a combination of nonlinear viscous flow and brittle
(plastic) deformation (e.g. Glerum et al., 2018; Naliboff et al., 2020;
Table A1).</p>
      <p id="d1e2115">The initial temperature distribution follows a characteristic conductive
geotherm for the continental lithosphere (Chapman, 1986). We solve for the
conductive profile by first assuming a thermal conductivity of 2.5 W m<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> K<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, a surface temperature of 273 K, a surface heat flow
of 55 mW m<inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and constant radiogenic heating in each compositional
layer (Table A1) that we use to calculate the temperature with depth within
each layer. The resulting temperatures at the base of the upper crust, lower
crust, and mantle lithosphere are 633, 893, and 1613 K, respectively.
The temperature remains fixed at the top and base of the model, while the
sides are insulating. The values of the compositional fields are only fixed
at the base of the model.</p>
      <p id="d1e2154">Rheological behaviour combines nonlinear viscous flow with brittle failure
(see Glerum et al., 2018). Viscous flow follows dislocation creep,
formulated as follows:
          <disp-formula id="App1.Ch1.S1.E5" content-type="numbered"><label>A5</label><mml:math id="M119" display="block"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">II</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msubsup><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">II</mml:mi><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:msubsup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi>e</mml:mi><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mo>+</mml:mo><mml:mi>P</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>R</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">II</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is the second invariant of the deviatoric stress,
<inline-formula><mml:math id="M121" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> is the viscous prefactor, <inline-formula><mml:math id="M122" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is the stress exponent, <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">II</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the second invariant of the deviatoric strain rate (effective
strain rate), <inline-formula><mml:math id="M124" display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula> is the activation energy, <inline-formula><mml:math id="M125" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> is pressure, <inline-formula><mml:math id="M126" display="inline"><mml:mi>V</mml:mi></mml:math></inline-formula> is the
activation volume, <inline-formula><mml:math id="M127" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is temperature, and <inline-formula><mml:math id="M128" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the gas constant. The
viscosity <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="italic">η</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> within ASPECT is calculated directly through
          <disp-formula id="App1.Ch1.S1.E6" content-type="numbered"><label>A6</label><mml:math id="M130" display="block"><mml:mrow><mml:mi mathvariant="italic">η</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:msubsup><mml:mi/><mml:mi mathvariant="normal">II</mml:mi><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:msubsup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi>e</mml:mi><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mo>+</mml:mo><mml:mi>P</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>R</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        with the resulting viscous stress equal to <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>⋅</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">η</mml:mi><mml:mo>⋅</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">II</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e2416">Brittle plastic deformation follows a Drucker–Prager yield criterion, which
accounts for softening of the angle of internal friction (<inline-formula><mml:math id="M132" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula>) and
cohesion (<inline-formula><mml:math id="M133" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>) as a function of accumulated plastic strain:
          <disp-formula id="App1.Ch1.S1.E7" content-type="numbered"><label>A7</label><mml:math id="M134" display="block"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">II</mml:mi><mml:mo>′</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">6</mml:mn><mml:mi>C</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">2</mml:mn><mml:mi>P</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow><mml:msqrt><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        When the viscous stress exceeds the plastic yield stress, the viscosity is
reduced such that the stress lies exactly on the<?pagebreak page382?> yield plane (i.e.
viscosity rescaling method; see Moresi and Solomatov, 1998; Glerum et al., 2018).</p>
      <p id="d1e2487">The initial friction angle and cohesion are 30<inline-formula><mml:math id="M135" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and 20 MPa,
respectively, and linearly weaken by a factor of 4 as a function of finite
plastic strain, which is derived from the second invariant of strain rate in
regions undergoing deformation. The initial plastic strain is partitioned
into 5.0 km<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> blocks that are randomly assigned binary values (e.g.
0.5–1.5) in the different tectonic domains (see Sect. 2.2). This pervasive
brittle damage field produces rapid localisation of a well-defined normal
fault network (e.g. Pan et al., 2022).</p>
      <p id="d1e2509">Nonlinearities from the Stokes equations are addressed by applying defect
correction Picard iterations (Fraters et al., 2019) to a tolerance of <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
with the maximum number of nonlinear iterations capped at 100. The maximum
numerical time step is limited to 20 kyr.</p><?xmltex \hack{\clearpage}?>
</app>

<?pagebreak page383?><app id="App1.Ch1.S2">
  <?xmltex \currentcnt{B}?><label>Appendix B</label><title/>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F8"><?xmltex \currentcnt{B1}?><?xmltex \def\figurename{Figure}?><label>Figure B1</label><caption><p id="d1e2540">Screenshot taken at 10 Myr. The left panel is a model 4 run showing the
non-initial plastic strain interval across 10 Myr. The right panel is a  model 4 run
across 10 Myr showing the strain-rate-invariant attribute. See Fig. 4a and
c for snapshots throughout the model run.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f08.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F9"><?xmltex \currentcnt{B2}?><?xmltex \def\figurename{Figure}?><label>Figure B2</label><caption><p id="d1e2553">Cross section at <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">375</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the non-initial plastic strain
attribute through 10 Myr of the model run. This location corresponds to the
boundary between the weak and reference (north) domains. See Fig. 4b for a
10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f09.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F10"><?xmltex \currentcnt{B3}?><?xmltex \def\figurename{Figure}?><label>Figure B3</label><caption><p id="d1e2579">Cross section at <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">375</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the strain rate attribute through
10 Myr of the model run. This location corresponds to the boundary between
the weak and reference (north) domains. See Fig. 4c for a 10 Myr snapshot.
Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f10.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F11"><?xmltex \currentcnt{B4}?><?xmltex \def\figurename{Figure}?><label>Figure B4</label><caption><p id="d1e2605">Cross section at <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the non-initial plastic strain
attribute through 10 Myr of the model run. This section crosses the centre of
the weak domain. See Fig. 4b for a 10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f11.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F12"><?xmltex \currentcnt{B5}?><?xmltex \def\figurename{Figure}?><label>Figure B5</label><caption><p id="d1e2630">Cross section at <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the strain rate attribute through
10 Myr of the model run. This section crosses the centre of the weak domain.
See Fig. 4c for a 10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f12.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F13"><?xmltex \currentcnt{B6}?><?xmltex \def\figurename{Figure}?><label>Figure B6</label><caption><p id="d1e2655">Cross section at <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">240</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the non-initial plastic strain
attribute through 10 Myr of the model run. This section is located 10 km into
the strong domain, proximal to the boundary with the weak domain. See Fig. 4b for a 10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f13.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F14"><?xmltex \currentcnt{B7}?><?xmltex \def\figurename{Figure}?><label>Figure B7</label><caption><p id="d1e2681">Cross section at <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">240</mml:mn></mml:mrow></mml:math></inline-formula> km, showing the strain rate attribute through
10 Myr of the model run. This section is located 10 km into the strong domain,
proximal to the boundary with the weak domain. See Fig. 4c for a 10 Myr
snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f14.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F15"><?xmltex \currentcnt{B8}?><?xmltex \def\figurename{Figure}?><label>Figure B8</label><caption><p id="d1e2707">Cross section traversing all domains at <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">250</mml:mn></mml:mrow></mml:math></inline-formula> km, perpendicular to
those shown in Figs. B2–B7. Cross section shows the non-initial plastic strain. See
Fig. 4a for a 10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f15.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F16"><?xmltex \currentcnt{B9}?><?xmltex \def\figurename{Figure}?><label>Figure B9</label><caption><p id="d1e2732">Cross section traversing all domains at <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">250</mml:mn></mml:mrow></mml:math></inline-formula> km, perpendicular to
those shown in Figs. B2–B7. Cross section shows the strain rate attribute. See
Fig. 4c for a 10 Myr snapshot. Screenshot taken at 10 Myr.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/369/2023/se-14-369-2023-f16.png"/>

