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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-meta>
<article-id pub-id-type="publisher-id">845126</article-id>
<article-id pub-id-type="doi">10.3389/feart.2022.845126</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Topographic Response of Hinterland Basins in Tibet to the India&#x2013;Asia Convergence: 3D Thermo-Mechanical Modeling</article-title>
<alt-title alt-title-type="left-running-head">Zhang et al.</alt-title>
<alt-title alt-title-type="right-running-head">Topographic Response of Hinterland Basins</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Pengpeng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1323015/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Chen</surname>
<given-names>Lin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1411150/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Xiao</surname>
<given-names>Wenjiao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/114119/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Ji&#x2019;en</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1359820/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>State Key Laboratory of Lithospheric Evolution</institution>, <institution>Institute of Geology and Geophysics</institution>, <institution>Chinese Academy of Sciences</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Institute of Geology and Planetary Sciences</institution>, <institution>University of Chinese Academy of Sciences</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Xinjiang Research Center for Mineral Resources</institution>, <institution>Xinjiang Institute of Ecology and Geography</institution>, <institution>Chinese Academy of Sciences</institution>, <addr-line>Urumqi</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1415252/overview">Manuele Faccenda</ext-link>, Universit&#xe0; Padova, Italy</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1628967/overview">Andrea Piccolo</ext-link>, University of Bayreuth, Germany</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/290203/overview">Chenglong Deng</ext-link>, Institute of Geology and Geophysics (CAS), China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Lin Chen, <email>chenlin@mail.iggcas.ac.cn&#x200a;</email>; Wenjiao Xiao, <email>Wj-xiao@mail.iggcas.ac.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Structural Geology and Tectonics, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>09</day>
<month>05</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>845126</elocation-id>
<history>
<date date-type="received">
<day>29</day>
<month>12</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>06</day>
<month>04</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Zhang, Chen, Xiao and Zhang.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Zhang, Chen, Xiao and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>A number of basins have developed in Tibet since the early stages of the India&#x2013;Asia collision, and now, they have become integral parts of the Tibetan Plateau. Geophysical and geochemical data reveal that these basins are currently characterized either by strong or weak basements. However, it remains unclear how these hinterland basins evolved during the India&#x2013;Asia collision and how they affected the post-collisional growth of the Tibetan Plateau. Here, we use 3D thermo-mechanical simulations to investigate the topographic response of a strength-varying hinterland basin imbedded in an orogenic plateau under the horizontal compression condition. Our results show that a strong hinterland basin experiences little deformation and develops into a lowland with respect to the surrounding plateau at the early stages of the collision. The lowland gradually shrinks and survives in the interior of the plateau for &#x223c;30&#x2013;40&#xa0;Myr before merging into the plateau. In contrast, a weak hinterland basin uplifts soon after the initial collision and develops into a highland after &#x223c;20&#xa0;Myr of convergence. Topographic analysis reveals that the strong hinterland basin experiences an evident elevation drop after &#x223c;20&#x2013;30&#xa0;Myr of convergence, followed by a rapid uplift. After compiling the paleoelevation data, we proposed that the Tibetan Plateau experienced a four-stage surface uplift, which was characterized by 1) the Gangdese and central watershed highlands isolating three lowlands during the Eocene, 2) the central lowland experiencing an elevation drop of &#x223c;2000 m during the Oligocene, 3) the central lowland suffering a rapid uplift and merging into the Tibetan Plateau in the Early Miocene, and 4) the south and north lowlands rising and developing into a plateau similar to the modern Tibetan Plateau since the Middle Miocene.</p>
</abstract>
<kwd-group>
<kwd>numerical modeling</kwd>
<kwd>Tibetan Plateau</kwd>
<kwd>topography</kwd>
<kwd>uplift history</kwd>
<kwd>Lunpola Basin</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The modern Tibetan Plateau is the most extensive elevated surface on the earth, characterized by a high elevation and a flat-topped landscape. However, a number of low-elevation sedimentary basins developed in Tibet during the Cenozoic era (<xref ref-type="bibr" rid="B44">Kapp et al., 2005</xref>; <xref ref-type="bibr" rid="B88">Zhang et al., 2010</xref>; <xref ref-type="bibr" rid="B19">Deng and Ding, 2015</xref>; <xref ref-type="bibr" rid="B43">Kapp and DeCelles, 2019</xref>) (<xref ref-type="fig" rid="F1">Figure 1</xref>). Sedimentary records and paleoelevation data reveal that many of these basins survived for a long period of time and maintained a low elevation before merging into the Tibetan Plateau. For example, the Lunpola Basin, located in central Tibet, contains &#x3e;4,000 m-thick of lacustrine sedimentary layers which deposited during the Middle Eocene to the Early Miocene (<xref ref-type="bibr" rid="B69">Sun et al., 2014</xref>; <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>). Fish and palm fossils indicate that the Lunpola Basin was in a warm and humid environment during the late Oligocene, implying an elevation &#x3c;2,300&#xa0;m (<xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>; <xref ref-type="bibr" rid="B26">Farnsworth et al., 2018</xref>). In the neighboring Nima Basin, the sedimentary layers were deposited from the Late Cretaceous to the Early Miocene (<xref ref-type="bibr" rid="B18">DeCelles et al., 2007</xref>; <xref ref-type="bibr" rid="B42">Kapp et al., 2007</xref>), and plants fossils indicate an elevation no more than 1,000&#xa0;m during the late Oligocene (<xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>; <xref ref-type="bibr" rid="B94">Liu et al., 2019</xref>). In the north-central Tibetan Plateau, the Hoh Xil Basin has a series of sedimentary sequences developed from the Middle Eocene to Early Miocene (<xref ref-type="bibr" rid="B49">Liu et al., 2003</xref>; <xref ref-type="bibr" rid="B73">Wang et al., 2008</xref>), and the leaf fossils indicate an elevation less than 3,000&#xa0;m during the Early Miocene (<xref ref-type="bibr" rid="B68">Sun et al., 2015</xref>). In contrast, there were some other basins that had uplifted and merged into the plateau soon after the India&#x2013;Asia collision. For example, the sedimentary strata in the Linzhou Basin ceased to deposit during the Late Eocene (<xref ref-type="bibr" rid="B31">He et al., 2007</xref>; <xref ref-type="bibr" rid="B23">Ding et al., 2014</xref>), and the oxygen isotope indicates that the Linzhou Basin had uplifted to attain its current elevation in the Early Eocene (<xref ref-type="bibr" rid="B23">Ding et al., 2014</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Simplified geological map of the Tibetan Plateau. The black curve represents the main frontal thrust (MFT). The blue dashed curves delineate the suture zones, and the colored regions are different terrains within the Tibetan Plateau (<xref ref-type="bibr" rid="B86">Yin and Harrison., 2000</xref>). Yellow dotted areas are Paleocene&#x2013;Eocene basins (<xref ref-type="bibr" rid="B88">Zhang et al., 2010</xref>; <xref ref-type="bibr" rid="B96">Zhang et al., 2013</xref>). The white dashed box outlines the area of <xref ref-type="fig" rid="F2">Figure 2A</xref>. IYS, Indus&#x2013;Yarlung suture zone; BNS, Bangong&#x2013;Nujiang suture zone; JS, Jinsha suture zone; AMS, Anyimaqen&#x2013;Muztagh suture zone; SQS, South Qilian suture; NQS, North Qilian suture; NL, Namling Basin; LZ, Linzhou Basin; LPL, Lunpola Basin; NM, Nima Basin; GZ, Gerze Basin; GJ, Gonjo Basin; NQ, Niangqian Basin; TTH, Tuotuohe Basin; HX, Hoh Xil Basin; SH, Shuanghu Basin; SQT, South Qiangtang Basin; NQT, North Qiangtang Basin; QDM, Qaidam Basin.</p>
</caption>
<graphic xlink:href="feart-10-845126-g001.tif"/>
</fig>
<p>Recent geophysical investigations show that some basins inside the Tibetan Plateau have relatively high seismic velocity crusts with respect to the surroundings (<xref ref-type="bibr" rid="B85">Yang et al., 2012</xref>; <xref ref-type="bibr" rid="B90">Zhao et al., 2013</xref>; <xref ref-type="bibr" rid="B8">Chen M. et al., 2017</xref>; and <xref ref-type="bibr" rid="B37">Huang et al., 2020</xref>) (<xref ref-type="fig" rid="F2">Figure 2A</xref>), such as the Lunpola and Nima basins, implying relatively strong basements beneath these basins. However, the others basins exhibit a low velocity anomalies in the crust (<xref ref-type="fig" rid="F2">Figure 2A</xref>), such as the Linzhou and the Hoh Xil basins, implying soft basements beneath them. Similar differences also manifest in geochemical data. For example, the Lunpola and Nima basins in the Lhasa terrane exhibit a negative Hf isotopic ratio of felsic igneous rocks (<xref ref-type="bibr" rid="B91">Zhu et al., 2011</xref>; <xref ref-type="bibr" rid="B34">Hou et al., 2015</xref>; <xref ref-type="bibr" rid="B35">Hou et al., 2020</xref>), correlated with the fast velocity zones (<xref ref-type="fig" rid="F2">Figure 2B</xref>), indicative of a strong basement underneath them. In contrast, other basins, such as the Linzhou and Namling basins, display positive Hf isotopic values (<xref ref-type="fig" rid="F2">Figure 2B</xref>), correlated with the slow velocity zones, implying a relatively weak basement beneath them. Therefore, both the available geophysical and geochemical data suggest that the strength of the hinterland basins in Tibet varies from region to region.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Shear wave velocity of the crust and Hf isotopic mapping. <bold>(A)</bold> Shear wave velocity at a 30&#xa0;km depth in the region shown in <xref ref-type="fig" rid="F1">Figure 1</xref> (<xref ref-type="bibr" rid="B85">Yang et al., 2012</xref>). Red curves delineate the hinterland basins with a relatively fast velocity. Blue curves delineate the hinterland basins with a relatively slow velocity. <bold>(B)</bold> Hf isotopic mapping showing the spatial variation of zircon &#x3b5;Hf(t) values for felsic igneous rocks in the Lhasa terrain (<xref ref-type="bibr" rid="B34">Hou et al., 2015</xref>). The region is outlined by a white dashed curve in <bold>(A)</bold>. SLS, southern Lhasa subterrane; CLS, central Lhasa subterrane; and NLS, northern Lhasa subterrane.</p>
</caption>
<graphic xlink:href="feart-10-845126-g002.tif"/>
</fig>
<p>Over the past several decades, a number of modeling studies have investigated the role of lateral lithospheric strength heterogeneities in the deformation pattern and growth of the orogenic plateau (<xref ref-type="bibr" rid="B24">England and Houseman, 1985</xref>; <xref ref-type="bibr" rid="B12">Cook and Royden, 2008</xref>; <xref ref-type="bibr" rid="B17">Dayem et al., 2009</xref>; <xref ref-type="bibr" rid="B63">Sokoutis and Willingshofer, 2011</xref>; <xref ref-type="bibr" rid="B7">Chen L. et al., 2017</xref>; <xref ref-type="bibr" rid="B2">Bischoff and Flesch, 2019</xref>; and <xref ref-type="bibr" rid="B9">Chen et al., 2020</xref>; <xref ref-type="bibr" rid="B81">Xie et al., 2021</xref>). These studies can be classified into two different categories: 1) weak lithosphere flanked by strong domains, and 2) strong block imbedded into a weak lithosphere. Most of these studies focus on the case of a weak domain sandwiched by a strong lithosphere (<xref ref-type="bibr" rid="B78">Willingshofer et al., 2005</xref>; <xref ref-type="bibr" rid="B63">Sokoutis and Willingshofer, 2011</xref>; <xref ref-type="bibr" rid="B9">Chen et al., 2020</xref>; and <xref ref-type="bibr" rid="B81">Xie et al., 2021</xref>). <xref ref-type="bibr" rid="B78">Willingshofer et al. (2005)</xref> used the lithosphere-scale analogue model to show that the strength contrast between the weak zone and surrounding lithosphere controls the scope and the shape of the collision orogen. <xref ref-type="bibr" rid="B63">Sokoutis and Willingshofer, (2011)</xref> demonstrated that the geometries and the decoupling degree of the weak zone play an important role in the geometric and topographic evolution of the mountain belts. <xref ref-type="bibr" rid="B9">Chen et al. (2020)</xref> using 3D numerical models revealed that the pre-existing weaknesses within the upper plate can alter the deformation propagation and the surface uplift pattern of the