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<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"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <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-14-213-2023</article-id><title-group><article-title>Analogue modelling of the inversion of multiple extensional<?xmltex \hack{\break}?> basins in
foreland fold-and-thrust belts</article-title><alt-title>Analogue modelling of the inversion of multiple basins</alt-title>
      </title-group><?xmltex \runningtitle{Analogue modelling of the inversion of multiple basins}?><?xmltex \runningauthor{N. Molnar and S. Buiter}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Molnar</surname><given-names>Nicolás</given-names></name>
          <email>nicolasemolnar@gmail.com</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Buiter</surname><given-names>Susanne</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2493-2377</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Tectonics and Geodynamics, RWTH Aachen University, 52064 Aachen,
Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Helmholtz Centre Potsdam – GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Nicolás Molnar (nicolasemolnar@gmail.com)</corresp></author-notes><pub-date><day>3</day><month>March</month><year>2023</year></pub-date>
      
      <volume>14</volume>
      <issue>2</issue>
      <fpage>213</fpage><lpage>235</lpage>
      <history>
        <date date-type="received"><day>29</day><month>September</month><year>2022</year></date>
           <date date-type="rev-request"><day>12</day><month>October</month><year>2022</year></date>
           <date date-type="rev-recd"><day>5</day><month>January</month><year>2023</year></date>
           <date date-type="accepted"><day>9</day><month>January</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 Nicolás Molnar</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/14/213/2023/se-14-213-2023.html">This article is available from https://se.copernicus.org/articles/14/213/2023/se-14-213-2023.html</self-uri><self-uri xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023.pdf">The full text article is available as a PDF file from https://se.copernicus.org/articles/14/213/2023/se-14-213-2023.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e98">The presence of pre-existing rheological heterogeneities in the lithosphere
plays a significant role during subsequent stages of deformation in
essentially every geological process. Extensional basins located in foreland
fold-and-thrust belts will alter the spatio-temporal evolution of its
associated orogen. It remains unclear how far horizontal stresses can act
and reactivate extensional structures due to their intrinsic irregular
patterns of deformation deflection and localisation. Overprinting events and
relative dating uncertainties in the geological record make it difficult to
interpret how stresses were transferred across a heterogeneous crust. Here
we examine the inversion of extensional basins in foreland fold-and-thrust
belts by using three-dimensional analogue experiments that simulate first an
extensional stage, followed by a shortening stage. Our results show how
extensional basins proximal to the orogenic front effectively localise
deformation in the shape of thrusts and prevent stress transfer beyond their
location. Basins that are located at large distances from the orogenic front
also show evidence of mild inversion at early stages but are characterised only
by basin infill contraction and uplift. When multiple extensional basins are
present, the degree and type of inversion will depend primarily on their
relative location and distance to the orogenic front. Here we also prove
that the presence of additional extensional features in the vicinity of a
basin can be a first-order controlling factor in their overall reactivation
history. We share additional insights of how a fold-and-thrust belt evolves
once the extensional basins have been incorporated by the advancing wedge,
and we provide comparisons with natural examples that shed light on some
still unanswered questions related to the process of basin inversion in
orogenic belts.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e110">The process in which compressional stresses induce basin uplift and reverse
reactivation of normal faults in former extensional basins is commonly
referred to as positive basin inversion (e.g. Bally, 1984; Cooper and Williams, 1989; Jackson, 1980; Sibson, 1990; Ziegler, 1989; Zwaan et al., 2022; Fig. 1a). The degree of inversion can range from mild, which only partly
nullifies the previous basin subsidence, to (over-)complete, which brings
the former basin floor back to or above its regional equivalent level.
Examples of mild inversion can be found in the North Sea (i.e. Nalpas et al., 1995; Scisciani et al., 2019), whereas an example of “over-inversion” can
be found in the Permo–Triassic Dorénaz basin that was strongly shortened
during formation of the Swiss Alps (Pfiffner, 2009). The incorporation of
extensional basins in an orogen will alter the spatio-temporal evolution of
that orogen, mainly by localising strain along rheological weaknesses
associated with pre-existing faults and/or uncompacted sedimentary infill
(Fig. 1a). Here the nature, size, geometry, and rheology of the extensional
basins plays a major role.</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="d1e115"><bold>(a)</bold> Conceptual model of crustal extension and later foreland
compressional deformation (redrawn from Ziegler, 1989). <bold>(b)</bold> Sketch
representing the equivalent modelling stages presented in this study.</p></caption>
        <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f01.png"/>

      </fig>

      <p id="d1e129">Relationships between inversion structures in the foreland of orogens,
sometimes located up to several hundred kilometres away, and
compressional far-field stresses caused by the orogenic fronts have long
been identified (Ziegler et al., 1995, 1998). Examples of compressional or
transpressional deformation have been shown in the Alpine foreland up to
1300 km north-west of the Alpine thrust front (Ziegler, 1989; Nalpas et al.,
1995; Kley, 2018), in the Laramides of North America 600 km to the east of
the Cordilleran thrust front (Brewer and Turcotte, 1980; Ziegler,
1989; Cooper and Warren, 2020), and in the foreland of the Variscan and
Alpine<?pagebreak page214?> chains of north-western Africa 800 km to the south of the orogenic
front (Ziegler, 1988, 1989; Guiraud and Bosworth, 1997). However,
mechanisms of stress transfer across a heterogeneous crust and conditions
that facilitate or hinder basin inversion in these settings remain unclear.
Transmission of stresses in the lithosphere depends on the degree of
interplate coupling (Lacombe and Bellahsen, 2016; Delvaux, 2001) and on the
rheological parameters (structural, thermal, and/or compositional) that
determine the spatial strength distribution within the lithosphere (Granado
and Ruh, 2019; Lacombe and Bellahsen, 2016; Ziegler, 1998). It has been long
recognised that areas with major pre-existing extensional faults are prone
to early inversion in collision-related intraplate deformation (e.g. Ziegler et al., 1995; Lacombe and Bellahsen, 2016; and references therein), but it remains
challenging to accurately describe how far horizontal stresses can act
through a heterogeneous crust and the extent to which these pre-existing
extensional structures are reactivated (e.g. Bosworth and Tari, 2021).</p>
      <p id="d1e133">There is a good understanding of how structural features at the metre to
kilometre scale are indicators of basin inversion, such as normal faults
that localise thrust ramps or act as stress risers, thrust ramps that
cross-cut earlier normal faults, folds, and the uplift of syn-rift strata
(e.g. Bonini et al., 2012; Scisciani, 2009; Granado et al., 2017).
Nevertheless, when compressional deformation is distributed across larger
regions of extended crust, the analysis of multiple overprinted geological
events becomes increasingly complex. The complexity lies in discerning
between individual structural features and establishing their chronological
order, even when there is good availability of sub-surface imaging or well
data (Butler and Bond, 2021; Coward, 1994).</p>
      <p id="d1e136">In this context, analogue modelling techniques, combined with modern
monitoring and visualisation methods, can provide a valuable approach for
better understanding mechanisms of basin inversion as they have the
advantage of quantifying deformation in time and space. Previous analogue
modelling works have provided great insights on the spatio-temporal
evolution of inverted basins, focussing on aspects such as the reactivation
of listric normal faults (McClay, 1996), the influence of ductile layers
during graben inversion (Brun and Nalpas, 1996), inversion of domino arrays
(Buchanan and McClay, 1991; Jagger and McClay, 2018), the roles of basin
orientation and basin fill (Panien et al., 2006), and pre-existing
discontinuities that localise shortening (Sassi et al., 1993; Di Domenica et
al., 2014), and thorough review papers on these topics are available (e.g.
McClay, 1995; Bonini et al., 2012; Zwaan et al., 2022). Additional numerical
modelling and seismic and field studies have also shown the influence of
specific boundary conditions such as the importance of salt tectonics in
thick- and thin-skinned basin inversion (Granado et al., 2021; Hansen et
al., 2021), the effect of changes in stress direction over time (Phillips et
al., 2018), or the influence of mechanically decoupled inverted systems
(Krzywiec et al., 2022) and of the relative strength between inherited
faults and syn-rift deposits (Granado and Ruh, 2019), among other things.</p>
      <p id="d1e139">Historically, wide, narrow, and core complex modes were proposed as end-members of continental extension (Buck, 1991). In this work we emphasise
wide rifting, which was originally suggested to be associated with
previously thickened domains with a dominant ductile behaviour (England,
1983; Buck, 1991; Brun, 1999), but which may also occur as a result of
strain migrating from zones of localised extension onto adjacent areas of
undeformed crust (Buck, 1991). Pre-existing weaknesses in the lithosphere
strongly influence the evolution of deformation in wide rifts by localising
strain in delimited areas, as interpreted for Mesozoic rifting in western
and central Europe (e.g. Ziegler, 1989) or for Cretaceous rifting in
northern Africa (e.g. Guiraud and<?pagebreak page215?> Maurin, 1992). Areas of distributed
extension are commonly characterised by an alternation of horsts and
grabens, with large-scale normal faults bordering basins filled with
unconsolidated sediments (e.g. Brun, 1999). In this study we simulate wide
extensional settings with the aim to (1) examine the inversion of
extensional basins in foreland fold-and-thrust belts and (2) to examine the
evolution of fold-and-thrust belts once these have incorporated the
extensional basins (Fig. 1b). We compare our experimental results to
natural observations where analogous conditions have been reported, such as
the Carpathians in central eastern Europe and the Atlas system in north-western Africa. Our goal is to better understand how compressional stresses build up
and are transferred from the orogenic wedge into a previously extended
crust. We expect our results to become useful for recognising basin
inversion in the geological record and to work as conceptual models for
comparison with other natural examples.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methodology</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Experimental design</title>
      <p id="d1e157">We employ a pull- and push-type apparatus with a computer-controlled moving
wall, a horizontal (slope <inline-formula><mml:math id="M1" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) film-faced plywood basal board,
and 12 mm security-grade side glass walls (Fig. 2) (Gottron, 2018). We use
only granular materials with brittle behaviour to simulate upper-crustal
deformation. The overall model dimensions are 40 <inline-formula><mml:math id="M3" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 60 <inline-formula><mml:math id="M4" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 3 cm (width, length,
and height, respectively). Experiments that incorporate extension are carried out
in two stages. For the initial extensional stage, removable basal sheets are
attached to the moving wall, following a technique employed in previous
analogue modelling studies (e.g. Panien et al., 2006; Granado et al., 2017;
Jara et al., 2018; Yagupsky et al., 2008; Likerman et al., 2013; López
et al., 2022). The basal plastic sheets are 0.4 mm thick each, and their
borders are cut perpendicular to the moving wall (Fig. 2c, left panel). Up
to three basal sheets can be stacked and attached independently to the
moving wall (Fig. 2c, right panel). The wall is moved backward (pull) at a
constant speed of 1 mm min<inline-formula><mml:math id="M5" 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>  for 3 cm, pulling the basal sheets with it to
create an extensional basin. The differential relative movement between the
uppermost basal sheet(s) and the apparatus basal board or the underlying
basal sheet(s) creates a velocity discontinuity where normal faults are
initiated. During the extensional stage (3 cm of backward displacement), the
wall motion is paused every 1 cm to fill the interior of the depocentres to
simulate syn-tectonic sedimentation (e.g. Panien et al., 2006; Jara et al.,
2018). The filling of the grabens is done by sifting microbeads from a
height of <inline-formula><mml:math id="M6" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 cm with a smaller sifting container in order to
avoid sedimentation in the rift shoulders. At the end of extensional basin
formation, the basal sheet is detached from the moving wall and fixed to the
basal board to prevent its motion in subsequent extensional stages.</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="d1e212">Modelling set-up. <bold>(a)</bold> Sketch of the employed apparatus, oblique
view. <bold>(b)</bold> Sketch showing the overall camera set-up for PIV processing. <bold>(c)</bold> Close-up view of the basal sheet system. Triangles indicate the end of each
sheet. <bold>(d)</bold> Illustrated example showing the steps involved in the basin
formation – extension – and basin inversion – shortening – stages of the
experiments. <bold>(e)</bold> Summary of initial conditions for the shortening
experiments.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f02.png"/>