      </fig>

</app>
  </app-group><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e2759">The numerical simulations were run with the open-source mantle convection
and lithospheric dynamics code ASPECT (<uri>https://github.com/geodynamics/aspect</uri>, last access: 25 May 2022), version 2.4.0-pre (commit
9355aec07). A copy of the ASPECT version used in this study is located with
the Zenodo repository associated with this publication
(<ext-link xlink:href="https://doi.org/10.5281/zenodo.7317598" ext-link-type="DOI">10.5281/zenodo.7317598</ext-link>, Phillips et al., 2022).</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2771">The parameter files required to reproduce the numerical experiments are
contained with the Zenodo repository associated with this publication
(<ext-link xlink:href="https://doi.org/10.5281/zenodo.7317598" ext-link-type="DOI">10.5281/zenodo.7317598</ext-link>, Phillips et al., 2022). In addition, this Zenodo
repository also contains the numerical solution files and postprocessing
scripts used to create the images for each figure in this publication.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e2777">Animated images of the model runs used throughout this paper are available in the
Supplement. The descriptions of each of these models are
available in Appendix B. The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/se-14-369-2023-supplement" xlink:title="zip">https://doi.org/10.5194/se-14-369-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2786">TBP devised the conceptual model used to examine the data, and TBP, JBN, KJWM, and SP designed
the experiments and model setup. The models were run by JBN and TBP. JBN and SP
developed automated model analysis tools. TBP prepared the manuscript along
with input from KJWM, JBN, and all other co-authors. All co-authors contributed to
writing, revising, and preparing of the manuscript.</p>
  </notes><?xmltex \hack{\newpage}?><?xmltex \hack{~\\[78mm]}?><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2795">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2801">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e2807">This article is part of the special issue “(D)rifting into the future: the relevance of rifts and divergent margins in the 21st century”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2813">We thank Ake Fagereng and Guillaume Duclaux for providing constructive reviews of an
earlier version of this paper, and we again thank Guillaume Duclaux and an
anonymous reviewer for their constructive reviews on this version. The
computational time for these simulations was provided under XSEDE project
EAR18000. Thomas B. Phillips was funded for this research via a Leverhulme Early
Career Fellowship at Durham University (ECF2018-065). Malte Froemchen is funded
through the NERC-funded IAPETUS2 Doctoral Training Program (DTP).</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2818">This research has been supported by the Leverhulme Trust (grant no. ECF-2018-645) and the Natural Environment Research Council (grant no. NE/S007431/1).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2824">This paper was edited by Tiago Alves and reviewed by Guillaume Duclaux and one anonymous referee.</p>
  </notes><ref-list>
    <title>References</title>