orogenic plateau. <xref ref-type="bibr" rid="B81">Xie et al. (2021)</xref> demonstrated that the crustal pre-existing weakness in the compressed lithosphere facilitates the local surface uplift at an early time and generates a second local surface uplift in a later time. In contrast, only a few studies investigated how the strong blocks in a weak lithosphere affect the continental deformation and surface topography (<xref ref-type="bibr" rid="B24">England and Houseman, 1985</xref>; <xref ref-type="bibr" rid="B12">Cook and Royden, 2008</xref>; <xref ref-type="bibr" rid="B17">Dayem et al., 2009</xref>; and <xref ref-type="bibr" rid="B5">Calignano et al., 2015</xref>). <xref ref-type="bibr" rid="B24">England and Houseman, (1985)</xref> used the thin viscous sheet model showed that the deformation is strongly concentrated around the strong crust and high mountain rise along its margins. <xref ref-type="bibr" rid="B12">Cook and Royden, (2008)</xref> built up a 3D numerical experiment demonstrating that the existence of a strong lower crust in the foreland slows the plateau propagation speed and develops a steep plateau margin. <xref ref-type="bibr" rid="B17">Dayem et al. (2009)</xref> found that the strong block&#x2019;s oblique orientation significantly affects the localization of shearing deformation. <xref ref-type="bibr" rid="B5">Calignano et al. (2015)</xref> using analogue models revealed that the depth of the strong domain strongly impacts the deformation patterns and topographic growth at the margins. In summary, these studies mainly concentrate on the deformation, localization, and surface topography induced by the lateral lithospheric strength heterogeneities. However, how the hinterland basins evolved during the India&#x2013;Asia convergence and how they affected the post-collisional growth of the Tibetan Plateau remain poorly understood.</p>
<p>In this study, we use 3D thermo-mechanical modeling to explore the topographic response of a hinterland basin to continental collision. We focus on the topographic evolution of a strength-varying basin imbedded in an orogenic plateau which is subject to horizontal compression and its influence on the plateau growth. For simplification, we do not include all of the hinterland basins in Tibet in the model. Instead, we set a single basin to explore the basin&#x2019;s topographic evolution to the India&#x2013;Asia collision and its influence on the growth of the Tibetan Plateau. We first describe the methodology and model setup. This is followed by presenting the simulation results of models in different situations. We then analyze the modeling results and summarize the topographic features and uplift history of basins inside the plateau. Finally, we apply the modeling results to understanding the uplift history of the Lunpola and Hoh Xil basins and discuss the growth pattern of the Tibetan Plateau.</p>
</sec>
<sec id="s2">
<title>Modeling Approach</title>
<p>Three-dimensional numerical simulations are carried out using the thermo-mechanical code I3ELVIS (<xref ref-type="bibr" rid="B28">Gerya, 2010</xref>). The code combines the finite difference method and the marker-in-cell technique to solve the continuity, momentum, and energy conservation equations on a staggered Eulerian grid (<xref ref-type="bibr" rid="B28">Gerya, 2010</xref>). It uses visco-plastic rheologies to describe the mechanical behavior of the rocks and considers thermo-mechanical properties for different rocks. These characteristics, together with an interior free surface, enable the simulation of a large-scale deformation and topographic evolution associated with continental collision.</p>
<sec id="s2-1">
<title>Governing Equations</title>
<p>The incompressible continuity equation, which accounts for mass conservation using the Boussineq approximation, is as follows:<disp-formula id="e1">
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</inline-formula> is the spatial coordinate.</p>
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<label>(3)</label>
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<p>The deviatoric stress tensor <inline-formula id="inf16">
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</inline-formula> and the strain rate tensor <inline-formula id="inf18">
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<label>(4)</label>
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<label>(5)</label>
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</p>
</sec>
<sec id="s2-2">
<title>Rheology and Partial Melting</title>
<p>The code considers the viscous and plastic rheologies, as well as the thermomechanical properties of different rocks. The lithospheric strength is determined by a combination of ductile and brittle deformation mechanisms at a mountain building time scale. The brittle deformation follows the Drucker&#x2013;Prager yield criterion, which describes the linear relationship of the material resistance on the total pressure (<xref ref-type="bibr" rid="B57">Ranalli, 1995</xref>):<disp-formula id="e6">
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</mml:mtable>
</mml:math>
<label>(6)</label>
</disp-formula>
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<mml:mi>d</mml:mi>
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<mml:mrow>
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</mml:msub>
</mml:mrow>
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<mml:mo>,</mml:mo>
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</mml:math>
<label>(7)</label>
</disp-formula>where <inline-formula id="inf19">
<mml:math id="m26">
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</mml:mrow>
</mml:msub>
</mml:mrow>
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</inline-formula> is the yield stress, P is the dynamic pressure, <inline-formula id="inf20">
<mml:math id="m27">
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<mml:math id="m29">
<mml:mrow>
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<mml:mrow>
<mml:msub>
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</mml:mrow>
</mml:math>
</inline-formula> (stands for dry rocks), <inline-formula id="inf23">
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</inline-formula> is the pore fluid pressure factor and <inline-formula id="inf24">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
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</mml:mrow>
</mml:math>
</inline-formula> is the second invariant of the strain rate, and <inline-formula id="inf25">
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<mml:mrow>
<mml:msub>
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<mml:mrow>