        </fig>

      <p id="d1e236">Since we evaluate the control that multiple extensional basins have on the
evolution of orogenic wedges, we systematically vary the number of basins
that are incorporated into the models. The number of basins created in the
models is defined by how many basal sheets are employed, and how many times
the extensional basin procedure previously described is repeated (Fig. 2d).
In all models, the final extensional stage is followed by a shortening
stage, imposed by the forward movement of the wall (push). Both stages of
deformation are carried out at a velocity of 1 mm min<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>. Environmental
conditions in the laboratory are controlled and kept within a range of 22 <inline-formula><mml:math id="M8" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C for temperature and 45 <inline-formula><mml:math id="M10" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 5 % for relative
humidity for all experiments. Deformation is monitored using four digital
single-lens reflex (DSLR) cameras that are simultaneously triggered, and
pictures are taken every 30 s. Surface and lateral strain, as well as
topography, is then quantified using a high-resolution particle image
velocimetry (PIV) and digital photogrammetry monitoring system (LaVision
DaVis<sup>®</sup>). We calculate the incremental strain at each time
increment, and progressive addition of these values is considered as
cumulative values.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Materials and scaling</title>
      <?pagebreak page216?><p id="d1e285">We use dry quartz sand to simulate crustal materials and microbeads to
simulate weaker detachment layers at the base of the sand pack. Sedimentary
infill is also carried out with microbeads, coloured for visualisation
purposes, to simulate less competent sedimentary rocks (e.g. Panien et al.,
2005). By using an approximate proportion of 0.1 g of dry powder pigment
per 1000 g of microbeads, the mix only differs in colour but not in
mechanical properties in comparison to the uncoloured microbeads used for
the detachment layer. Both sand and microbeads obey the Mohr–Coulomb
criterion (Coulomb, 1773; Krantz, 1991; Vermeer, 1990; Teixell and Koyi,
2003), where a strain-rate-independent rheological behaviour can be assumed.
We performed shear box tests to obtain values for angle of internal friction
and cohesion. Our values are similar to previously published results for the
same materials (Klinkmüller et al., 2016). The employed quartz sand,
prepared by Schlingmeier Quarzsand GmbH (Type G12T), has a bulk density of
1.53 g cm<inline-formula><mml:math id="M11" 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>, grain size range between 0.1 and 0.4 mm, average grain size
of 0.24 mm, an angle of internal peak friction of 33<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, angle of
reactivation of 30<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, and a cohesion of 58 Pa. The microbeads,
manufactured by Kuhmichel Abrasiv GmbH, have a bulk density of 1.51 g cm<inline-formula><mml:math id="M14" 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>, grain size range between 100 and 200 <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, average grain size
of 174 <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, an angle of internal peak friction of 28<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, angle
of reactivation of 24<inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, and a cohesion of 28 Pa. The
microbead–plywood board interface friction angle is 19<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>.
Microbeads used for the basal layer and quartz sand are sifted using a
purpose-built sifting device based on Maillot (2013), from a fixed height of
<inline-formula><mml:math id="M20" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 40 cm from the base of the apparatus.
<?xmltex \hack{\newpage}?>
Analogue experiments must be scaled in terms of length, time, and forces to
appropriately reproduce natural scenarios. We follow Hubbert (1937) and
Ramberg (1981) to scale stress in materials with brittle behaviour, a
standard approach in analogue modelling studies, following the relationship
given by <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>⋅</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi>g</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>⋅</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi>l</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M22" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M23" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M24" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M25" display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula> are stress, density, gravity, and
length, respectively. Asterisks indicate they are scaling factors, which are
calculated as the ratio of model (<inline-formula><mml:math id="M26" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>) to nature (<inline-formula><mml:math id="M27" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>):
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M28" display="block"><mml:mrow><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Our experiments are performed in a normal gravity field; therefore <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>. We obtain our density scaling ratio by
considering our quartz sand bulk density of <inline-formula><mml:math id="M30" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1530 kg m<inline-formula><mml:math id="M31" 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 crustal rock densities of <inline-formula><mml:math id="M32" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2700 kg m<inline-formula><mml:math id="M33" 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> to obtain
<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.567, and we fix a length
relation of 1 cm <inline-formula><mml:math id="M35" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5 km in order to obtain a length scaling ratio
<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>l</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M37" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M38" 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>, which is appropriate for
properly modelling scaled material strength using quartz sand (Ritter et
al., 2016). The stress ratio is then (Eq. 2)
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M39" display="block"><mml:mrow><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.13</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>×</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          meaning that a cohesion of 58 Pa for quartz sand in the model
corresponds to <inline-formula><mml:math id="M40" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 51 MPa in nature, and 28 Pa for microbeads
corresponds to <inline-formula><mml:math id="M41" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 25 MPa in nature, falling within the range of
<inline-formula><mml:math id="M42" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20–110 MPa calculated with uniaxial compressive strength
tests on natural rocks (Jaeger and Cook, 1976; Twiss and Moores, 1992;
Handin, 1969). The angle of internal friction is dimensionless; therefore,
our model materials represent an appropriate analogue as 33<inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for
quartz sand and 28<inline-formula><mml:math id="M44" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for microbeads fall within the range derived
from experimental rock tests (Jaeger and Cook, 1976). Our models are not
dynamically scaled since the rheology of granular materials is strain-rate-independent. General scaling parameters are summarised in Table 1.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e767">Material properties and scaling parameters.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <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:colspec colnum="5" colname="col5" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Material</oasis:entry>
         <oasis:entry colname="col2">Property</oasis:entry>
         <oasis:entry colname="col3">Model</oasis:entry>
         <oasis:entry colname="col4">Nature</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Quartz sand</oasis:entry>
         <oasis:entry colname="col2">Bulk density</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M46" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1530 kg m<inline-formula><mml:math id="M47" 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"><inline-formula><mml:math id="M48" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2700 kg m<inline-formula><mml:math id="M49" 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="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Grain size</oasis:entry>
         <oasis:entry colname="col3">100–400 <inline-formula><mml:math id="M50" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">–</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Internal friction angle | peak</oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">33<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"><?xmltex \hack{\hspace*{2.85cm}}?>| reactivation</oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">30<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Cohesion</oasis:entry>
         <oasis:entry colname="col3">58 Pa</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M53" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 51 MPa</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Microbeads</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">Bulk density</oasis:entry>
         <oasis:entry rowsep="1" colname="col3"><inline-formula><mml:math id="M54" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1510 kg m<inline-formula><mml:math id="M55" 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 rowsep="1" colname="col4"><inline-formula><mml:math id="M56" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2665 kg m<inline-formula><mml:math id="M57" 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="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Grain size</oasis:entry>
         <oasis:entry colname="col3">100–200 <inline-formula><mml:math id="M58" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">–</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Internal friction angle | peak</oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">28<inline-formula><mml:math id="M59" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"><?xmltex \hack{\hspace*{2.85cm}}?>| reactivation</oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">24<inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Cohesion</oasis:entry>
         <oasis:entry colname="col3">28 Pa</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M61" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 25 MPa</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col2">Model scaling factors </oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Length</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msup><mml:mi>l</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M63" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M64" 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></oasis:entry>
         <oasis:entry colname="col3">1 cm</oasis:entry>
         <oasis:entry colname="col4">5 km</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Gravity field</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msup><mml:mi>g</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">9.8 m s<inline-formula><mml:math id="M66" 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></oasis:entry>
         <oasis:entry colname="col4">9.8 m s<inline-formula><mml:math id="M67" 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></oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Deformation rate<inline-formula><mml:math id="M68" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">–</oasis:entry>
         <oasis:entry colname="col3">6 cm h<inline-formula><mml:math id="M69" 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">–</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e770"><inline-formula><mml:math id="M45" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Rheology of granular materials is strain-rate-independent; scaling would be applicable only to viscous materials.</p></table-wrap-foot></table-wrap>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Experimental limitations</title>
      <p id="d1e1261">Analogue modelling has inherent limitations, mainly related to the
difficulty of reproducing complex rheologies and<?pagebreak page217?> simulating realistic
temperature evolution of rocks, therefore representing a simplification of
nature (Koyi, 1997). In addition to this simplification, we have identified
a number of limitations in our models. Sidewall friction in a push-type
apparatus like ours is inevitable, and we therefore treat the internal side
of the glass walls with a water-repellent product (Rain
X<sup>®</sup>) as it reduces the sand–glass interface
friction (Cubas et al., 2013). Since the side contact area is relatively
small due to the thin layering, the unwanted side effect can be considered
negligible for this series of experiments. This is supported by a
consideration of the ratio between the top surface area and the side surface
area in our experiments, which is 0.075 and thus below the value of 0.1, which
Souloumiac et al. (2012) determined as the upper limit for negligible
sidewall effects. The apparatus was designed to prevent material from
sliding through the gap between the moving wall and the basal board during
shortening. However, a very thin layer of microbeads still passes beneath
the wall at early stages of deformation. As soon as crustal rupture is
achieved, the entire thrust sheet is translated by the moving wall, and no
extra material slides through the gap. Although we recognise that the
deformation imposed in our experiments strictly creates shear zones, we
refer for ease of comparison to natural examples to areas of material
failure in this study as faults and/or thrusts.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Analytical expectations</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Mechanics of basin inversion</title>
      <p id="d1e1283">In terms of orientation of principal stresses in the upper crust, basin
inversion can be generally described as a change from an extensional
setting, where <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is vertical, and <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is
horizontal, to a compressional setting with <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> horizontal and
<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> vertical. Assuming a Mohr–Coulomb criterion of failure for
upper-crustal rocks, the dip angle at which normal and reverse faults should
form can be calculated when the cohesion and angle-of-internal-friction
values are known. Considering a rock analogue to the quartz sand employed in
our experiments with an angle of internal friction of 33<inline-formula><mml:math id="M74" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>,
extension would result in the formation of normal faults at <inline-formula><mml:math id="M75" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 66<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> from the horizontal, while compression would lead to new
thrusts forming at 33<inline-formula><mml:math id="M77" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Fig. 3a). The resulting unfavourable
orientation of normal faults to reactivate under compressive stress has been
the subject of numerous studies (i.e. Jaeger and Cook, 1976; Cooper and Williams, 1989; Bonini et al., 2012; Zwaan et al., 2022), and it is the main reason why complete fault
reactivation remains a challenging process to recreate by means of analogue
modelling that employ materials with a simplified rheology in relation to
nature. Analogous set-ups in numerical models have successfully simulated the
reactivation of misoriented extensional faults by compressive stresses (e.g.
Granado and Ruh, 2019). Despite the limitations of analogue materials,
certain conditions such as obliquity of fault strike to <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Del
Ventisette et al., 2006), weaker basin infill (Panien et al., 2005),
horizontal stress direction rotation (Ritter et al., 2016; Bonini et al.,
2012), and type of post-rift sediments (Granado et al., 2017) have been
tested in laboratory experiments and demonstrated to promote basin inversion
and/or partial fault reactivation.</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="d1e1378">Mohr plots representing stress state at the base of a 3 cm thick
layer of <bold>(a)</bold> microbeads and <bold>(b)</bold> quartz sand (dotted red lines indicate the
stress state in the extensional phase; <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> angle of the failure
plane). <bold>(c)</bold> Inset showing the state of the crust after extension and before
the onset of compression, including observed (light blue, extensional) and
theoretical (black, contractional) faulting and their spatial relationship
with principal stresses <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The right panel
shows a schematic representation of stratigraphic columns for extensional
basins (BA) and homogeneous crust (HC). Thicknesses of the syn-rift
sediments, extended crust, and basal microbead layer are not included as
they vary slightly between basins and experiments. <bold>(d)</bold> Schematic representation
of Mohr circle theoretical evolution with a <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> increase. <bold>(e)</bold> Schematic representation of Mohr circle theoretical evolution with
simultaneous <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> increase. MB: microbeads; dMB: dyed microbeads; QzS: quartz sand; eQzS: extended
quartz sand.</p></caption>
          <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f03.png"/>