      <ref id="bib1.bib1"><label>1</label><?label 1?><mixed-citation>Allibone, A. H.  and Tulloch, A. J.: Geology of the plutonic basement rocks
of Stewart Island, New Zealand, New Zeal. J Geol.
Geop., 47, 233–256,
<ext-link xlink:href="https://doi.org/10.1080/00288306.2004.9515051" ext-link-type="DOI">10.1080/00288306.2004.9515051</ext-link>, 2004</mixed-citation></ref>
      <ref id="bib1.bib2"><label>2</label><?label 1?><mixed-citation>Barrier, A., Nicol, A., Browne, G. H., and Bassett, K. N.: Late Cretaceous
coeval multi-directional extension in South Zealandia: Implications for
eastern Gondwana breakup, Mar. Petrol. Geol., 118, 104383,
<ext-link xlink:href="https://doi.org/10.1016/j.marpetgeo.2020.104383" ext-link-type="DOI">10.1016/j.marpetgeo.2020.104383</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib3"><label>3</label><?label 1?><mixed-citation>Beniest, A., Willingshofer, E., Sokoutis, D., and Sassi, W.: Extending
continental lithosphere with lateral strength variations: effects on
deformation localization and margin geometries, Front. Earth Sci.,
6, 148, <ext-link xlink:href="https://doi.org/10.3389/feart.2018.00148" ext-link-type="DOI">10.3389/feart.2018.00148</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bib4"><label>4</label><?label 1?><mixed-citation>Brune, S., Corti, G., and Ranalli, G.: Controls of inherited lithospheric
heterogeneity on rift linkage: Numerical and analog models of interaction
between the Kenyan and Ethiopian rifts across the Turkana depression,
Tectonics, 36, 1767–1786, <ext-link xlink:href="https://doi.org/10.1002/2017TC004739" ext-link-type="DOI">10.1002/2017TC004739</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bib5"><label>5</label><?label 1?><mixed-citation>Campbell, H. J.: Biostratigraphic age review of New Zealand's
Permian–Triassic central terranes, Geological Society, London, Memoirs,
49, 31-41, <ext-link xlink:href="https://doi.org/10.1144/M49.6" ext-link-type="DOI">10.1144/M49.6</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib6"><label>6</label><?label 1?><mixed-citation>Campbell, H. J., Mortimer, N., and Turnbull, I. M.: Murihiku Supergroup,
New Zealand: redefined, J. Roy. Soc. New Zeal., 33,
85–95, <ext-link xlink:href="https://doi.org/10.1080/03014223.2003.9517722" ext-link-type="DOI">10.1080/03014223.2003.9517722</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bib7"><label>7</label><?label 1?><mixed-citation>
Chapman, D. S.: Thermal gradients in the continental crust, Geol. Soc.  Spec. Publ., 24, 63–70, 1986.</mixed-citation></ref>
      <ref id="bib1.bib8"><label>8</label><?label 1?><mixed-citation>Cowie, P. A., Gupta, S., and Dawers, N. H.: Implications of fault array
evolution for synrift depocentre development: insights from a numerical
fault growth model, Basin Res., 12, 241–261, <ext-link xlink:href="https://doi.org/10.1111/j.1365-2117.2000.00126.x" ext-link-type="DOI">10.1111/j.1365-2117.2000.00126.x</ext-link>, 2000.</mixed-citation></ref>
      <ref id="bib1.bib9"><label>9</label><?label 1?><mixed-citation>Cowie, P. A., Underhill, J. R., Behn, M. D., Lin, J., and Gill, C. E.:
Spatio-temporal evolution of strain accumulation derived from multi-scale
observations of Late Jurassic rifting in the northern North Sea: A critical
test of models for lithospheric extension, Earth Planet. Sc.
Lett., 234, 401–419, <ext-link xlink:href="https://doi.org/10.1016/j.epsl.2005.01.039" ext-link-type="DOI">10.1016/j.epsl.2005.01.039</ext-link>, 2005.</mixed-citation></ref>
      <ref id="bib1.bib10"><label>10</label><?label 1?><mixed-citation>Daly, M. C., Chorowicz, J., and Fairhead, J. D.: Rift basin evolution in
Africa: the influence of reactivated steep basement shear zones, Geol.
Soc.   Spec. Publ., 44, 309–334, <ext-link xlink:href="https://doi.org/10.1144/GSL.SP.1989.044.01.17" ext-link-type="DOI">10.1144/GSL.SP.1989.044.01.17</ext-link>, 1989.</mixed-citation></ref>
      <ref id="bib1.bib11"><label>11</label><?label 1?><mixed-citation>Doré, A. G., Lundin, E. R., Fichler, C., and Olesen, O.: Patterns of
basement structure and reactivation along the NE Atlantic margin, J.
Geol. Soc., 154, 85–92, <ext-link xlink:href="https://doi.org/10.1144/gsjgs.154.1.0085" ext-link-type="DOI">10.1144/gsjgs.154.1.0085</ext-link>, 1997.</mixed-citation></ref>
      <ref id="bib1.bib12"><label>12</label><?label 1?><mixed-citation>Duclaux, G., Huismans, R. S., and May, D. A.: Rotation, narrowing, and
preferential reactivation of brittle structures during oblique rifting,
Earth Planet. Sc. Lett., 531, 115952, <ext-link xlink:href="https://doi.org/10.1016/j.epsl.2019.115952" ext-link-type="DOI">10.1016/j.epsl.2019.115952</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib13"><label>13</label><?label 1?><mixed-citation>Duretz, T., Petri, B., Mohn, G., Schmalholz, S. M., Schenker, F. L., and
Müntener, O.: The importance of structural softening for the evolution
and architecture of passive margins, Sci. Rep., 6, 1–7,
<ext-link xlink:href="https://doi.org/10.1038/srep38704" ext-link-type="DOI">10.1038/srep38704</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bib14"><label>14</label><?label 1?><mixed-citation>Fossen, H., Khani, H. F., Faleide, J. I., Ksienzyk, A. K., and Dunlap, W.
J.: Post-Caledonian extension in the West Norway–northern North Sea region:
the role of structural inheritance, Geol.
Soc.   Spec. Publ., 439, 465–486, <ext-link xlink:href="https://doi.org/10.1144/SP439.6" ext-link-type="DOI">10.1144/SP439.6</ext-link>,
2017.</mixed-citation></ref>
      <ref id="bib1.bib15"><label>15</label><?label 1?><mixed-citation>Fraser, A. J. and Gawthorpe, R. L.: Tectono-stratigraphic development and
hydrocarbon habitat of the Carboniferous in northern England, Geol.
Soc.   Spec. Publ., 55, 49–86, <ext-link xlink:href="https://doi.org/10.1144/GSL.SP.1990.055.01.03" ext-link-type="DOI">10.1144/GSL.SP.1990.055.01.03</ext-link>, 1990.</mixed-citation></ref>
      <ref id="bib1.bib16"><label>16</label><?label 1?><mixed-citation>
Fraters, M. R., Bangerth, W., Thieulot, C., Glerum, A. C., and Spakman, W.: Efficient and practical Newton solvers for non-linear Stokes systems in geodynamic problems, Geophys. J. Int., 218, 873–894, 2019.</mixed-citation></ref>
      <ref id="bib1.bib17"><label>17</label><?label 1?><mixed-citation>
Ghisetti, F.: Seismic interpretation, prospects and structural analysis, Great South Basin, Ministry of Economic Development New Zealand, unpublished Petroleum Report PR4173, 2010.</mixed-citation></ref>
      <ref id="bib1.bib18"><label>18</label><?label 1?><mixed-citation>
Gleason, G. C. and Tullis, J.: A flow law for dislocation creep of quartz aggregates determined with the molten salt cell, Tectonophysics, 247, 1–23, 1995.</mixed-citation></ref>
      <ref id="bib1.bib19"><label>19</label><?label 1?><mixed-citation>Glerum, A., Thieulot, C., Fraters, M., Blom, C., and Spakman, W.: Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction, Solid Earth, 9, 267–294, <ext-link xlink:href="https://doi.org/10.5194/se-9-267-2018" ext-link-type="DOI">10.5194/se-9-267-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bib20"><label>20</label><?label 1?><mixed-citation>Gouiza, M. and Naliboff, J.: Rheological inheritance controls the formation of
segmented rifted margins in cratonic lithosphere, Nat. Commun., 12,
4653, <ext-link xlink:href="https://doi.org/10.1038/s41467-021-24945-5" ext-link-type="DOI">10.1038/s41467-021-24945-5</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bib21"><label>21</label><?label 1?><mixed-citation>Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High
accuracy mantle convection simulation through modern numerical methods–II:
realistic models and problems, Geophys. J. Int., 210,
833–851, <ext-link xlink:href="https://doi.org/10.1093/gji/ggx195" ext-link-type="DOI">10.1093/gji/ggx195</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bib22"><label>22</label><?label 1?><mixed-citation>Heron, P. J., Peace, A. L., McCaffrey, K. J., Welford, J. K., Wilson, R.,
van Hunen, J., and Pysklywec, R. N.: Segmentation of rifts through
structural inheritance: Creation of the Davis Strait, Tectonics, 38,