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<mml:mi>i</mml:mi>
<mml:mi>c</mml:mi>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the viscosity for plastic rheology.</p>
<p>The viscosity for ductile creep takes the form (<xref ref-type="bibr" rid="B1">Beaumont et al., 2004</xref>)<disp-formula id="e8">
<mml:math id="m33">
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<mml:mo>&#x2061;</mml:mo>
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<mml:mi>E</mml:mi>
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</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>P</mml:mi>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:msup>
<mml:mi>B</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>f</mml:mi>
<mml:mi mathvariant="normal">&#x2217;</mml:mi>
<mml:msubsup>
<mml:mi>A</mml:mi>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mi>n</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:msubsup>
<mml:mo>,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:math>
<label>(8)</label>
</disp-formula>where <inline-formula id="inf26">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the activation energy, <inline-formula id="inf27">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the activation volume, n is the stress exponent, <inline-formula id="inf28">
<mml:math id="m36">
<mml:mi>R</mml:mi>
</mml:math>
</inline-formula> is the gas constant, <inline-formula id="inf29">
<mml:math id="m37">
<mml:mi>T</mml:mi>
</mml:math>
</inline-formula> is the absolute temperature, <inline-formula id="inf30">
<mml:math id="m38">
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the material constant, and <inline-formula id="inf31">
<mml:math id="m39">
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a pre-exponential scaling factor. The factor <inline-formula id="inf32">
<mml:math id="m40">
<mml:mi>f</mml:mi>
</mml:math>
</inline-formula> is applied to scale the effective ductile viscosity calculated from the reference flow laws.</p>
<p>The effective viscosity <inline-formula id="inf33">
<mml:math id="m41">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is defined as the minimum value between the plastic and ductile viscosities (<xref ref-type="bibr" rid="B57">Ranalli, 1995</xref>):<disp-formula id="e9">
<mml:math id="m42">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>min</mml:mi>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>Laboratory-determined flow laws of &#x2018;wet quartzite,&#x2019; &#x2018;plagioclase An<sub>75</sub>,&#x2019; and &#x2018;dry olivine&#x2019; are used for the continental upper crust, lower crust, and asthenospheric mantle, respectively (<xref ref-type="bibr" rid="B57">Ranalli, 1995</xref>). Note that a modulated &#x2018;plagioclase An<sub>75</sub>&#x2019; is used for the lower crust of the hinterland basin. The detailed rheological parameters used in this study are shown in <xref ref-type="table" rid="T1">Table 1</xref>. We set a lower cutoff viscosity of 10<sup>18</sup>&#xa0;Pa&#xa0;s and an upper cutoff viscosity of 10<sup>26</sup>&#xa0;Pa&#xa0;s for all rocks.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Material properties used in the numerical experiments.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Material</th>
<th align="center">
<inline-formula id="inf34">
<mml:math id="m43">
<mml:mrow>
<mml:msub>
<mml:mtext>&#x3c1;</mml:mtext>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kg/m<sup>3</sup>)</th>
<th align="center">K (W/m/K)</th>
<th align="center">
<inline-formula id="inf35">
<mml:math id="m44">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (K)</th>
<th align="center">
<inline-formula id="inf36">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (K)</th>
<th align="center">H<sub>L</sub> (kJ/kg)</th>
<th align="center">H<sub>r</sub> (<inline-formula id="inf37">
<mml:math id="m46">
<mml:mtext>&#x3bc;</mml:mtext>
</mml:math>
</inline-formula> W/m<sup>3</sup>)</th>
<th align="center">Flow Law</th>
<th align="center"> A<sub>D</sub>(<inline-formula id="inf38">
<mml:math id="m47">
<mml:mrow>
<mml:msup>
<mml:mtext>Pa</mml:mtext>
<mml:mi>n</mml:mi>
</mml:msup>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>)</th>
<th align="center">n</th>
<th align="center">
<inline-formula id="inf40">
<mml:math id="m49">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (J)</th>
<th align="center">
<inline-formula id="inf41">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf42">
<mml:math id="m51">
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mtext>J</mml:mtext>
<mml:mo>/</mml:mo>
<mml:mtext>bar</mml:mtext>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">
<inline-formula id="inf43">
<mml:math id="m52">
<mml:mrow>
<mml:mtext>sin</mml:mtext>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mtext>&#x3c6;</mml:mtext>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">C (Mpa)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">UCC</td>
<td align="center">2700 (S)</td>
<td rowspan="2" align="center">K1</td>
<td rowspan="2" align="center">TS1</td>
<td rowspan="2" align="center">TL1</td>
<td rowspan="2" align="center">300</td>
<td rowspan="2" align="char" char=".">1.5</td>
<td rowspan="2" align="center">WQZ</td>
<td rowspan="2" align="char" char=".">1.97<inline-formula id="inf44">
<mml:math id="m53">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>17</sup>
</td>
<td rowspan="2" align="char" char=".">2.3</td>
<td rowspan="2" align="char" char=".">1.54<inline-formula id="inf45">
<mml:math id="m54">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>5</sup>
</td>
<td rowspan="2" align="char" char=".">0.0</td>
<td rowspan="2" align="char" char=".">0.15</td>
<td rowspan="2" align="char" char=".">1</td>
</tr>
<tr>
<td align="center">2400 (M)</td>
</tr>
<tr>
<td rowspan="2" align="left">LCC</td>
<td align="center">12,800 (S)</td>
<td rowspan="2" align="center">K2</td>
<td rowspan="2" align="center">TS2</td>
<td rowspan="2" align="center">TL2</td>
<td rowspan="2" align="center">380</td>
<td rowspan="2" align="char" char=".">0.5</td>
<td rowspan="2" align="center">PL</td>
<td rowspan="2" align="char" char=".">4.80<inline-formula id="inf46">
<mml:math id="m55">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>22</sup>
</td>
<td rowspan="2" align="char" char=".">3.2</td>
<td rowspan="2" align="char" char=".">2.38<inline-formula id="inf47">
<mml:math id="m56">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>5</sup>
</td>
<td rowspan="2" align="char" char=".">0.0</td>
<td rowspan="2" align="char" char=".">0.15</td>
<td rowspan="2" align="char" char=".">1</td>
</tr>
<tr>
<td align="center">2500 (M)</td>
</tr>
<tr>