        </fig>

      <p id="d1e1468">In this study we present various models with a different arrangement of
internal mechanical heterogeneities prior to the onset of shortening: a
reference model with a homogeneous crust and models with one, two, and three
extensional basins (Fig. 2e). Considering the materials' density, cohesion,
and angle of internal friction, Mohr diagrams representing the state of
stress at the base of different sections of the models at the onset of
shortening are plotted in Fig. 3b and c. With this theoretical framework
(Fig. 3) as a basis, the following preliminary hypotheses can be drawn:
<list list-type="order"><list-item>
      <p id="d1e1473">Under conditions where layers have the same thickness and
similar densities, the lower angle of internal friction of the microbeads
will make the model sedimentary infill more prone to failure with the onset
of shortening. Thrusts are expected to propagate through the weaker
extensional basins (Fig. 3b–c).</p></list-item><list-item>
      <p id="d1e1477">Normal faults in the models have a theoretical dip angle of
66<inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Even considering the lower reactivation values of internal
friction, their reactivation during the shortening stage will be inhibited
by their misorientation. Only a considerable rotation of <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> about a vertical axis during shortening could favour fault
reactivation, although observations from analogue models suggest that stress
rotations would only be in the range of 5–15<inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Bonini
et al., 2012, and references therein) and would therefore be insufficient.</p></list-item><list-item>
      <?pagebreak page219?><p id="d1e1510">Vertical loading resulting from thickening in the sand wedge
leads to strengthening of the sand pack as <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> increases (Fig. 3d). With ongoing shortening, the thicker sand pile will require an increase
of <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to maintain the same differential stress (Fig. 3e). This
process may favour the reactivation of normal faults due to protracted
compression within the basin or may lead to the formation of new thrusts to
the foreland side of the extensional basin, the latter event being subject
to the status of wedge stability (Sect. 3.2).</p></list-item></list></p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Critical taper theory</title>
      <p id="d1e1543">During shortening, the extensional basins are incorporated in a thrust
wedge, which has heterogeneous material properties caused by the mixing of
the microbeads of the basin fill with quartz sand. Critical taper theory
(Dahlen, 1984, 1990) predicts a lower taper angle of 6.2<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
(unsoftened) to 7.2<inline-formula><mml:math id="M91" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (softened) for a pure quartz sand wedge
overlying a thin microbead basal layer. Theoretical dip values of forward-verging thrusts are <inline-formula><mml:math id="M92" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, and steeper back thrusts
dip at <inline-formula><mml:math id="M94" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 37<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Dahlen, 1990). The critical taper
angle (which equals surface slope for our horizontal base experiments) for a
pure microbead wedge is 7.9<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (unsoftened) to 9.7<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
(softened). For our wedges, surface slopes between 6.2 and
9.7<inline-formula><mml:math id="M98" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> can thus be argued to be valid values, where we would expect
a tendency towards the higher values within the lower taper angle due to the
mixing of microbeads into the sand (Buiter, 2012).</p>
      <p id="d1e1624">As thrust sheets are emplaced over the extensional basins during shortening
the resulting strength increase caused by the increase in <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
may be significant enough to keep the system stresses in a state such that
the localisation of new thrusts would be determined by not only the internal
rheological heterogeneities but also the need of the wedge to reach a
critical taper value. New frontal thrusts then develop to decrease the taper
angle.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results</title>
      <p id="d1e1647">We carried out eight experiments with identical handling procedures (Table 2),
and here we present the results of the five experiments with different initial
conditions; three selected experiments were run twice to check for
reproducibility. Two experiments, <italic>REFNB</italic> (no basal sheet) and
<italic>REFWB</italic> (with basal sheet), examine shortening of a homogeneous
layering, without extension, with the objective of having two reference
shortening experiments to compare our basin inversion experiments against.
The basin inversion experiments (<italic>1B</italic>, <italic>2B</italic>, and <italic>3B</italic>, or <italic>EXP1B</italic>, <italic>EXP2B</italic>, and <italic>EXP3B</italic>)
include an extensional phase forming one, two, or three extensional basins,
respectively. For description purposes, a terminology based on the analogy
with the location of the foreland and hinterland in fold-and-thrust belts is
used, and the extensional basins are called proximal, central, and distal
based on their proximity to the moving wall (Fig. 2e).</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1678">List of the performed analogue models.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Experiment ID</oasis:entry>
         <oasis:entry colname="col2">Basins</oasis:entry>
         <oasis:entry colname="col3">Description</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">REFNB</oasis:entry>
         <oasis:entry colname="col2">–</oasis:entry>
         <oasis:entry colname="col3">Reference model, no basal sheets</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">REFWB</oasis:entry>
         <oasis:entry colname="col2">–</oasis:entry>
         <oasis:entry colname="col3">Reference model, with basal sheets</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">1B</oasis:entry>
         <oasis:entry colname="col2">1</oasis:entry>
         <oasis:entry colname="col3">Basin located 24.5 cm from moving wall</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2B</oasis:entry>
         <oasis:entry colname="col2">2</oasis:entry>
         <oasis:entry colname="col3">Basins located 19.5 and 24.5 cm from moving wall</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3B</oasis:entry>
         <oasis:entry colname="col2">3</oasis:entry>
         <oasis:entry colname="col3">Basins located 9.5, 19.5, and 24.5 cm from moving wall</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\newpage}?>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Reference experiments</title>
      <p id="d1e1780">Experiment REFNB (reference experiment, no basal sheets) consists of a 5 mm
thick microbead layer overlain by a 25 mm thick cover of quartz sand, with
interbedded coloured horizontal layers that act as passive markers. No basal
plastic sheets are employed in this model. Results of experiment REFNB show
a typical piggyback deformation style, with thrust sheets developing in
sequence and being gradually transported towards the foreland. Shortening is
accommodated first by a pop-up structure consisting of a forward and back
thrust stemming from the basal detachment layer 2.3 cm from the moving
wall (T1 in Fig. 4a). Activity in the back thrust decreases, and strain is
then only accommodated for by the frontal thrust T1 until a new pop-up
structure forms, 12.9 cm from the moving wall (T2 in Fig. 4a). The entire
thrust sheet is translated towards the foreland until a third pop-up
structure develops, after 16 cm of displacement (T3 in Fig. 4a). After 20 cm
of displacement, the measured wedge taper angle is 8.5<inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Fig. 4a).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e1794">Deformation evolution, comparison between reference experiments.
Experiment REFNB, no basal sheet: <bold>(a)</bold> side-view photographs, <bold>(b)</bold> incremental
strain, and <bold>(c)</bold> cumulative strain. Experiment REFWB, with basal sheet: <bold>(d)</bold> side-view photographs, <bold>(e)</bold> incremental strain, and <bold>(f)</bold> cumulative strain.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f04.png"/>

        </fig>

      <p id="d1e1822">Experiment REFWB (reference experiment, with basal sheets) was designed to
create the exact same initial conditions as experiment REFNB, with the only
addition of including plastic basal sheets fixed to the apparatus base, with
vertical sub-millimetric steps – perpendicular to the shortening direction –
located 9.5, 19.5, and 24.5 cm from the initial position of the moving
wall (Fig. 4b). The plastic sheets are used in subsequent experiments to
create extensional basins and remain in a passive role during the shortening
phase. We test here their potential influence during shortening. Experiment
REFWB develops a pop-up structure almost immediately after the initiation
of the wall movement (T1 in Fig. 4b), as observed in experiment REFNB.
However, in REFWB the pop-up structure forms 7 cm from the moving wall,
which is closer to the edge of the first basal sheet step, meaning that its
associated basal velocity discontinuity could play a role in determining the
location of the first thrust sheet in the accretionary wedge evolution.
After approximately 7.5 cm of displacement, the initial pop-up structure is
progressively abandoned, and a new frontal thrust forms towards the foreland,
stemming from the basal detachment layer 14 cm from the moving wall (T2 in
Fig. 4b). In this case, the location of the frontal thrust and its conjugate
back thrust is not aligned with one of the basal sheet steps (Fig. 4b). Most
of the shortening is accommodated by the second frontal thrust until the
system reaches <inline-formula><mml:math id="M101" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 17 cm of displacement. At this point, a new
pop-up structure develops, stemming from the basal detachment layer 20.5 cm from the moving wall (T3 in Fig. 4b). The new frontal thrust localises
most of the wedge deformation until the final stages of the experiment (Fig. 4b). After 20 cm of displacement, the measured wedge taper angle is
9.3<inline-formula><mml:math id="M102" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Fig. 4b)</p>
      <?pagebreak page221?><p id="d1e1842">The overall evolution of the accretionary wedge in REFWB is similar to
experiment REFNB. Both experiments were run twice, showing little
variability in terms of pop-up structure formation and thrust localisation.
The velocity discontinuities formed by the sub-millimetric geometrical steps
of the basal sheets only influence the model in early stages, defining the
onset of the first thrusts. However, the fact that the sheet edges are not
aligned with the subsequent floor thrusts allows us to assume that their
effect in the evolution of the modelled accretionary wedge is negligible for
the purpose of our study.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Experiment 1B: one extensional basin</title>
      <p id="d1e1853">Experiment 1B consists of two stages. An initial stage of 3 cm extension in
which an extensional basin with border faults located between 24.5 and 27.5 cm from the wall (measured along the base) is created, followed by a stage
of 20 cm of compressional displacement. Shortly after the initiation of
shortening, frontal and back thrusts develop approximately 5 cm from the
moving wall (T1 in Fig. 5). During the first 6 mm of displacement, before
the onset of the first frontal thrust, the distal extensional basin shows
internal horizontal compression, reaching peak values of up to 16 % of
cumulative strain (7 % on average) but without fault reactivation or the
formation of new thrusts. No further internal deformation of the basin is
observed between 0.6 and 4 cm shortening.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1858">Experiment 1B summary. <bold>(a)</bold> Side-view photograph and interpreted
close-up view at the end of the extensional stage. Shortening stage
evolution, showing <bold>(b)</bold> side-view photographs, <bold>(c)</bold> incremental strain, and
<bold>(d)</bold> cumulative strain.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f05.png"/>