2411–2430, <ext-link xlink:href="https://doi.org/10.1029/2019TC005578" ext-link-type="DOI">10.1029/2019TC005578</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib23"><label>23</label><?label 1?><mixed-citation>Henza, A. A., Withjack, M. O., and Schlische, R. W.: How do the properties
of a pre-existing normal-fault population influence fault development during
a subsequent phase of extension?, J. Struct. Geol., 33,
1312–1324, <ext-link xlink:href="https://doi.org/10.1016/j.jsg.2011.06.010" ext-link-type="DOI">10.1016/j.jsg.2011.06.010</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bib24"><label>24</label><?label 1?><mixed-citation>
Hirth, G. and Kohlstedf, D.: Rheology of the upper mantle and the mantle wedge: A view from the experimentalists, Geophys. Monogr., 138, 83–106, 2003.</mixed-citation></ref>
      <ref id="bib1.bib25"><label>25</label><?label 1?><mixed-citation>Holdsworth, R. E., Handa, M., Miller, J. A., and Buick, I. S.: Continental
reactivation and reworking: an introduction, Geol.
Soc.   Spec. Publ.,  184, 1–12, <ext-link xlink:href="https://doi.org/10.1144/GSL.SP.2001.184.01.01" ext-link-type="DOI">10.1144/GSL.SP.2001.184.01.01</ext-link>, 2001.</mixed-citation></ref>
      <ref id="bib1.bib26"><label>26</label><?label 1?><mixed-citation>Howell, L., Egan, S., Leslie, G., and Clarke, S.: Structural and geodynamic
modelling of the influence of granite bodies during lithospheric extension:
application to the Carboniferous basins of northern England, Tectonophysics,
755, 47–63, <ext-link xlink:href="https://doi.org/10.1016/j.tecto.2019.02.008" ext-link-type="DOI">10.1016/j.tecto.2019.02.008</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib27"><label>27</label><?label 1?><mixed-citation>Howell, L., Egan, S., Leslie, G., Clarke, S., Mitten, A., and Pringle, J.:
The influence of low-density granite bodies on extensional basins, Geology
Today, 36, 22–26, <ext-link xlink:href="https://doi.org/10.1111/gto.12297" ext-link-type="DOI">10.1111/gto.12297</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib28"><label>28</label><?label 1?><mixed-citation>Jourdon, A., Kergaravat, C., Duclaux, G., and Huguen, C.: Looking beyond kinematics: 3D thermo-mechanical modelling reveals the dynamics of transform margins, Solid Earth, 12, 1211–1232, <ext-link xlink:href="https://doi.org/10.5194/se-12-1211-2021" ext-link-type="DOI">10.5194/se-12-1211-2021</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bib29"><label>29</label><?label 1?><mixed-citation>Kirkpatrick, J. D., Bezerra, F. H. R., Shipton, Z. K., Do Nascimento, A. F.,
Pytharouli, S. I., Lunn, R. J., and Soden, A. M.: Scale-dependent influence
of pre-existing basement shear zones on rif<?pagebreak page387?>t faulting: a case study from NE
Brazil, J. Geol. Soc., 170, 237–247, <ext-link xlink:href="https://doi.org/10.1144/jgs2012-043" ext-link-type="DOI">10.1144/jgs2012-043</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bib30"><label>30</label><?label 1?><mixed-citation>Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle
convection simulation through modern numerical methods, Geophys. J.
Int., 191, 12–29, <ext-link xlink:href="https://doi.org/10.1111/j.1365-246X.2012.05609.x" ext-link-type="DOI">10.1111/j.1365-246X.2012.05609.x</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bib31"><label>31</label><?label 1?><mixed-citation>Lang, G., ten Brink, U. S., Hutchinson, D. R., Mountain, G. S., and
Schattner, U.: The Role of Premagmatic Rifting in Shaping a Volcanic
Continental Margin: An Example From the Eastern North American Margin,
J. Geophys. Res.-Sol. Ea., 125, e2020JB019576, <ext-link xlink:href="https://doi.org/10.1029/2020JB019576" ext-link-type="DOI">10.1029/2020JB019576</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib32"><label>32</label><?label 1?><mixed-citation>Larsen, B. T., Olaussen, S., Sundvoll, B., and Heeremans, M.: The
Permo-Carboniferous Oslo Rift through six stages and 65 million years,
Episodes Journal of International Geoscience, 31, 52–58, <ext-link xlink:href="https://doi.org/10.18814/epiiugs/2008/v31i1/008" ext-link-type="DOI">10.18814/epiiugs/2008/v31i1/008</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bib33"><label>33</label><?label 1?><mixed-citation>
Moresi, L. and Solomatov, V.: Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus, Geophys. J. Int., 133, 669–682, 1998.</mixed-citation></ref>
      <ref id="bib1.bib34"><label>34</label><?label 1?><mixed-citation>Mortimer, N., Davey, F. J., Melhuish, A., Yu, J., and Godfrey, N. J.:
Geological interpretation of a deep seismic reflection profile across the
Eastern Province and Median Batholith, New Zealand: crustal architecture of
an extended Phanerozoic convergent orogen, New Zeal. J.  Geol.
Geop., 45, 349–363, <ext-link xlink:href="https://doi.org/10.1080/00288306.2002.9514978" ext-link-type="DOI">10.1080/00288306.2002.9514978</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bib35"><label>35</label><?label 1?><mixed-citation>Naliboff, J. and Buiter, S. J.: Rift reactivation and migration during
multiphase extension, Earth  Planet. Sc. Lett., 421, 58–67,
<ext-link xlink:href="https://doi.org/10.1016/j.epsl.2015.03.050" ext-link-type="DOI">10.1016/j.epsl.2015.03.050</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bib36"><label>36</label><?label 1?><mixed-citation>Naliboff, J. B., Buiter, S. J., Péron-Pinvidic, G., Osmundsen, P. T.,
and Tetreault, J.: Complex fault interaction controls continental rifting,
Nat. Commun., 8, 1–9, <ext-link xlink:href="https://doi.org/10.1038/s41467-017-00904-x" ext-link-type="DOI">10.1038/s41467-017-00904-x</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bib37"><label>37</label><?label 1?><mixed-citation>Naliboff, J. B., Glerum, A., Brune, S., Péron-Pinvidic, G., and Wrona,
T.: Development of 3-D rift heterogeneity through fault network evolution,
Geophys. Res. Lett., 47, e2019GL086611, <ext-link xlink:href="https://doi.org/10.1029/2019GL086611" ext-link-type="DOI">10.1029/2019GL086611</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib38"><label>38</label><?label 1?><mixed-citation>Pan, S., Bell, R. E., Jackson, C. A. L., and Naliboff, J.: Evolution of
normal fault displacement and length as continental lithosphere stretches,
Basin Res., 34, 121–140, <ext-link xlink:href="https://doi.org/10.1111/bre.12613" ext-link-type="DOI">10.1111/bre.12613</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bib39"><label>39</label><?label 1?><mixed-citation>Peace, A., McCaffrey, K., Imber, J., van Hunen, J., Hobbs, R., and Wilson,
R.: The role of pre-existing structures during rifting, continental breakup
and transform system development, offshore West Greenland, Basin Res.,
30, 373–394, <ext-link xlink:href="https://doi.org/10.1111/bre.12257" ext-link-type="DOI">10.1111/bre.12257</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bib40"><label>40</label><?label 1?><mixed-citation>Phillips, T. B. and Magee, C.: Structural controls on the location,
geometry and longevity of an intraplate volcanic system: the Tuatara
Volcanic Field, Great South Basin, New Zealand, J. Geol.
Soc., 177, 1039–1056, <ext-link xlink:href="https://doi.org/10.1144/jgs2020-050" ext-link-type="DOI">10.1144/jgs2020-050</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib41"><label>41</label><?label 1?><mixed-citation>Phillips, T. B. and McCaffrey, K. J.: Terrane Boundary Reactivation,
Barriers to Lateral Fault Propagation and Reactivated Fabrics: Rifting
Across the Median Batholith Zone, Great South Basin, New Zealand, Tectonics,
38, 4027–4053, <ext-link xlink:href="https://doi.org/10.1029/2019TC005772" ext-link-type="DOI">10.1029/2019TC005772</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib42"><label>42</label><?label 1?><mixed-citation>Phillips, T. B., Fazlikhani, H., Gawthorpe, R. L., Fossen, H., Jackson, C.
A. L., Bell, R. E., Faleide, J. I., and Rotevatn, A.: The influence of
structural inheritance and multiphase extension on rift development, the
Northern North Sea, Tectonics, 38, 4099–4126, <ext-link xlink:href="https://doi.org/10.1029/2019TC005756" ext-link-type="DOI">10.1029/2019TC005756</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib43"><label>43</label><?label 1?><mixed-citation>Phillips, T. B., Naliboff, J., McCaffrey, K., Pan, S., van Hunen, J., and