<td rowspan="2" align="left">Mantle</td>
<td align="center">3300 (S)</td>
<td rowspan="2" align="center">K3</td>
<td rowspan="2" align="center">TS3</td>
<td rowspan="2" align="center">TL3</td>
<td rowspan="2" align="center">400</td>
<td rowspan="2" align="char" char=".">0.022</td>
<td rowspan="2" align="center">DOL</td>
<td rowspan="2" align="char" char=".">3.98<inline-formula id="inf48">
<mml:math id="m57">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>16</sup>
</td>
<td rowspan="2" align="char" char=".">3.5</td>
<td rowspan="2" align="char" char=".">5.32<inline-formula id="inf49">
<mml:math id="m58">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>5</sup>
</td>
<td rowspan="2" align="char" char=".">0.8</td>
<td rowspan="2" align="char" char=".">0.60</td>
<td rowspan="2" align="char" char=".">1</td>
</tr>
<tr>
<td align="center">2700 (M)</td>
</tr>
<tr>
<td rowspan="2" align="left">WZ</td>
<td align="center">3300 (S)</td>
<td rowspan="2" align="center">K3</td>
<td rowspan="2" align="center">&#x2014;</td>
<td rowspan="2" align="center">&#x2014;</td>
<td rowspan="2" align="center">400</td>
<td rowspan="2" align="char" char=".">0.022</td>
<td rowspan="2" align="center">WOL</td>
<td rowspan="2" align="char" char=".">5.01<inline-formula id="inf50">
<mml:math id="m59">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>20</sup>
</td>
<td rowspan="2" align="char" char=".">4.0</td>
<td rowspan="2" align="char" char=".">4.70<inline-formula id="inf51">
<mml:math id="m60">
<mml:mo>&#xd7;</mml:mo>
</mml:math>
</inline-formula>10<sup>5</sup>
</td>
<td rowspan="2" align="char" char=".">0.8</td>
<td rowspan="2" align="char" char=".">0.00</td>
<td rowspan="2" align="char" char=".">1</td>
</tr>
<tr>
<td align="center">2700 (M)</td>
</tr>
<tr>
<td align="left">Ref.s</td>
<td align="center">1,2</td>
<td align="center">3</td>
<td align="center">4,5,6,7,8</td>
<td align="center">4,8</td>
<td align="center">1,2</td>
<td align="char" char=".">1</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>UCC, upper continental crust; LCC, lower continental crust; WZ, weak zone; S, solid; M, molten. K1 &#x3d; [0.64 &#x2b; 807/(T&#x2b;77)]; K2 &#x3d; [1.18 &#x2b; 474/(T&#x2b;77)]; K3 &#x3d; [0.73 &#x2b; 1293/(T&#x2b;77)]&#xd7; (1 &#x2b; 0.00004P). TS1 &#x3d; 889 &#x2b; 17,900/(P&#x2b;54)&#x2b;20,200/(P&#x2b;54)<sup>2</sup>&#xa0;at&#xa0;<italic>p</italic> &#x3c; 1200&#xa0;MPa, or 831 &#x2b; 0.06P at <italic>p</italic> &#x3e; 1200&#xa0;MPa; TL1 &#x3d; 1262 &#x2b; 0.09P; TS2 &#x3d; 1327.15 &#x2b; 0.0906P; TL2 &#x3d; 1423 &#x2b; 0.105P. TS3 and TL3 follow the melting model of <xref ref-type="bibr" rid="B45">Katz et al. (2003)</xref>. WQZ, wet quartzite; PL, Plagioclase (An75); DOL, dry olivine; WOL, Wet Olivine. 1, <xref ref-type="bibr" rid="B71">Turcotte and Schubert (2002)</xref>; 2, <xref ref-type="bibr" rid="B3">Bittner and Schmeling (1995)</xref>; 3, <xref ref-type="bibr" rid="B11">Clauser and Huenges (1995)</xref>; 4, <xref ref-type="bibr" rid="B61">Schmidt and Poli (1998)</xref>; 5, <xref ref-type="bibr" rid="B32">Hess (1989)</xref>; 6, <xref ref-type="bibr" rid="B33">Hirschmann (2000)</xref>; 7, <xref ref-type="bibr" rid="B41">Johannes (1985)</xref>; 8, <xref ref-type="bibr" rid="B55">Poli and Schmidt (2002)</xref>.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The degree of the partial melting of rocks is calculated by P-T&#x2013;dependent solidus and liquidus curves (<xref ref-type="table" rid="T1">Table 1</xref>). The volumetric fraction <inline-formula id="inf52">
<mml:math id="m61">
<mml:mi>M</mml:mi>
</mml:math>
</inline-formula> of the melt is assumed to linearly increase between the solidus and liquidus temperatures at a given pressure (<xref ref-type="bibr" rid="B4">Burg and Gerya, 2005</xref>):<disp-formula id="e10">
<mml:math id="m62">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>w</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
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<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi>w</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
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</mml:mtd>
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</mml:mtable>
</mml:mrow>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>where <inline-formula id="inf53">
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<mml:mrow>
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</inline-formula> are the solidus and liquidus temperatures of the rocks, respectively.</p>
<p>The effective density of partially molten rocks changes with the amount of melt fraction and <italic>P-T</italic> conditions:<disp-formula id="e11">
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</mml:math>
<label>(11)</label>
</disp-formula>
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<mml:mo>)</mml:mo>
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<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>where <inline-formula id="inf55">
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</mml:mrow>
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</inline-formula> and <inline-formula id="inf56">
<mml:math id="m68">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
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<mml:mi>n</mml:mi>
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</mml:msub>
</mml:mrow>
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</inline-formula> are the densities of the solid and molten rock, respectively; <inline-formula id="inf57">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the density at <inline-formula id="inf58">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
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<mml:mn>0.1</mml:mn>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> MPa and <inline-formula id="inf59">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>298</mml:mn>
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</mml:math>
</inline-formula> K; and <inline-formula id="inf60">
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<mml:mi>&#x3b1;</mml:mi>
</mml:math>
</inline-formula> <inline-formula id="inf61">
<mml:math id="m73">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#xd7;</mml:mo>
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<mml:mn>10</mml:mn>
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</inline-formula> and <inline-formula id="inf62">
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</inline-formula> <inline-formula id="inf63">
<mml:math id="m75">
<mml:mrow>
<mml:mrow>
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<mml:mn>10</mml:mn>