        </fig>

      <p id="d1e1879">The initial thrust sheet is transported towards the foreland, and after 5 cm
of total displacement, strain accommodation is partitioned, and stress
builds up again in the extensional basin. Subsequently, the initial forward
thrust is progressively abandoned, and strain localisation is transferred
entirely near the pre-existing extensional basin (T2 in Fig. 5). A new
forward thrust forms along the limit between the faulted blocks in the
foreland side and the weak microbead depocentre filling, without
reactivating the extensional border faults. The extensional faults on the
hinterland side are cross-cut, and the thrust sheet propagates towards the
foreland, above the pre-rift sediments (Fig. 5; 8 cm displacement). With
ongoing deformation, no further deformation is observed beyond the
extensional basin, and the wedge grows in height through the development of
three new back thrusts that form progressively towards the location of the
wall. After 20 cm of displacement, a wedge taper angle cannot be accurately
estimated, as the wedge is in transition to a critical taper, and two
distinctive wedge fronts can be established at 27.7<inline-formula><mml:math id="M103" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (determined
by the angle of repose of the microbeads) and 3.7<inline-formula><mml:math id="M104" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in the more
planar, higher section (Fig. 5).</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Experiment 2B: two extensional basins</title>
      <p id="d1e1908">The 3 cm extensional phase for experiment 2B leads to the formation of a
distal basin with border faults located between 24.5 and 27.5 cm from the
wall (measured along the base) and a central basin with border faults
located between 19.5 and 22.5 cm from the wall. Initial compressional
deformation is accommodated by the development of a pop-up structure,
forming 14.3 cm from the wall, aligned with the pre-existing extensional
basin located closer to the hinterland (T1 in Fig. 6). The frontal thrust
cross-cuts the border faults on the hinterland side and progressively
transports the basin fill over the pre-rift sand pack, towards the foreland.
After 2.3 cm of displacement, a new forward thrust develops in the proximity
of the wall (T2 in Fig. 6). As observed in experiment 1B, the early
development of a thrust sheet located relatively farther away from the wall
than in the reference models causes the wedge to grow in a subcritical,
unstable manner (Fig. 6; 4 cm displacement). Internal deformation of the
wedge is therefore controlled by a new forward thrust forming 2.4 cm from
the moving wall (T2). This out-of-sequence thrust accommodates shortening
for another 2.5 cm of displacement, when the frontal thrust T1, located
along the weak graben fill, is reactivated (Fig. 6; 8 cm displacement). PIV
analysis at 8 cm of displacement indicates no normal fault reactivation, but
the frontal thrust does show a strong deflection of its dip angle, from
20<inline-formula><mml:math id="M105" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> at the base to 37<inline-formula><mml:math id="M106" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> when it interacts with the
extensional basin (Fig. 6; 8 cm displacement). Coevally, a series of back
thrusts become active on the hinterland side of the thrust sheet as the
wedge continues to advance. At later stages, the frontal thrust located
along the central basin and its conjugate back thrust decrease their
activity, and strain localisation is progressively transferred to the distal
basin (Fig. 6; 12 cm displacement). Before the onset of a new pop-up
structure in the distal basin, cumulative strain within the syn-rift strata
reached values of up to 24 %. After 12 cm of total displacement,
shortening in the foreland is accommodated first by a back thrust aligned
with the extensional basin border faults, later replaced by the formation of
a new forward thrust (T3 in Fig. 6). At 16 cm of displacement, the wedge
continues to grow, with most of the strain localised along the two forward
thrusts and steeply dipping back thrusts (Fig. 6; 16 cm displacement). The final
stages of deformation are characterised by a new pop-up structure forming in
the foreland (T4 in Fig. 6). The wedge taper angle after 20 cm of shortening
is 9.7<inline-formula><mml:math id="M107" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Fig. 6).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1940">Experiment 2B summary. <bold>(a)</bold> Side-view photograph and interpreted
close-up view at the end of the extensional stage. Shortening stage
evolution, showing <bold>(b)</bold> side-view photographs, <bold>(c)</bold> incremental strain, and
<bold>(d)</bold> cumulative strain.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f06.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Experiment 3B: three extensional basins</title>
      <?pagebreak page223?><p id="d1e1969">Experiment 3B is carried out following the same procedure as experiments 1B
and 2B, but now creating three extensional basins before the onset of
shortening. The extensional phase for this experiment results in the first
basin located between 28.5 and 31.5 cm from the moving wall, the second
basin between 19.5 and 22.5 cm from the moving wall, and the third and last
basin located between 9.5 and 12.5 cm from the moving wall (all measured
along the base). Early compressional stages are characterised by the
formation of a forward thrust, with its location being controlled by the
weak basin fill of the basin, cross-cutting the extensional border faults
located on the side of the moving wall (T1 in Fig. 7). This forward thrust
is followed by the formation of a back thrust, both stemming from the basal
detachment layer 5.8 cm from the moving wall. Close inspection of PIV
data shows that the interior of the proximal extensional basin localises up
to 20 % of strain before the onset of the pop-up structure. After 6.5 cm
of displacement, strain is partitioned and progressively transferred to the
central extensional basin, where a new forward thrust develops, aligned with
the interface between the rifted blocks and the weak sedimentary infill, as
occurred in earlier stages of this experiment (T2 in Fig. 7). No clear
reactivation of border faults can be detected in this process, although the
high angle (49<inline-formula><mml:math id="M108" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) of the associated back thrust could be
associated with the partial reactivation of the hinterland border faults.
The central basin shows horizontal compression and a partial uplift of 2.2 mm prior to crustal failure. Cumulative strain is calculated to reach values
of up to 26 % within the basin before the onset of new thrusts.</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="d1e1983">Experiment 3B summary. <bold>(a)</bold> Side-view photograph and interpreted
close-up view at the end of the extensional stage. Shortening stage
evolution, showing <bold>(b)</bold> side-view photographs, <bold>(c)</bold> incremental strain, and
<bold>(d)</bold> cumulative strain.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f07.png"/>