Malte, F.: The influence of crustal strength on rift geometry and
development – Insights from 3D numerical modelling, Zenodo [code and data set], <ext-link xlink:href="https://doi.org/10.5281/zenodo.7317598" ext-link-type="DOI">10.5281/zenodo.7317598</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bib44"><label>44</label><?label 1?><mixed-citation>Ragon, T., Nutz, A., Schuster, M., Ghienne, J. F., Ruffet, G., and Rubino,
J. L.: Evolution of the northern Turkana Depression (East African Rift
System, Kenya) during the Cenozoic rifting: New insights from the Ekitale
Basin (28–25.5 Ma), Geol. J., 54, 3468–3488, <ext-link xlink:href="https://doi.org/10.1002/gj.3339" ext-link-type="DOI">10.1002/gj.3339</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib45"><label>45</label><?label 1?><mixed-citation>Rose, I., Buffett, B., and Heister, T.: Stability and accuracy of free
surface time integration in viscous flows, Phys. Earth
Planet. In., 262, 90–100, <ext-link xlink:href="https://doi.org/10.1016/j.pepi.2016.11.007" ext-link-type="DOI">10.1016/j.pepi.2016.11.007</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bib46"><label>46</label><?label 1?><mixed-citation>Ryan, J., Frassetto, A. M., Hurd, O., Jones, C. H., Unruh, J., Zandt, G.,
Gilbert, H., and Owens, T. J.: Unusually deep earthquakes in the central
Sierra Nevada (California, USA): Foundering ultramafic lithosphere?
Geosphere, 16, 357–377, <ext-link xlink:href="https://doi.org/10.1130/GES02158.1" ext-link-type="DOI">10.1130/GES02158.1</ext-link>,
2020.</mixed-citation></ref>
      <ref id="bib1.bib47"><label>47</label><?label 1?><mixed-citation>Rybacki, E., Gottschalk, M., Wirth, R., and Dresen, G.: Influence of water fugacity and activation volume on the flow properties of fine‐grained anorthite aggregates, J. Geophys. Res.-Sol. Ea., 111,  B03203, <ext-link xlink:href="https://doi.org/10.1029/2005JB003663" ext-link-type="DOI">10.1029/2005JB003663</ext-link>, 2006.</mixed-citation></ref>
      <ref id="bib1.bib48"><label>48</label><?label 1?><mixed-citation>Sahoo, T. R., Nicol, A., Browne, G. H., and Strogen, D. P.: Evolution of a
normal fault system along eastern Gondwana, New Zealand, Tectonics, 39, e2020TC006181,
<ext-link xlink:href="https://doi.org/10.1029/2020TC006181" ext-link-type="DOI">10.1029/2020TC006181</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib49"><label>49</label><?label 1?><mixed-citation>Samsu, A., Cruden, A. R., Molnar, N. E., and Weinberg, R. F.: Inheritance
of penetrative basement anisotropies by extension-oblique faults: Insights
from analogue experiments, Tectonics, 40, e2020TC006596, <ext-link xlink:href="https://doi.org/10.1029/2020TC006596" ext-link-type="DOI">10.1029/2020TC006596</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bib50"><label>50</label><?label 1?><mixed-citation>Schiffer, C., Doré, A. G., Foulger, G. R., Franke, D., Geoffroy, L.,
Gernigon, L., Holdsworth, R., Kusznir, N., Lundin, E., McCaffrey, K. J. W.,
Peace, A. L., Petersen, K. D., Phillips, T. B., Stephenson, R., Stoker, M.
S., and Welford, J. K.: Structural inheritance in the North Atlantic,
Earth-Sci. Rev., 206, 102975, <ext-link xlink:href="https://doi.org/10.1016/j.earscirev.2019.102975" ext-link-type="DOI">10.1016/j.earscirev.2019.102975</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib51"><label>51</label><?label 1?><mixed-citation>Schmid, T. C., Brune, S., Glerum, A., and Schreurs, G.: Tectonic interactions during rift linkage: Insights from analog and numerical experiments, EGUsphere [preprint], <ext-link xlink:href="https://doi.org/10.5194/egusphere-2022-1203" ext-link-type="DOI">10.5194/egusphere-2022-1203</ext-link>, 2022.</mixed-citation></ref>
      <ref id="bib1.bib52"><label>52</label><?label 1?><mixed-citation>Sutton, J. and Watson, J. V.: Architecture of the continental lithosphere,
Philos. T. Roy. Soc. Lond.  A, 317, 5–12, <ext-link xlink:href="https://doi.org/10.1098/rsta.1986.0020" ext-link-type="DOI">10.1098/rsta.1986.0020</ext-link>, 1986.</mixed-citation></ref>
      <ref id="bib1.bib53"><label>53</label><?label 1?><mixed-citation>Tarling, M. S., Smith, S. A. F., Scott, J. M., Rooney, J. S., Viti, C., and Gordon, K. C.: The internal structure and composition of a plate-boundary-scale serpentinite shear zone: the Livingstone Fault, New Zealand, Solid Earth, 10, 1025–1047, <ext-link xlink:href="https://doi.org/10.5194/se-10-1025-2019" ext-link-type="DOI">10.5194/se-10-1025-2019</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib54"><label>54</label><?label 1?><mixed-citation>Thomas, W. A.: Tectonic inheritance at a continental margin, GSA Today,
16, 4–11, <ext-link xlink:href="https://doi.org/10.1130/1052-5173(2006)016&lt;4:TIAACM&gt;2.0.CO;2" ext-link-type="DOI">10.1130/1052-5173(2006)016&lt;4:TIAACM&gt;2.0.CO;2</ext-link>, 2006.</mixed-citation></ref>
      <ref id="bib1.bib55"><label>55</label><?label 1?><mixed-citation>Thomas, W. A.: Tectonic inheritance at multiple scales during more than two
complete Wilson cycles recorded in eastern North America, Geol.
Soc. Spec. Publ., 470, 337, <ext-link xlink:href="https://doi.org/10.1144/SP470.4" ext-link-type="DOI">10.1144/SP470.4</ext-link>,
2019.</mixed-citation></ref>
      <ref id="bib1.bib56"><label>56</label><?label 1?><mixed-citation>Tiberi, C., Gautier, S., Ebinger, C., Roecker, S., Plasman, M., Albaric, J.,
Déverchère, J., Peyrat, S., Perrot, J., Ferdinand Wambura, R.,
Msabi, M., Muzuka, A., Mulibo, G., and Kianji, G.: Lithospheric modification by
extension an<?pagebreak page388?>d magmatism at the craton-orogenic boundary: North Tanzania
Divergence, East Africa, Geophys. J. Int.,  216,
1693–1710, 4 <ext-link xlink:href="https://doi.org/10.1093/gji/ggy521" ext-link-type="DOI">10.1093/gji/ggy521</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib57"><label>57</label><?label 1?><mixed-citation>Tulloch, A. J., Mortimer, N., Ireland, T. R., Waight, T. E., Maas, R.,
Palin, J. M., Sahoo, T., Seebeck, H., Sagar, M. W., Barrier, A., and
Turnbull, R. E.: Reconnaissance basement geology and tectonics of South
Zealandia, Tectonics, 38, 516–551, <ext-link xlink:href="https://doi.org/10.1029/2018TC005116" ext-link-type="DOI">10.1029/2018TC005116</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib58"><label>58</label><?label 1?><mixed-citation>Vasconcelos, D. L., Bezerra, F. H., Clausen, O. R., Medeiros, W. E., de
Castro, D. L., Vital, H., and Barbosa, J. A.: Influence of Precambrian
shear zones on the formation of oceanic fracture zones along the continental
margin of Brazil, Mar. Petrol. Geol., 101, 322–333, <ext-link xlink:href="https://doi.org/10.1016/j.marpetgeo.2018.12.010" ext-link-type="DOI">10.1016/j.marpetgeo.2018.12.010</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib59"><label>59</label><?label 1?><mixed-citation>Wilson, R. W., Klint, K. E. S., Van Gool, J. A. M., McCaffrey, K. J. W.,
Holdsworth, R. E., and Chalmers, J. A.: Faults and fractures in central West
Greenland: onshore expression of continental break-up and sea-floor spreading
in the Labrador–Baffin Bay Sea, GEUS Bulletin, 11,
185–204, <ext-link xlink:href="https://doi.org/10.34194/geusb.v11.4931" ext-link-type="DOI">10.34194/geusb.v11.4931</ext-link>, 2006.
</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bib60"><label>60</label><?label 1?><mixed-citation>Wright, L. J., Muirhead, J. D., and Scholz, C. A.: Spatiotemporal
Variations in Upper Crustal Extension Across the Different Basement Terranes
of the Lake Tanganyika Rift, East Africa, Tectonics, 39, e2019TC006019, <ext-link xlink:href="https://doi.org/10.1029/2019TC006019" ext-link-type="DOI">10.1029/2019TC006019</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bib61"><label>61</label><?label 1?><mixed-citation>Zwaan, F., Chenin, P., Erratt, D., Manatschal, G., and Schreurs, G.: Complex rift patterns, a result of interacting crustal and mantle weaknesses, or multiphase rifting? Insights from analogue models, Solid Earth, 12, 1473–1495, <ext-link xlink:href="https://doi.org/10.5194/se-12-1473-2021" ext-link-type="DOI">10.5194/se-12-1473-2021</ext-link>, 2021.</mixed-citation></ref>