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<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mtext>MPa</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
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<mml:mo>)</mml:mo>
</mml:mrow>
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</mml:math>
</inline-formula> are the thermal expansion and compressibility coefficients, respectively.</p>
<p>The effects of latent heating generated by melting or crystallization are accounted for by an increased effective heat capacity <inline-formula id="inf64">
<mml:math id="m76">
<mml:mrow>
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</mml:mrow>
<mml:mo>)</mml:mo>
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</mml:mrow>
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</inline-formula> and thermal expansion <inline-formula id="inf65">
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</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B4">Burg and Gerya, 2005</xref>):<disp-formula id="e13">
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<mml:mrow>
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<label>(13)</label>
</disp-formula>
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<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>where <inline-formula id="inf66">
<mml:math id="m80">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the heat capacity of the solid rock and <inline-formula id="inf67">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the latent heat of the melting rock (<xref ref-type="bibr" rid="B4">Burg and Gerya, 2005</xref>).</p>
</sec>
<sec id="s2-3">
<title>Model Setup</title>
<p>We investigate the topographic response of a hinterland basin imbedded in the upper plate under horizontal compression condition. The computational domain is a 4000 &#xd7; 200 &#xd7; 4000&#xa0;km (in the order of x, y, and z) Cartesian box, and is resolved by 501 &#xd7; 101&#xd7;501 grid points with a uniform resolution of 8 &#xd7; 2 &#xd7; 8&#xa0;km (<xref ref-type="fig" rid="F3">Figure 3</xref>). There are approximately 200&#xa0;million Lagrangian markers randomly distributed inside the box, which are used to advect the physical properties. As <xref ref-type="bibr" rid="B7">Chen L. et al. (2017)</xref> demonstrated that the lower crust rheology plays an important role in the deformation of the continental lithosphere. We vary the scaling factor <italic>f</italic> (<xref ref-type="disp-formula" rid="e8">Eq. (8)</xref>) of the lower crust flow law to represent the different strengths of the basin inside the plateau. Previous studies indicate that the composition of the continental lower crust ranges from basaltic to andesitic (<xref ref-type="bibr" rid="B30">Hacker et al., 2015</xref>) and the basaltic lower crust is &#x223c;1 order of a magnitude more viscous than the andesitic lower crust (<xref ref-type="bibr" rid="B62">Shinevar et al., 2015</xref>). Therefore, in the reference model, we set a rectangle basin with the scaling factor f &#x3d; 10, which means that the viscosity of its lower crust is 10 times higher than that of the surrounding regions. The basin is 500 &#xd7; 800&#xa0;km in size, and its location is varied in the study.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Model setup. <bold>(A)</bold> the 3D model domain (4,000 &#xd7; 200 &#xd7; 4,000&#xa0;km). The colors covering the top of the model indicate the magnitude of the topography as shown in the vertical color bar. The cyan-colored area represents the strong basin. The left bottom chart shows the convergence rate applied in this study and previous estimates (Cande and Stegman; <xref ref-type="bibr" rid="B13">Copley et al., 2010</xref>; <xref ref-type="bibr" rid="B52">Molnar and Stock, 2009</xref>). <bold>(B)</bold> The composition field along the section x &#x3d; 2000&#xa0;km, as denoted by the red line in <xref ref-type="fig" rid="F2">Figure 2A</xref>. And viscosity contrast between strong basin and surrounding areas whose localities are shown as P1 and P2 in <bold>(A)</bold>. The blue curve represents the viscosity profile of the strong basin, and the red curve represents the viscosity profile of the surrounding areas. Composition numbers represent different rock types: 0- sticky air; 5- Asian upper crust; 6- Asian lower crust; 7- Indian upper crust; 8- Indian lower crust; 9- Asian lithospheric mantle; 10- asthenosphere; 12- weak zone; 14- Indian lithospheric mantle; and 16- strong lower crust of the basin.</p>
</caption>
<graphic xlink:href="feart-10-845126-g003.tif"/>
</fig>
<p>In the model, back and side walls are set to be free slip. We take 55&#xa0;Ma as the initial continental collision time (<xref ref-type="bibr" rid="B52">Molnar and Stock, 2009</xref>; <xref ref-type="bibr" rid="B36">Hu et al., 2016</xref>), which corresponds to the onset of the model. A starting convergence rate of 10&#xa0;cm/yr is imposed at the central region of the front wall (1000 &#x3c; X &#x3c; 3000). It gradually decreases to 5&#xa0;cm/yr after 5&#xa0;Ma, and is fixed at 5&#xa0;cm/yr henceforth. The time-dependent convergence rate used here is generally consistent with the estimates from plate reconstructions or paleomagnetic data (<xref ref-type="bibr" rid="B52">Molnar and Stock, 2009</xref>; <xref ref-type="bibr" rid="B13">Copley et al., 2010</xref>; and <xref ref-type="bibr" rid="B6">Cande and Stegman, 2011</xref>) (<xref ref-type="fig" rid="F3">Figure 3A</xref>). It should be noted that when the India&#x2013;Asia collision began is still controversial. Recently, <xref ref-type="bibr" rid="B80">Xiao et al. (2017)</xref> proposed that the terminal India&#x2013;Asia collision occurred after 14&#xa0;Ma based on the anatomy of composition and tectonic nature of the Himalayas, which supports a multi-stage collision process between India and Asia. The material influx at the front boundary is limited in the central region to simulate the indentation of the Indian continent, beside which (x &#x3d; 0&#x2013;1000&#xa0;km and x &#x3d; 3000&#x2013;4000&#xa0;km) the free slip condition applies. To keep mass balance within the layer, a constant outflow velocity is applied at the upper boundary, which is determined by <inline-formula id="inf68">
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<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>z</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf69">
<mml:math id="m83">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the thickness of the sticky air; <inline-formula id="inf70">
<mml:math id="m84">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf71">