        </fig>

      <p id="d1e2004">Strain localisation along this central basin is short-lived, and a new
forward thrust develops 16.2 cm from the moving wall, with its
localisation being determined by the existence of the distal basin (T3 in
Fig. 7). The new frontal thrust becomes the most active structure at this
stage of the accretionary wedge evolution. Two new back thrusts form and
show a noticeable deflection in their dipping angle when interacting with
the uplifted central basin. After 16 cm of displacement, the entire
sedimentary fill of the first basin is transported past the frontal thrust
tip point. At this stage, internal deformation of the wedge is accommodated
by the frontal thrust T3 and its conjugate back thrust, as well as by a
forward thrust stemming from the base of the wall and aligned with the
location of the weak remobilised sediments in the interior of the wedge
(Fig. 7; 16 cm displacement). After 20 cm of shortening, strain is localised
only along the frontal thrust and a back thrust that transects the entire
wedge, with a variable dip angle of 39<inline-formula><mml:math id="M109" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in its lower section and
60<inline-formula><mml:math id="M110" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in its upper section (Fig. 7; 20 cm displacement). The measured
wedge taper angle is averaged to 10.7<inline-formula><mml:math id="M111" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, although two wedge fronts
with different slopes can alternatively be measured as 28  and
5.5<inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> (Fig. 7).</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion</title>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Overall evolution of the experiments</title>
      <p id="d1e2060">Certain features can be observed across all experiments with pre-existing
extensional basins. Independent of the position of the graben (proximal,
central, or distal), detailed analysis shows that normal fault reactivation
sensu stricto is not the main mechanism for basin inversion during shortening stages. The
change from extension to shortening is instead characterised by a partial
inversion that can be outlined in three stages:
<list list-type="order"><list-item>
      <p id="d1e2065">Horizontal stresses are transferred across the quartz sand (analogous to
stronger crust), resulting in the shortening of the microbeads (analogous to
weak sedimentary infill) and an associated upward bulging. Cumulative strain
localising in the interior of the basins prior to the development of forward
thrusts ranges from 5 %–26 %. When multiple extensional basins are present,
the proximal basin absorbs most of the stress transferred through the quartz
sand as it is closest to the wedge.</p></list-item><list-item>
      <p id="d1e2069">Thrusts develop in the microbeads and produce the partial inversion of the
basin, resulting in the asymmetric dome-shaped deformation of the microbeads
(syn-rift growth strata). In all cases, the thrust producing the internal
deformation of the basin is a frontal thrust, except for the distal basin in
EXP2B, where the basin uplift is accommodated by both a frontal thrust and a
back thrust aligned with the basin border faults instead (Fig. 6; 12 cm
displacement).</p></list-item><list-item>
      <p id="d1e2073">The mechanism of shortening accommodation finally ends with the development
of a new frontal thrust, located farther away from the moving wall. This
mechanism is the result of two processes combined: (1) the prograding wedge
pushes new material on top of the extensional basin to the point that the
locally increased crustal thickness makes it rheologically stronger (through
the increase in vertical stress), thereby making the region towards the
foreland relatively weaker, and (2) the orogenic wedge is transitioning
towards its critical taper angle and needs to grow forward to decrease its
angle and remain in the stable field, following critical taper theory.</p></list-item></list>
Beyond these similarities in the general mechanism of (partial) basin
inversion, there are important differences in the spatio-temporal evolution
of deformation and thrust sequencing as a function of the number of
extensional basins.</p>
      <p id="d1e2077">EXP1B shows the largest thrust spacing among the experiments, with the first
pop-up structure developing in the vicinity of the moving wall (Fig. 5; 2 cm
displacement), followed by the transfer of horizontal stresses onto the
pre-existing extensional basin, located <inline-formula><mml:math id="M113" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 17 cm beyond the
basal detachment of the initial frontal thrust (Fig. 5; 8 cm displacement).
This experiment shows the maximum amount of strain accumulation in the
extensional basin prior to its failure by shortening and represents the
distal extensional basin with the earliest evidence of a certain degree of
inversion. The emplacement of frontal thrusts differs from the reference
experiments as in EXP1B they are conditioned by the location of the
extensional basin (cf. Figs. 4 and 5). The distal extensional basin acts as
an efficient localiser that takes up stress, and no thrusts develop beyond
its position throughout the entire experiment.</p>
      <p id="d1e2087">EXP2B is the only experiment of this series that developed out-of-sequence
frontal thrusts. The first frontal thrust localised along the central
extensional basin, before strain was accommodated by a pop-up structure in
the vicinity of the wall (Fig. 6; 4 cm displacement). Thrust spacing closely
resembles that of the reference experiments, although they follow a
different chronological order. Contrary to what is<?pagebreak page224?> observed in the other
experiments, the distal graben normal faults that are cross-cut are those
located at the foreland side of the basin, resulting in an oppositely
verging uplift of the sedimentary infill (Fig. 6; 16 cm displacement)</p>
      <p id="d1e2090">EXP3B evolution is characterised by in-sequence thrusts that localise along
each of the extensional basins (Fig. 7). The main difference with EXP1B and
EXP2B is that the inversion of the central basin is more complex: early
stages of deformation produce partial uplift, but it is short-lived as
prograding sediments from the wedge result in an overburden that makes the
basin rheologically stronger, and deformation is soon transferred to the
distal basin (Fig. 7; 12 cm displacement). As in EXP1B, no further
shortening structures are observed beyond the position of the distal basin
(Fig. 7; 20 cm displacement).</p>
</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>Comparison to critical taper theory</title>
      <p id="d1e2101">Fault dip angles in the analogue experiments average 26–32<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for the forward thrusts and 31–46<inline-formula><mml:math id="M115" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for
the back thrusts. The forward thrusts are thus somewhat shallower than the
theoretical dip angle of 33<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for reverse faults in undeformed
sand, whereas the back thrusts are mainly steeper than this value. For mature
wedges, the theoretical dip angles become 20<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for forward thrusts
and <inline-formula><mml:math id="M118" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 37<inline-formula><mml:math id="M119" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> for back thrusts (Dahlen, 1990; Sect. 3.2 herein). The measured forward thrusts are thus steeper than the theoretical
value, whereas the back thrusts could be argued to fit fairly well. However,
in our opinion the thrust dip measurements have limited validity as they are
a manifestation of internal wedge deformation during its transition to become
critical.</p>
      <p id="d1e2157">When comparing the experiments in which basins are incorporated in the