  </ref-list></back>
    <!--<article-title-html>The influence of crustal strength on rift geometry and development – insights from 3D numerical modelling</article-title-html>
<abstract-html/>
<ref-html id="bib1.bib1"><label>1</label><mixed-citation>
      
Allibone, A. H.  and Tulloch, A. J.: Geology of the plutonic basement rocks
of Stewart Island, New Zealand, New Zeal. J Geol.
Geop., 47, 233–256,
<a href="https://doi.org/10.1080/00288306.2004.9515051" target="_blank">https://doi.org/10.1080/00288306.2004.9515051</a>, 2004

    </mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>2</label><mixed-citation>
      Barrier, A., Nicol, A., Browne, G. H., and Bassett, K. N.: Late Cretaceous
coeval multi-directional extension in South Zealandia: Implications for
eastern Gondwana breakup, Mar. Petrol. Geol., 118, 104383,
<a href="https://doi.org/10.1016/j.marpetgeo.2020.104383" target="_blank">https://doi.org/10.1016/j.marpetgeo.2020.104383</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>3</label><mixed-citation>
      Beniest, A., Willingshofer, E., Sokoutis, D., and Sassi, W.: Extending
continental lithosphere with lateral strength variations: effects on
deformation localization and margin geometries, Front. Earth Sci.,
6, 148, <a href="https://doi.org/10.3389/feart.2018.00148" target="_blank">https://doi.org/10.3389/feart.2018.00148</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>4</label><mixed-citation>
      Brune, S., Corti, G., and Ranalli, G.: Controls of inherited lithospheric
heterogeneity on rift linkage: Numerical and analog models of interaction
between the Kenyan and Ethiopian rifts across the Turkana depression,
Tectonics, 36, 1767–1786, <a href="https://doi.org/10.1002/2017TC004739" target="_blank">https://doi.org/10.1002/2017TC004739</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>5</label><mixed-citation>
      Campbell, H. J.: Biostratigraphic age review of New Zealand's
Permian–Triassic central terranes, Geological Society, London, Memoirs,
49, 31-41, <a href="https://doi.org/10.1144/M49.6" target="_blank">https://doi.org/10.1144/M49.6</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>6</label><mixed-citation>
      Campbell, H. J., Mortimer, N., and Turnbull, I. M.: Murihiku Supergroup,
New Zealand: redefined, J. Roy. Soc. New Zeal., 33,
85–95, <a href="https://doi.org/10.1080/03014223.2003.9517722" target="_blank">https://doi.org/10.1080/03014223.2003.9517722</a>, 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>7</label><mixed-citation>
      
Chapman, D. S.: Thermal gradients in the continental crust, Geol. Soc.  Spec. Publ., 24, 63–70, 1986.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>8</label><mixed-citation>
      Cowie, P. A., Gupta, S., and Dawers, N. H.: Implications of fault array
evolution for synrift depocentre development: insights from a numerical
fault growth model, Basin Res., 12, 241–261, <a href="https://doi.org/10.1111/j.1365-2117.2000.00126.x" target="_blank">https://doi.org/10.1111/j.1365-2117.2000.00126.x</a>, 2000.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>9</label><mixed-citation>
      Cowie, P. A., Underhill, J. R., Behn, M. D., Lin, J., and Gill, C. E.:
Spatio-temporal evolution of strain accumulation derived from multi-scale
observations of Late Jurassic rifting in the northern North Sea: A critical
test of models for lithospheric extension, Earth Planet. Sc.
Lett., 234, 401–419, <a href="https://doi.org/10.1016/j.epsl.2005.01.039" target="_blank">https://doi.org/10.1016/j.epsl.2005.01.039</a>, 2005.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>10</label><mixed-citation>
      Daly, M. C., Chorowicz, J., and Fairhead, J. D.: Rift basin evolution in
Africa: the influence of reactivated steep basement shear zones, Geol.
Soc.   Spec. Publ., 44, 309–334, <a href="https://doi.org/10.1144/GSL.SP.1989.044.01.17" target="_blank">https://doi.org/10.1144/GSL.SP.1989.044.01.17</a>, 1989.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>11</label><mixed-citation>
      Doré, A. G., Lundin, E. R., Fichler, C., and Olesen, O.: Patterns of
basement structure and reactivation along the NE Atlantic margin, J.
Geol. Soc., 154, 85–92, <a href="https://doi.org/10.1144/gsjgs.154.1.0085" target="_blank">https://doi.org/10.1144/gsjgs.154.1.0085</a>, 1997.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>12</label><mixed-citation>
      Duclaux, G., Huismans, R. S., and May, D. A.: Rotation, narrowing, and
preferential reactivation of brittle structures during oblique rifting,
Earth Planet. Sc. Lett., 531, 115952, <a href="https://doi.org/10.1016/j.epsl.2019.115952" target="_blank">https://doi.org/10.1016/j.epsl.2019.115952</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>13</label><mixed-citation>
      Duretz, T., Petri, B., Mohn, G., Schmalholz, S. M., Schenker, F. L., and
Müntener, O.: The importance of structural softening for the evolution
and architecture of passive margins, Sci. Rep., 6, 1–7,
<a href="https://doi.org/10.1038/srep38704" target="_blank">https://doi.org/10.1038/srep38704</a>, 2016.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>14</label><mixed-citation>
      Fossen, H., Khani, H. F., Faleide, J. I., Ksienzyk, A. K., and Dunlap, W.
J.: Post-Caledonian extension in the West Norway–northern North Sea region:
the role of structural inheritance, Geol.
Soc.   Spec. Publ., 439, 465–486, <a href="https://doi.org/10.1144/SP439.6" target="_blank">https://doi.org/10.1144/SP439.6</a>,
2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>15</label><mixed-citation>
      Fraser, A. J. and Gawthorpe, R. L.: Tectono-stratigraphic development and
hydrocarbon habitat of the Carboniferous in northern England, Geol.
Soc.   Spec. Publ., 55, 49–86, <a href="https://doi.org/10.1144/GSL.SP.1990.055.01.03" target="_blank">https://doi.org/10.1144/GSL.SP.1990.055.01.03</a>, 1990.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>16</label><mixed-citation>
      
Fraters, M. R., Bangerth, W., Thieulot, C., Glerum, A. C., and Spakman, W.: Efficient and practical Newton solvers for non-linear Stokes systems in geodynamic problems, Geophys. J. Int., 218, 873–894, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>17</label><mixed-citation>
      
Ghisetti, F.: Seismic interpretation, prospects and structural analysis, Great South Basin, Ministry of Economic Development New Zealand, unpublished Petroleum Report PR4173, 2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>18</label><mixed-citation>
      
Gleason, G. C. and Tullis, J.: A flow law for dislocation creep of quartz aggregates determined with the molten salt cell, Tectonophysics, 247, 1–23, 1995.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>19</label><mixed-citation>
       Glerum, A., Thieulot, C., Fraters, M., Blom, C., and Spakman, W.: Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction, Solid Earth, 9, 267–294, <a href="https://doi.org/10.5194/se-9-267-2018" target="_blank">https://doi.org/10.5194/se-9-267-2018</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>20</label><mixed-citation>
      Gouiza, M. and Naliboff, J.: Rheological inheritance controls the formation of
segmented rifted margins in cratonic lithosphere, Nat. Commun., 12,
4653, <a href="https://doi.org/10.1038/s41467-021-24945-5" target="_blank">https://doi.org/10.1038/s41467-021-24945-5</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>21</label><mixed-citation>
      Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High
accuracy mantle convection simulation through modern numerical methods–II:
realistic models and problems, Geophys. J. Int., 210,
833–851, <a href="https://doi.org/10.1093/gji/ggx195" target="_blank">https://doi.org/10.1093/gji/ggx195</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>22</label><mixed-citation>
      Heron, P. J., Peace, A. L., McCaffrey, K. J., Welford, J. K., Wilson, R.,
van Hunen, J., and Pysklywec, R. N.: Segmentation of rifts through
structural inheritance: Creation of the Davis Strait, Tectonics, 38,
2411–2430, <a href="https://doi.org/10.1029/2019TC005578" target="_blank">https://doi.org/10.1029/2019TC005578</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>23</label><mixed-citation>
      Henza, A. A., Withjack, M. O., and Schlische, R. W.: How do the properties
of a pre-existing normal-fault population influence fault development during
a subsequent phase of extension?, J. Struct. Geol., 33,
1312–1324, <a href="https://doi.org/10.1016/j.jsg.2011.06.010" target="_blank">https://doi.org/10.1016/j.jsg.2011.06.010</a>, 2011.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>24</label><mixed-citation>
      