<mml:math id="m85">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>z</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the model widths in the <italic>x</italic> and <italic>z</italic> directions, respectively; and <inline-formula id="inf72">
<mml:math id="m86">
<mml:mrow>
<mml:msubsup>
<mml:mi>W</mml:mi>
<mml:mi>x</mml:mi>
<mml:mo>&#x27;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is the horizontal range on the front wall that the convergence is imposed. At the bottom boundary, an infinity-like external free slip boundary condition is imposed (<xref ref-type="bibr" rid="B4">Burg and Gerya, 2005</xref>). In order to simulate the quasi-free surface and hence allow for the topography development, a 20&#xa0;km-thick &#x201c;sticky air&#x201d; layer, which is characterized by a density of 1 <inline-formula id="inf73">
<mml:math id="m87">
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mtext>kg</mml:mtext>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>m</mml:mtext>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and a viscosity of <inline-formula id="inf74">
<mml:math id="m88">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>19</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> Pa&#xa0;s, is placed above the rocky model (<xref ref-type="bibr" rid="B60">Schmeling et al., 2008</xref>).</p>
<p>The initial temperature first increases linearly from 0&#xb0;C at the surface to the Moho with 500&#xb0;C for the indenter and 600&#xb0;C for the upper plate, and then continues to increase to 1,360&#xb0;C at the lithosphere base. The thermal gradient gradually changes in the transition zone between the indenter and its surrounding upper plate. The underlying asthenospheric mantle has an initial temperature gradient of 0.5&#xb0;C/km. The top thermal boundary maintains a constant temperature of 0&#xb0;C, and all the vertical thermal boundaries are insulating (no horizontal heat flow). At the bottom thermal boundary, an infinity-like external constant temperature condition is applied (<xref ref-type="bibr" rid="B4">Burg and Gerya, 2005</xref>). This implies that a constant temperature condition is satisfied at &#x223c;200&#xa0;km below the model base, allowing a spontaneous adjustment of the temperature and heat flux at the bottom of the model.</p>
<p>Taking into account that multiple ocean closure and intercontinental suturing events occurred at the southern Asian continental margin prior to the India&#x2013;Asia collision (<xref ref-type="bibr" rid="B86">Yin and Harrison, 2000</xref>; <xref ref-type="bibr" rid="B43">Kapp and DeCelles, 2019</xref>), a relatively weak plate is set to simulate the pre-collisional Asian continental margin. The Asian plate has a 40&#xa0;km thick continental crust composed of a 17&#xa0;km thick upper crust and a 23&#xa0;km thick lower crust, and a 80&#xa0;km thick lithospheric mantle. The indenter has a 35&#xa0;km thick continental crust composed of a 15&#xa0;km thick upper crust and a 20&#xa0;km thick lower crust, and a 105&#xa0;km thick lithospheric mantle, to simulate the northern moving Indian craton. In consideration of oceanic subduction before continental indentation, we set a weak zone with a dip angle of 30 in front of the indenter cutting through the entire lithosphere (<xref ref-type="fig" rid="F3">Figure 3B</xref>). Our focus is on the topography evolution in the hinterland of the Tibetan Plateau, where the erosion and sedimentation is not as significant as that at the plateau margins. Here, we do not consider the effects of the surface processes on the topographic evolution, but we will discuss the possible limitations for simplification.</p>
</sec>
</sec>
<sec id="s3">
<title>Modeling Results</title>
<p>According to sedimentary records (<xref ref-type="fig" rid="F1">Figure 1</xref>) and geophysical observations (<xref ref-type="fig" rid="F2">Figure 2</xref>), we found that the basins inside the Tibetan Plateau vary in location, size, and strength. We first designed a reference model with a strong basin (f &#x3d; 10) that is located 500&#xa0;km north of the convergent boundary and is 500&#xa0;km in width (<xref ref-type="table" rid="T2">Table 2</xref>). Then, we tested the influence of the basin&#x2019;s distance to the convergent boundary and the basin&#x2019;s width on the topographic response. After that, we investigated the effect of the basin strength on the uplift history and the topographic development of the plateau. In order to test the effect of the initial convergence rate on the modeling results, an additional model with a faster velocity was performed.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Parameters and results of experiments.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Model</th>
<th align="center">Dis (km)</th>
<th align="center">Width (km)</th>
<th align="center">Strength (f)</th>
<th align="center">Figures</th>
<th align="center">Comments</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Model-1</td>
<td align="char" char=".">500</td>
<td align="char" char=".">500</td>
<td align="char" char=".">10</td>
<td align="center">4&#x2013;5</td>
<td align="left">Reference model</td>
</tr>
<tr>
<td align="left">Model-2</td>
<td align="char" char=".">0</td>
<td align="char" char=".">500</td>
<td align="char" char=".">10</td>
<td align="center">6 and 7</td>
<td align="left">Close to the suture</td>
</tr>
<tr>
<td align="left">Model-3</td>
<td align="char" char=".">1000</td>
<td align="char" char=".">500</td>
<td align="char" char=".">10</td>
<td align="center">6 and 7</td>
<td align="left">Further north</td>
</tr>
<tr>
<td align="left">Model-4</td>
<td align="char" char=".">500</td>
<td align="char" char=".">250</td>
<td align="char" char=".">10</td>
<td align="center">8</td>
<td align="left">Narrow basin</td>
</tr>
<tr>
<td align="left">Model-5</td>
<td align="char" char=".">500</td>
<td align="char" char=".">500</td>
<td align="char" char=".">2</td>
<td align="center">9</td>
<td align="left">Less-strong basin</td>
</tr>
<tr>
<td align="left">Model-6</td>
<td align="char" char=".">500</td>
<td align="char" char=".">500</td>
<td align="char" char=".">0.5</td>
<td align="center">10</td>
<td align="left">Weak basin</td>
</tr>
<tr>
<td align="left">Model-7</td>
<td align="char" char=".">500</td>
<td align="char" char=".">500</td>
<td align="char" char=".">10</td>
<td align="center">11</td>
<td align="left">Faster initial convergence rate</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Note that <bold>Dis</bold> is the distance between the strong basin and the convergent boundary, representing the strong basin&#x2019;s position inside the plateau.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<sec id="s3-1">