thrust wedge to the reference experiments without basins, we find a
perceptible effect of the pre-existing extensional basins on the final taper
angle of the wedge: the taper angle increases. The reference experiments
with a homogeneous quartz sand layer had measured taper angles of
8.5 and 9.3<inline-formula><mml:math id="M120" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> after 20 cm of shortening, which are
somewhat higher than the predicted values of 6.2–7.2<inline-formula><mml:math id="M121" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. Measured values for experiments 2B and 3B are higher again, at
9.7 and 10.7<inline-formula><mml:math id="M122" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, respectively (Fig. 8). In experiments
1B and 3B the shape of the advancing wedge is irregular, making it harder to
draw a best-fit line that determines the taper angle (Fig. 8c and d). In
these cases, the protracted localisation of shortening along the distal
extensional basin results in greater accumulation of scraped-off and slope
materials in the frontal section. As a result, the frontal slope is
determined by the angle of repose of the mix of quartz sand and microbeads.
When comparing experiments 1B, 2B, and 3B after the same amount of shortening
(Fig. 8), experiment 2B displays the lowest wedge taper angle, as it formed
a new frontal thrust at a slightly earlier stage of deformation (Fig. 8c–d).
However, the overall temporal evolution of the wedge taper angle during
shortening is similar for the experiments with a previously extended crust.
Results point towards an increase in the taper angle in comparison to wedges
with a homogenous<?pagebreak page225?> crust (cf. Fig. 8a–b and c–d). This agrees with our
predictions (Sect. 3.2) as the inclusion of the weaker microbeads of the
basin fill is expected to increase the taper angle.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e2189">Side-view photographs and interpretation sketches for all models
after 20 cm of displacement, including visual guide for taper angle
measurements. Values for EXP1B could not be determined as the taper is in
transition into a critical taper, where no clear valleys or peaks are yet
discernible in order to display a best-fitting line (Stockmal et al., 2007).</p></caption>
          <?xmltex \igopts{width=469.470472pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S5.SS3">
  <label>5.3</label><title>Mechanisms of basin inversion in the experiments</title>
      <p id="d1e2206">In terms of local structures and transient mechanisms of strain
accommodation, we can classify partial inversion in the models into three
stages: basin shortening and uplift, thrust localisation and reactivation,
and deformation relocalisation due to changes in brittle strength.</p>
<sec id="Ch1.S5.SS3.SSS1">
  <label>5.3.1</label><title>Basin shortening and uplift</title>
      <p id="d1e2216">Early stages are generally manifested by the displacement of the crustal
section between the moving wall and the most proximal extensional basin, as
a whole, and in the shortening direction (Fig. 9). This crustal section is
rheologically stronger than the extensional basin infill; therefore stress
is transferred along the crust, and shortening is absorbed by the
unconsolidated sediments of the basin. This produces an early compaction and
subsequent upward bulging of the basin fill, prior to the failure of the
crust in the form of a thrust (Fig. 9).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e2221">Close-up view of selected basins. In EXP2B, despite having only two
basins, the basin closest to the moving wall is referred to as “central”
for ease of comparison between experiments. The left panel shows <inline-formula><mml:math id="M123" display="inline"><mml:mi>Y</mml:mi></mml:math></inline-formula> displacement
(vertical) before crustal failure, the central panel shows total displacement at
the indicated time intervals, and the right panel is a drawn comparison between
the original basin and its status before thrust development.</p></caption>
            <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f09.png"/>

          </fig>

      <p id="d1e2237">During this initial stage, there is no displacement observed distalward from
the basin for relatively long periods of time, meaning that extensional
basins act as an efficient feature to localise stress and prevent further
transfer within the crust (Fig. 9, central panels). However, in the case of
EXP1B, where the distance between the moving wall and the extensional basin
is relatively higher (28.5 cm vs. 19.5 and 9.5), shortening is initially
manifested as a classic pop-up structure near the moving wall, preceding the
basin fill compaction stage. This observation indicates that, in conditions
analogous to our models, there may be a distance threshold of how much
compressional stresses can be transferred from the orogenic front laterally
far into the crust.</p>
      <p id="d1e2241">An uplift of up to <inline-formula><mml:math id="M124" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 9 % of its initial thickness and a
horizontal contraction of up to <inline-formula><mml:math id="M125" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 8 % of its initial width
is observed among the extensional basins in all models (Fig. 9). PIV
analysis shows that up to <inline-formula><mml:math id="M126" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 25 % of strain can be
accumulated in the interior of the extensional basins before any type of
faulting is manifested. These observations are in line with previous
analogue modelling results (Panien et al., 2006) and field studies (Butler,
1989; Chadwick, 1993; Gillcrist et al., 1987; Granado et al., 2018), where
it has been identified that inversion of extensional basins initiates by
bulk shortening of the graben fill, localised minor reverse faulting,
buttressing with associated folding, and subsequent regional upwarp (Fig. 9).</p>
</sec>
<sec id="Ch1.S5.SS3.SSS2">
  <label>5.3.2</label><title>Thrust localisation and reactivation</title>
      <p id="d1e2273">After the initial stage of stress build-up in the interior of the basins,
crustal failure –  identified as such when incremental strain values are over
1 % – is manifested as forward-verging thrusts. Except for the early pop-up
structure formed in the vicinity of the moving wall in EXP1B (Fig. 5; 2 cm
displacement), all initial frontal thrusts are localised along the
pre-existing extensional basins. These results are in line with early
observations of how extant hinterland-dipping normal faults favour the
development of foreland-directed thrusts (Cooper and Williams, 1989). Thrusts that
cross-cut the basin have dip angles in the range of 20–38<inline-formula><mml:math id="M127" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. When analysed in detail, examples of EXP3B and EXP2B show
that dip angle variations within the thrust are associated with the location
of the pre-existing normal faults (Fig. 10b and d), without reactivation
sensu stricto due to their misorientation. The only significant difference in this
process is observed in the distal basin of EXP2B, where the weak sedimentary
infill determines the position of the back thrust instead of the frontal
thrust. A forward-verging thrust forms that cuts through the homogenous
crust (Fig. 10d).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e2287">Close-up view of selected basins, highlighting thrust
localisation. <bold>(a)</bold> Experiment 1B, distal basin. <bold>(b)</bold> Experiment 2B, central
basin. <bold>(c)</bold> Experiment 3B, proximal basin. <bold>(d)</bold> Experiment 2B, distal basin.
<bold>(e)</bold> Close-up view visualising different time increments for cumulative
vertical displacement and <bold>(f)</bold> incremental strain of the distal basin in
EXP2B.</p></caption>
            <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f10.png"/>