Hirth, G. and Kohlstedf, D.: Rheology of the upper mantle and the mantle wedge: A view from the experimentalists, Geophys. Monogr., 138, 83–106, 2003.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>25</label><mixed-citation>
      Holdsworth, R. E., Handa, M., Miller, J. A., and Buick, I. S.: Continental
reactivation and reworking: an introduction, Geol.
Soc.   Spec. Publ.,  184, 1–12, <a href="https://doi.org/10.1144/GSL.SP.2001.184.01.01" target="_blank">https://doi.org/10.1144/GSL.SP.2001.184.01.01</a>, 2001.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>26</label><mixed-citation>
      Howell, L., Egan, S., Leslie, G., and Clarke, S.: Structural and geodynamic
modelling of the influence of granite bodies during lithospheric extension:
application to the Carboniferous basins of northern England, Tectonophysics,
755, 47–63, <a href="https://doi.org/10.1016/j.tecto.2019.02.008" target="_blank">https://doi.org/10.1016/j.tecto.2019.02.008</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>27</label><mixed-citation>
      Howell, L., Egan, S., Leslie, G., Clarke, S., Mitten, A., and Pringle, J.:
The influence of low-density granite bodies on extensional basins, Geology
Today, 36, 22–26, <a href="https://doi.org/10.1111/gto.12297" target="_blank">https://doi.org/10.1111/gto.12297</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>28</label><mixed-citation>
      Jourdon, A., Kergaravat, C., Duclaux, G., and Huguen, C.: Looking beyond kinematics: 3D thermo-mechanical modelling reveals the dynamics of transform margins, Solid Earth, 12, 1211–1232, <a href="https://doi.org/10.5194/se-12-1211-2021" target="_blank">https://doi.org/10.5194/se-12-1211-2021</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>29</label><mixed-citation>
      Kirkpatrick, J. D., Bezerra, F. H. R., Shipton, Z. K., Do Nascimento, A. F.,
Pytharouli, S. I., Lunn, R. J., and Soden, A. M.: Scale-dependent influence
of pre-existing basement shear zones on rift faulting: a case study from NE
Brazil, J. Geol. Soc., 170, 237–247, <a href="https://doi.org/10.1144/jgs2012-043" target="_blank">https://doi.org/10.1144/jgs2012-043</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>30</label><mixed-citation>
      Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle
convection simulation through modern numerical methods, Geophys. J.
Int., 191, 12–29, <a href="https://doi.org/10.1111/j.1365-246X.2012.05609.x" target="_blank">https://doi.org/10.1111/j.1365-246X.2012.05609.x</a>, 2012.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib31"><label>31</label><mixed-citation>
      Lang, G., ten Brink, U. S., Hutchinson, D. R., Mountain, G. S., and
Schattner, U.: The Role of Premagmatic Rifting in Shaping a Volcanic
Continental Margin: An Example From the Eastern North American Margin,
J. Geophys. Res.-Sol. Ea., 125, e2020JB019576, <a href="https://doi.org/10.1029/2020JB019576" target="_blank">https://doi.org/10.1029/2020JB019576</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib32"><label>32</label><mixed-citation>
      Larsen, B. T., Olaussen, S., Sundvoll, B., and Heeremans, M.: The
Permo-Carboniferous Oslo Rift through six stages and 65 million years,
Episodes Journal of International Geoscience, 31, 52–58, <a href="https://doi.org/10.18814/epiiugs/2008/v31i1/008" target="_blank">https://doi.org/10.18814/epiiugs/2008/v31i1/008</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib33"><label>33</label><mixed-citation>
      
Moresi, L. and Solomatov, V.: Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus, Geophys. J. Int., 133, 669–682, 1998.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib34"><label>34</label><mixed-citation>
      Mortimer, N., Davey, F. J., Melhuish, A., Yu, J., and Godfrey, N. J.:
Geological interpretation of a deep seismic reflection profile across the
Eastern Province and Median Batholith, New Zealand: crustal architecture of
an extended Phanerozoic convergent orogen, New Zeal. J.  Geol.
Geop., 45, 349–363, <a href="https://doi.org/10.1080/00288306.2002.9514978" target="_blank">https://doi.org/10.1080/00288306.2002.9514978</a>, 2002.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib35"><label>35</label><mixed-citation>
      Naliboff, J. and Buiter, S. J.: Rift reactivation and migration during
multiphase extension, Earth  Planet. Sc. Lett., 421, 58–67,
<a href="https://doi.org/10.1016/j.epsl.2015.03.050" target="_blank">https://doi.org/10.1016/j.epsl.2015.03.050</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib36"><label>36</label><mixed-citation>
      Naliboff, J. B., Buiter, S. J., Péron-Pinvidic, G., Osmundsen, P. T.,
and Tetreault, J.: Complex fault interaction controls continental rifting,
Nat. Commun., 8, 1–9, <a href="https://doi.org/10.1038/s41467-017-00904-x" target="_blank">https://doi.org/10.1038/s41467-017-00904-x</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib37"><label>37</label><mixed-citation>
      Naliboff, J. B., Glerum, A., Brune, S., Péron-Pinvidic, G., and Wrona,
T.: Development of 3-D rift heterogeneity through fault network evolution,
Geophys. Res. Lett., 47, e2019GL086611, <a href="https://doi.org/10.1029/2019GL086611" target="_blank">https://doi.org/10.1029/2019GL086611</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib38"><label>38</label><mixed-citation>
      Pan, S., Bell, R. E., Jackson, C. A. L., and Naliboff, J.: Evolution of
normal fault displacement and length as continental lithosphere stretches,
Basin Res., 34, 121–140, <a href="https://doi.org/10.1111/bre.12613" target="_blank">https://doi.org/10.1111/bre.12613</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib39"><label>39</label><mixed-citation>
      Peace, A., McCaffrey, K., Imber, J., van Hunen, J., Hobbs, R., and Wilson,
R.: The role of pre-existing structures during rifting, continental breakup
and transform system development, offshore West Greenland, Basin Res.,
30, 373–394, <a href="https://doi.org/10.1111/bre.12257" target="_blank">https://doi.org/10.1111/bre.12257</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib40"><label>40</label><mixed-citation>
      Phillips, T. B. and Magee, C.: Structural controls on the location,
geometry and longevity of an intraplate volcanic system: the Tuatara
Volcanic Field, Great South Basin, New Zealand, J. Geol.
Soc., 177, 1039–1056, <a href="https://doi.org/10.1144/jgs2020-050" target="_blank">https://doi.org/10.1144/jgs2020-050</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib41"><label>41</label><mixed-citation>
      Phillips, T. B. and McCaffrey, K. J.: Terrane Boundary Reactivation,
Barriers to Lateral Fault Propagation and Reactivated Fabrics: Rifting
Across the Median Batholith Zone, Great South Basin, New Zealand, Tectonics,
38, 4027–4053, <a href="https://doi.org/10.1029/2019TC005772" target="_blank">https://doi.org/10.1029/2019TC005772</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib42"><label>42</label><mixed-citation>
      Phillips, T. B., Fazlikhani, H., Gawthorpe, R. L., Fossen, H., Jackson, C.
A. L., Bell, R. E., Faleide, J. I., and Rotevatn, A.: The influence of
structural inheritance and multiphase extension on rift development, the
Northern North Sea, Tectonics, 38, 4099–4126, <a href="https://doi.org/10.1029/2019TC005756" target="_blank">https://doi.org/10.1029/2019TC005756</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib43"><label>43</label><mixed-citation>
      Phillips, T. B., Naliboff, J., McCaffrey, K., Pan, S., van Hunen, J., and
Malte, F.: The influence of crustal strength on rift geometry and
development – Insights from 3D numerical modelling, Zenodo [code and data set], <a href="https://doi.org/10.5281/zenodo.7317598" target="_blank">https://doi.org/10.5281/zenodo.7317598</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib44"><label>44</label><mixed-citation>
      Ragon, T., Nutz, A., Schuster, M., Ghienne, J. F., Ruffet, G., and Rubino,
J. L.: Evolution of the northern Turkana Depression (East African Rift
System, Kenya) during the Cenozoic rifting: New insights from the Ekitale
Basin (28–25.5&thinsp;Ma), Geol. J., 54, 3468–3488, <a href="https://doi.org/10.1002/gj.3339" target="_blank">https://doi.org/10.1002/gj.3339</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib45"><label>45</label><mixed-citation>
      Rose, I., Buffett, B., and Heister, T.: Stability and accuracy of free
surface time integration in viscous flows, Phys. Earth
Planet. In., 262, 90–100, <a href="https://doi.org/10.1016/j.pepi.2016.11.007" target="_blank">https://doi.org/10.1016/j.pepi.2016.11.007</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib46"><label>46</label><mixed-citation>
      Ryan, J., Frassetto, A. M., Hurd, O., Jones, C. H., Unruh, J., Zandt, G.,
Gilbert, H., and Owens, T. J.: Unusually deep earthquakes in the central
Sierra Nevada (California, USA): Foundering ultramafic lithosphere?
Geosphere, 16, 357–377, <a href="https://doi.org/10.1130/GES02158.1" target="_blank">https://doi.org/10.1130/GES02158.1</a>,
2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib47"><label>47</label><mixed-citation>
      
Rybacki, E., Gottschalk, M., Wirth, R., and Dresen, G.: Influence of water fugacity and activation volume on the flow properties of fine‐grained anorthite aggregates, J. Geophys. Res.-Sol. Ea., 111,  B03203, <a href="https://doi.org/10.1029/2005JB003663" target="_blank">https://doi.org/10.1029/2005JB003663</a>, 2006.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib48"><label>48</label><mixed-citation>
      Sahoo, T. R., Nicol, A., Browne, G. H., and Strogen, D. P.: Evolution of a
normal fault system along eastern Gondwana, New Zealand, Tectonics, 39, e2020TC006181,
<a href="https://doi.org/10.1029/2020TC006181" target="_blank">https://doi.org/10.1029/2020TC006181</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib49"><label>49</label><mixed-citation>
      Samsu, A., Cruden, A. R., Molnar, N. E., and Weinberg, R. F.: Inheritance
of penetrative basement anisotropies by extension-oblique faults: Insights
from analogue experiments, Tectonics, 40, e2020TC006596, <a href="https://doi.org/10.1029/2020TC006596" target="_blank">https://doi.org/10.1029/2020TC006596</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib50"><label>50</label><mixed-citation>
      Schiffer, C., Doré, A. G., Foulger, G. R., Franke, D., Geoffroy, L.,
Gernigon, L., Holdsworth, R., Kusznir, N., Lundin, E., McCaffrey, K. J. W.,
Peace, A. L., Petersen, K. D., Phillips, T. B., Stephenson, R., Stoker, M.
S., and Welford, J. K.: Structural inheritance in the North Atlantic,
Earth-Sci. Rev., 206, 102975, <a href="https://doi.org/10.1016/j.earscirev.2019.102975" target="_blank">https://doi.org/10.1016/j.earscirev.2019.102975</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib51"><label>51</label><mixed-citation>
      
Schmid, T. C., Brune, S., Glerum, A., and Schreurs, G.: Tectonic interactions during rift linkage: Insights from analog and numerical experiments, EGUsphere [preprint], <a href="https://doi.org/10.5194/egusphere-2022-1203" target="_blank">https://doi.org/10.5194/egusphere-2022-1203</a>, 2022.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib52"><label>52</label><mixed-citation>
      Sutton, J. and Watson, J. V.: Architecture of the continental lithosphere,
Philos. T. Roy. Soc. Lond.  A, 317, 5–12, <a href="https://doi.org/10.1098/rsta.1986.0020" target="_blank">https://doi.org/10.1098/rsta.1986.0020</a>, 1986.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib53"><label>53</label><mixed-citation>
      Tarling, M. S., Smith, S. A. F., Scott, J. M., Rooney, J. S., Viti, C., and Gordon, K. C.: The internal structure and composition of a plate-boundary-scale serpentinite shear zone: the Livingstone Fault, New Zealand, Solid Earth, 10, 1025–1047, <a href="https://doi.org/10.5194/se-10-1025-2019" target="_blank">https://doi.org/10.5194/se-10-1025-2019</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib54"><label>54</label><mixed-citation>
      Thomas, W. A.: Tectonic inheritance at a continental margin, GSA Today,
16, 4–11, <a href="https://doi.org/10.1130/1052-5173(2006)016&lt;4:TIAACM&gt;2.0.CO;2" target="_blank">https://doi.org/10.1130/1052-5173(2006)016&lt;4:TIAACM&gt;2.0.CO;2</a>, 2006.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib55"><label>55</label><mixed-citation>
      Thomas, W. A.: Tectonic inheritance at multiple scales during more than two
complete Wilson cycles recorded in eastern North America, Geol.
Soc. Spec. Publ., 470, 337, <a href="https://doi.org/10.1144/SP470.4" target="_blank">https://doi.org/10.1144/SP470.4</a>,
2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib56"><label>56</label><mixed-citation>
      Tiberi, C., Gautier, S., Ebinger, C., Roecker, S., Plasman, M., Albaric, J.,
Déverchère, J., Peyrat, S., Perrot, J., Ferdinand Wambura, R.,
Msabi, M., Muzuka, A., Mulibo, G., and Kianji, G.: Lithospheric modification by
extension and magmatism at the craton-orogenic boundary: North Tanzania
Divergence, East Africa, Geophys. J. Int.,  216,
1693–1710, 4 <a href="https://doi.org/10.1093/gji/ggy521" target="_blank">https://doi.org/10.1093/gji/ggy521</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib57"><label>57</label><mixed-citation>
      Tulloch, A. J., Mortimer, N., Ireland, T. R., Waight, T. E., Maas, R.,
Palin, J. M., Sahoo, T., Seebeck, H., Sagar, M. W., Barrier, A., and
Turnbull, R. E.: Reconnaissance basement geology and tectonics of South
Zealandia, Tectonics, 38, 516–551, <a href="https://doi.org/10.1029/2018TC005116" target="_blank">https://doi.org/10.1029/2018TC005116</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib58"><label>58</label><mixed-citation>
      Vasconcelos, D. L., Bezerra, F. H., Clausen, O. R., Medeiros, W. E., de
Castro, D. L., Vital, H., and Barbosa, J. A.: Influence of Precambrian
shear zones on the formation of oceanic fracture zones along the continental
margin of Brazil, Mar. Petrol. Geol., 101, 322–333, <a href="https://doi.org/10.1016/j.marpetgeo.2018.12.010" target="_blank">https://doi.org/10.1016/j.marpetgeo.2018.12.010</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib59"><label>59</label><mixed-citation>
      Wilson, R. W., Klint, K. E. S., Van Gool, J. A. M., McCaffrey, K. J. W.,
Holdsworth, R. E., and Chalmers, J. A.: Faults and fractures in central West
Greenland: onshore expression of continental break-up and sea-floor spreading
in the Labrador–Baffin Bay Sea, GEUS Bulletin, 11,
185–204, <a href="https://doi.org/10.34194/geusb.v11.4931" target="_blank">https://doi.org/10.34194/geusb.v11.4931</a>, 2006.


    </mixed-citation></ref-html>
<ref-html id="bib1.bib60"><label>60</label><mixed-citation>
      Wright, L. J., Muirhead, J. D., and Scholz, C. A.: Spatiotemporal
Variations in Upper Crustal Extension Across the Different Basement Terranes
of the Lake Tanganyika Rift, East Africa, Tectonics, 39, e2019TC006019, <a href="https://doi.org/10.1029/2019TC006019" target="_blank">https://doi.org/10.1029/2019TC006019</a>, 2020.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib61"><label>61</label><mixed-citation>
      Zwaan, F., Chenin, P., Erratt, D., Manatschal, G., and Schreurs, G.: Complex rift patterns, a result of interacting crustal and mantle weaknesses, or multiphase rifting? Insights from analogue models, Solid Earth, 12, 1473–1495, <a href="https://doi.org/10.5194/se-12-1473-2021" target="_blank">https://doi.org/10.5194/se-12-1473-2021</a>, 2021.

    </mixed-citation></ref-html>--></article>