          </fig>

      <p id="d1e2315">Considering that strain softening in fine sands is relatively minor, and
therefore faults do not weaken considerably, it is mainly due to the
misorientation of normal faults that their reactivation and inversion do
not occur in any of the basins, with one potential exception in the distal
basin of EXP2B (Fig. 10d–f). Prior to the formation of the pop-up structure
that lifts the basin up, strain builds up along the middle and lower part of
both border faults (Fig. 10f; 117 min). However, the degree of strain
localisation is too low and short-lived for normal fault reactivation, and
two frontal thrusts form instead (Fig. 10f; 121 min). When this happens,
normal faults are cross-cut as in the rest of the extensional basins located
at the foreland of the modelled orogenic wedges.</p>
</sec>
<sec id="Ch1.S5.SS3.SSS3">
  <label>5.3.3</label><title>Variations in brittle strength</title>
      <p id="d1e2326">Our modelling outcomes allow the identification of the chronological order
in which crustal thickening and vertical loading may result in locally
stronger areas of the crust. The rheological heterogeneities formed by the
basins play an important role in determining how long lived each of the
frontal and back thrusts are. Prior to thrust sheet translation and the
associated vertical load, the weakest area is always the interior of the
basins (see Sect. 4), where shortening is expected to localise. Thrusts
effectively form in the proximity of the basin and cross-cut border faults.
With ongoing deformation and transport of material on top of the extensional
basins, the previously weaker interior becomes stronger due to an increase
in the vertical principal stress <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. 3e). At this point,
strain localisation and overall evolution of deformation becomes a trade-off
between (a) the location of the rheologically weaker sections of the crust
and (b) the need of the wedge to reach the critical point predicted by
critical taper theory.</p>
      <p id="d1e2340">In EXP2B, before reaching 12 cm of total displacement, an early frontal
thrust that localised along the central extensional basin is active, while
new frontal and back thrusts start developing in the vicinity of the distal
extensional basin<?pagebreak page226?> (Fig. 11a; 117 mm displacement). Initially, the new back
thrust seems to accommodate most shortening in the new orogenic front.
However, the early-formed thrust sheet continues to transport material on
top of the basin until the vertical load is sufficiently high to hinder the
partial basin inversion (Fig. 11a; 127 mm displacement). Strain subsequently
jumps to the foreland and localises beyond the distal extensional basin, as
a mechanism to aid the wedge taper angle to a critical value.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e2345">Interpreted sections of selected experiments showing thrust sheet
progression and impact on basin inversion. <bold>(a)</bold> Experiment 2B, distal basin.
<bold>(b)</bold> Experiment 3B, central basin.</p></caption>
            <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f11.png"/>

          </fig>

      <p id="d1e2361">A similar process is observed in the central basin of EXP3B. The forward-verging thrust formed early along the proximal extensional basin is active
at the moment of stress build-up and strain localisation in the central
basin (Fig. 7; 74 mm displacement). Translation of the thrust sheet on top
of the partially inverted central basin creates the same hindering effect as
in EXP2B, and the back thrust becomes inactive. Instead of transferring all
the stress to the new orogenic front, both forward thrusts are coevally
active for <inline-formula><mml:math id="M129" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 min (2 cm of displacement), until the
growth of the wedge is such that shortening is accommodated by a new frontal
thrust along the distal extensional basin (Fig. 11b; 94 mm displacement).
After this process, internal deformation of the wedge ceases, and all
shortening is accommodated by the new orogenic front. These two examples are
indicative of how extensional basins in foreland fold-and-thrust belts are
likely to localise the onset of thrusts, but their effectivity, duration, and
chronological order will depend on their initial position, distance between
basins, and relative distance to the indenter.</p>
</sec>
</sec>
<sec id="Ch1.S5.SS4">
  <label>5.4</label><title>Comparison with previous case studies</title>
      <p id="d1e2380">Our modelling results can be compared to case studies of fold-and-thrust
belts forming over previously extended crust. While aspects such as crustal
composition, type of syn-rift infill, shortening direction and its variation
over time, and distances or thicknesses may differ, we argue that our
findings can be extrapolated from modelling to nature in order to provide
first-order insights on the evolution of deformation and basin inversion in
fold-and-thrust belts. Here we compare the most relevant aspects of our
models with natural examples across multiple length scales.</p>
<sec id="Ch1.S5.SS4.SSS1">
  <label>5.4.1</label><title>Carpathians</title>
      <p id="d1e2390">The Carpathian Mountains in central eastern Europe formed as a result of the
subduction of the European plate below the Adriatic plate and the associated
closure of two extensional basins located behind an extended margin (e.g.
Picha et al., 2006) (Fig. 12a, left panel). These conditions resemble those
for EXP3B, where three sections of previously extended crust are subjected
to shortening mainly from one direction (i.e. moving wall). Convergence and
early stages of collision, lasting from the Late Cretaceous to the Palaeocene,
initially manifested as a series of frontal thrusts that localised along the
pre-orogenic extensional basin closest to the orogenic front (Picha et al.,
2006; Fig. 12a, left panel). As interpreted for EXP3B, there is also
evidence of contraction and partial inversion of the extensional basins at
these early stages in the Carpathians, without manifestation of crustal rupture
at the surface. While estimating the amount of shortening having occurred in the
extensional basins in such natural scenarios can be difficult, from our
models we can quantify up to 19 % and 27 % of cumulative strain in the
central and distal basins, respectively, before new contractional faults form
in their surroundings. Ongoing deformation in the Late Oligocene was
characterised by the formation of in-sequence thrust sheets along the
central basin (Magura Flysch; Fig. 12a, left panel), forming the Inner
Carpathians. This stage culminated in the cross-cutting of the central basin
as the indenter formed by the Adriatic plate continued its<?pagebreak page229?> progression
towards the European Plate. At later stages, strain localisation was
transferred to the most distal extensional basin (Silesian unit; Fig. 12a,
left panel), giving rise to the Outer Carpathians. A very similar behaviour
was observed in EXP3B, where the central basin showed evidence of mild basin
inversion until it was cross-cut by the incoming thrust sheet from the
accretionary front (Fig. 12a, right panel). The final stages in EXP3B were
characterised by the formation of a wedge with a frontal thrust that
originated along the most distal extensional basin, which uplifted and
folded the syn-extensional strata (Fig. 12a, right panel). Similarly, the
Late Miocene in the Carpathians is distinguished by the progression of the
fold-and-thrust belt, which completely uplifted the distant extensional
Silesian units (Fig. 12a, left panel), which is the only syn-extensional
unit widely exposed in the surface of the western Outer Carpathians (Picha
et al., 2006). Both the natural prototype and the experimental results
indicate that, when multiple extensional basins are present, the most
proximal one will absorb the majority of the stress at initial stages, and
the complete tectonic wedge will then continue its deformation, in sequence,
from the deformation front towards the foreland.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><?xmltex \currentcnt{12}?><?xmltex \def\figurename{Figure}?><label>Figure 12</label><caption><p id="d1e2395">Temporal evolution comparison between selected natural examples
and our analogue modelling results. <bold>(a)</bold> Carpathians vs. EXP3B (redrawn from
Picha et al., 2006). MF: Magura Flysch; SU: Silesian Unit. <bold>(b)</bold> Atlas vs.
EXP2B (redrawn from Bracène and de Lamotte, 2002).</p></caption>
            <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f12.png"/>

          </fig>

</sec>
<sec id="Ch1.S5.SS4.SSS2">
  <label>5.4.2</label><title>Atlas</title>
      <p id="d1e2418">The Atlas Mountains in north-western Africa formed as a result of multiple
episodes of extension and compression, governed by major changes in global
plate kinematics. Two main stages of deformation can be discerned for them:
first an extensional phase, linked to the opening of the Maghrebian Tethys
and North Atlantic oceans, and then the posterior compression and inversion,
associated with the convergence and collision of the African and European
plates (Mattauer et al., 1977; Roca et al., 2004; Teixell et al., 2003).
Although there is general agreement on this first-order multistage tectonic
history, understanding the temporal relationships of structural features
observed in the geological record remains a challenge. Comparison with EXP2B
may shed light on how a fold-and-thrust belt evolves when multiple extended
regions of crust are present in the foreland. Prior to convergence, the
geological setting in the Atlas region consisted of the Tell passive margin
in the north-west, inherited from the Maghrebian Tethys ocean opening and
characterised by mostly north-west-dipping normal faults, and the Atlas trough to
the south-east, oriented parallel to the extension of the passive margin (Bracène
and de Lamotte, 2002; Fig. 12b, left panel). Early stages of compression in
the Late Lutetian resulted in a mild basin inversion in the Atlas trough.
Despite the presence of inherited rifting structures in the margin, it has
been suggested that the Tell passive margin behaved as a rigid body, and
far-field compressional stresses were transmitted along a deep detachment
through the crust (Bracène and de Lamotte, 2002). Strain subsequently
localised within the limits of the Atlas trough (Fig. 12b, left panel),
which is analogous to observations in EXP2B. In this experiment, initial
stages of deformation showed a partial inversion and localisation of forward
and back thrusts along the central extensional basin (Fig. 12b, right
panel), keeping the proximal crustal section undeformed. At later stages, a
new out-of-sequence thrust formed, and a pop-up structure developed in the
proximity of the moving wall. In the natural example, deformation during the
Miocene consisted of the accommodation of shortening with frontal thrusts in
the proximal area (Tell margin) and the creation of a typical accretionary
wedge, growing from the north-west towards the south-east (Fig. 12b, left panel). Ongoing
deformation in the Pleistocene triggered the reactivation of the partially
inverted structures that formed during the Late Lutetian in the Atlas
trough, and strain localisation was transferred again to these distal
regions of the foreland, exactly as observed in EXP2B. The amount of
shortening at this stage for the Atlas system is estimated to be between
15 % and 25 % (e.g. Teixell et al., 2003; Bracène and de Lamotte, 2002;
Beauchamp et al., 1999). Similarly, PIV-derived calculations from our models
indicate values of up to 26 % of cumulative strain prior to significant
crustal rupture. Differences in the initial conditions prior to inversion
can be pointed out between the Atlas system and EXP2B. However, the complex
first-order evolution, with special emphasis on the intermediate stage where
compressional stresses are transferred along the rigid crust and onto a
basin located further in the foreland of the accretionary wedge, remains
very similar between nature and our selected model. Comparison with other
models from this series also suggests there might be a threshold distance
between the indenter or orogenic front and the first extensional basin in
order to observe intense reactivation or not. In EXP1B, where a distal basin
was located away from the moving wall, first a series of contractional
faults developed in the proximity of the moving wall, and subsequently
deformation was also transferred towards the foreland. In contrast, when an
extensional basin was incorporated in the crust at a closer distance to the
moving wall (EXP2B), strain was first accommodated by basin contraction and
uplift, and then it jumped back to the proximity of the indenter.</p>
</sec>
<sec id="Ch1.S5.SS4.SSS3">
  <label>5.4.3</label><title>Basin uplift</title>
      <p id="d1e2429">Several components of basin inversion at a more local scale, identified in
the experiments during the stress build-up phase, can be directly compared
to previous observations of basin uplift from the geological record. The
Winterton High (southern North Sea) is a widely studied classic symmetrically inverted graben (e.g. Badley et al., 1989; Panien et al., 2005; Zwaan et
al., 2022). Analysis from seismic data has revealed that the basin infill
was compacted and vertically expelled from the original basin (Badley et
al., 1989), as observed in the distal basin of EXP1B (Fig. 13a). Due to the
experimental set-up in our models, compressional forces are only inbound from
one side of the basins, which explains the asymmetry in the basin
uplift and vertical upwarping, as<?pagebreak page230?> opposed to the symmetry observed in this
natural scenario. Reverse reactivation of the rift boundary faults has been
proposed for the Winterton High. We do not observe strong localisation along
the former normal faults in the models, but the limits of the area being
vertically uplifted are strongly determined by the location of the
extensional basin (Figs. 10 and 13a). It is also important to point out that
this graben has suffered contraction and uplift during stages of Cenozoic
compression that affected north-western Europe; despite not being present in
the immediate proximity of a fold-and-thrust belt, its reactivation
demonstrates that basin inversion can be associated with compressional forces
originating several hundred kilometres away from the affected area.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13" specific-use="star"><?xmltex \currentcnt{13}?><?xmltex \def\figurename{Figure}?><label>Figure 13</label><caption><p id="d1e2434">Side-by-side comparison between selected natural examples and
small-scale observations from experimental results. <bold>(a)</bold> Winterton High and
EXP1B distal basin. <bold>(b)</bold> Eastern Java Sea basin and EXP3B distal basin, early
stages. <bold>(c)</bold> Denison Trough and EXP3B distal basin, late stages. Red arrows
indicate compressional forces. The section highlighted in green in panel <bold>(c)</bold>
indicates pop-up structures being uplifted during inversion.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://se.copernicus.org/articles/14/213/2023/se-14-213-2023-f13.png"/>

          </fig>

      <p id="d1e2455">In natural scenarios, partially inverted grabens may also show strong
asymmetry when they are closer to the emplacement of the fold-and-thrust
belt, as interpreted for the eastern Java Sea basin, Southeast Asia. In this
natural example, compressional forces proceeding from the north<?pagebreak page231?> invert
wedge-shaped syn-extensional strata, resulting in harpoon or arrowhead
geometries (McClay, 1995). Similar structures
have been identified in our models, such as in the distal basin of EXP3B,
where contractional faulting localised along the weaker microbeads resulted
in an asymmetric harpoon geometry (Fig. 13b). Certain areas of the eastern Java
Sea basin show basin inversion due to reverse motion along the extensional
listric fault (Zwaan et al., 2022). However, analysis from seismic data
indicates that other inverted regions in the same basin localise
compressional deformation partially via normal fault reactivation and
partially via new frontal thrusts that originate in the proximity of the
normal faults (McClay, 1995) (Fig. 13b). This pattern is also observed in
our experiments; the unfavourable orientation of steep normal faults prevents
their contractional reactivation, but new thrusts always form in the
proximity of pre-existing extensional faults.</p>
      <p id="d1e2459">Another expression of an inverted graben has been identified in the Denison
Trough, eastern Australia (Korsch et al., 2009; Buiter et al., 2009).
Previous studies have estimated an uplift along the syn-rift strata
(<inline-formula><mml:math id="M130" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 400 m) that doubles that observed for the surrounding
basement rocks (<inline-formula><mml:math id="M131" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 200 m) (Buiter et al., 2009), as recognised
in several of the partially inverted basins in all our models (Fig. 9). In
the example of the Denison Trough, the fact that not only syn-rift strata were
uplifted but also a section of the crystalline basement surrounding the
basin is comparable to observations from the distal basin of EXP2B. In
this model, a back thrust formed in line with the rift boundary faults, while
a new frontal thrust originated at the same location from the detachment
layer but propagated towards the surface along the quartz sand layer (i.e.
proxy for crystalline basement) instead (Fig. 13b). Whether it is the
forward or backward thrust that reactivates border-normal faults remains
difficult to predict. Still, from our models we can suggest the following
boundary conditions that may lean towards one or the other: (a) occurrence
of a single extensional basin tends to always localise the frontal thrust
along the foreland-most border-normal fault and (b) when multiple extensional
basins are present in the foreland, the distance between them will be
the factor controlling how each basin will be inverted. The longer the
distance between the basins, the higher the probability of observing frontal
thrust localisation along the foreland-most normal faults.</p>
</sec>
</sec>
</sec>
<?pagebreak page232?><sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e2486">We draw the following conclusions from our series of analogue experiments
investigating the inversion of multiple basins in foreland fold-and-thrust
belts:
<list list-type="bullet"><list-item>
      <p id="d1e2491">Extensional basins proximal to the orogenic front tend to strongly localise
shortening, with frontal thrusts developing along weak basin and provoking
its contraction and uplift very early in the shortening stage.</p></list-item><list-item>
      <p id="d1e2495">Extensional basins will act as efficient stress localisers and will prevent
stress transfer beyond their location; no thrusts form beyond their position
until very advanced stages of deformation, in which the wedge taper angle
gets too high, and the system counteracts such instability by forming a new
frontal thrust beyond the extensional basin.</p></list-item><list-item>
      <p id="d1e2499">The presence of extensional basins seems to slightly increase the value of
the critical wedge taper angle, possibly associated with longer periods of
thrust <italic>localisation</italic> along the weak basins. Heterogeneities in
terms of physical properties in the interior of the wedge do not seem to
substantially affect the overall evolution of deformation.</p></list-item><list-item>
      <p id="d1e2506">Inversion of basins located between the other two basins tends to be short-lived,
as its brittleness is strongly dependent on the amount of overburden
and/or prograding thrust sheets, which hinder the inversion of extensional
structures by increasing the vertical principal stress (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p></list-item><list-item>
      <p id="d1e2522">The degree and type of inversion of extensional basins depends on both the
relative location and distance to the orogenic front and the presence of
another extensional basin between a given basin and the orogenic front.</p></list-item><list-item>
      <p id="d1e2526">Extensional basins located at large distances from the indenter show early
evidence of inversion, as interpreted in nature. While EXP1B showed the
maximum values of average cumulative strain within the basin prior to its
failure by shortening, we cannot extrapolate our observations to nature
because the amount of inversion will also depend on factors such as the
degree of interplate coupling and on the structural, thermal, and/or
compositional conditions of the lithosphere, variables that are not modelled here. Although we cannot define a threshold distance or define the
nature of the basin inversion for distal extensional basins in the foreland
of fold-and-thrust belts, our analogue models provide conceptual models for
comparison with natural examples.</p></list-item></list></p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2533">Images, videos, and selected raw PIV-exported files are freely available as a
data publication deposited in the GFZ Data Services database (<ext-link xlink:href="https://doi.org/10.5880/fidgeo.2023.011" ext-link-type="DOI">10.5880/fidgeo.2023.011</ext-link>, Molnar and
Buiter, 2023).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2542">NM and SB planned and developed the experimental plan. NM performed the
experiments, and NM and SB analysed and interpreted the model results. NM wrote
the initial manuscript draft, then both NM and SB reviewed and edited the
manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2548">At least one of the (co-)authors is a member of the editorial board of <italic>Solid Earth</italic>. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2557">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="d1e2563">This article is part of the special issue “Analogue modelling of basin inversion”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2569">We would like to thank Werner Kraus for his endless support in the laboratory
and to Lina Gotzen and Jan Wagner for their invaluable assistance during
laboratory experiments and for the fruitful discussions when analysing the
results. Pablo Granado and Daniele Maestrelli are sincerely thanked for
their constructive comments that helped improve the manuscript considerably.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2574">This paper was edited by Riccardo Reitano and reviewed by Daniele Maestrelli and Pablo Granado.</p>
  </notes><ref-list>
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