<title>Reference Model</title>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> shows the topographic evolution of the reference model (model-1 in <xref ref-type="table" rid="T2">Table 2</xref>). The deformation propagates northward quickly and localizes around the borders of the strong basin soon after the convergence starts. From the cross-sections, the existence of the strong basin causes the surrounding crusts to intensely thicken and buckle, resulting in the development of a high topography around the basin. In contrast, the strong basin itself experiences little deformation and underthrusts beneath the surrounding thickened crust. As a consequence, a lowland area develops in the interior of the plateau, characterized by a notable topographic relief. As the convergence continues, the lowland gradually shrinks and migrates northward. The lowland exists in the interior of the plateau until &#x223c;46&#xa0;Myr, after which it merges into the surrounding high plateau.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Topographic evolution of the reference model (model-1 in <xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography and slices at <bold>(A)</bold> 8.5&#xa0;Myr <bold>(B)</bold>20&#xa0;Myr <bold>(C)</bold> 35.0&#xa0;Myr, and <bold>(D)</bold> 45.3&#xa0;Myr. The red dashed rectangles outline the scope of the strong basins&#x2019; lower crust. The black lines represent the different positions (x &#x3d; 2,000, 2,400, and 2,800) of the slices.</p>
</caption>
<graphic xlink:href="feart-10-845126-g004.tif"/>
</fig>
<p>The lowland area displays significant topographic relief in its interior. At the early stage of the collision, topographic depressions with negative elevation developed along the margins of the strong basin and uplifted belts developed adjacently (<xref ref-type="fig" rid="F4">Figure 4</xref>). In terms of the uplift process, the elevation of a lowland does not rise monotonously. During the convergence, the distributed width of the strong lower crust changes slightly. Here, we assume that the length of the basin&#x2019;s lower crust remains unchanged. This allows us to track the elevation variations of the basin&#x2019;s different regions (points A1, B1, C, B2, and A2) with time (<xref ref-type="fig" rid="F5">Figure 5</xref>). The surface of the lowland uplifts progressively from the margins to the center of the strong basin. The uplift histories of different regions vary significantly, but all undergo a considerable elevation drop followed by a rapid uplift. It is noteworthy that the lowland center (Point C) maintains a constant elevation for a long period and then experiences a noticeable elevation drop, followed by a quick uplift to the elevation of the surrounding mountains (<xref ref-type="fig" rid="F5">Figure 5</xref>).</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Plots of elevation versus time for different points within the strong basin. In <bold>(A)</bold> and <bold>(B)</bold>, the red curves represent the uplift history at the center point <bold>(C)</bold>. The blue curves represent the uplift history of the marginal points (A2, B2). The green curves represent the uplift history at points A1 and B1 <bold>(C)</bold> Positions of points A1, A2, B1, B2, and C in the interior of the strong basin.</p>
</caption>
<graphic xlink:href="feart-10-845126-g005.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>Effects of a Strong Basin&#x2019;s Position</title>
<p>In this section, we design a group of models (models two to three in <xref ref-type="table" rid="T2">Table 2</xref>) to investigate the impacts of a strong basin&#x2019;s position on the topographic evolution of the plateau. Model-2 and model-3 are identical to the reference model, except that the distances of the strong basin to the convergent boundary are 0 and 1,000&#xa0;km, respectively, instead of 500&#xa0;km in the reference model. <xref ref-type="fig" rid="F6">Figure 6</xref> shows the topographic evolution of model-2 and model-3. The strong basins in model-2 and model-3 represent the rigid basins located at the south and north Tibetan Plateau, respectively. The plateau growth patterns in model-2 and model-3 are similar to the reference model, with lowlands developing in the interior of strong basins and plateaus forming in the surrounding region. Differently, the formation of the hinterland basin in model-2 occurs roughly 10&#xa0;Myr earlier than that in model-3 (<xref ref-type="fig" rid="F6">Figure 6</xref>). In addition, the time of the lowland merging into the plateau in model-2 also occurs earlier than that in model-3, at approximately 5 Myr. At 38&#xa0;Myr of convergence, the lowland in model-2 has shrunk into a small residual basin, whereas the lowland in model-3 is still broad (<xref ref-type="fig" rid="F6">Figure 6</xref>).</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Topographic evolution of the model-2 and model-3 (<xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography of model-2 at <bold>(Ai)</bold> 10.3 Myr <bold>(Aii)</bold> 24.8&#xa0;Myr, and <bold>(Aiii)</bold> 38.0&#xa0;Myr. Snapshots showing the surface topography of model-3 at <bold>(Bi)</bold> 10.5&#xa0;Myr <bold>(Bii)</bold> 25.0&#xa0;Myr, and <bold>(Biii)</bold> 38.0&#xa0;Myr. The red dashed rectangles outline the scope of the strong basins.</p>
</caption>
<graphic xlink:href="feart-10-845126-g006.tif"/>
</fig>
<p>The topographic features in the interior of the lowland region are significantly different in the model-1, model-2, and model-3 (<xref ref-type="fig" rid="F7">Figure 7</xref>). In model-2, the center region of the lowland has been elevated from the early stage and displays a locally positive topography. Specifically, the lowland center (Point C) in model-2 uplifts nearly 2,000&#xa0;m after 20&#xa0;Myr of convergence, whereas the height of the lowland center in model-1 remains unchanged until 32&#xa0;Myr of convergence. In addition, in model-2, the depression formed at the south margin of the lowland is more visible and deeper than that in the reference model. In detail, the subsidence of the south depression in model-2 exceeds 3,000&#xa0;m, compared to less than 2,000 m in the reference model. By contrast, the lowland in model-3 has similar topographic features to the reference model.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Contrasting the topographic features among mode-1, model-2, and model-3. Topographic evolution with time along section x &#x3d; 2000&#xa0;km in <bold>(A)</bold> model-1 <bold>(B)</bold> model-2, and <bold>(C)</bold> model-3. The red dotted curves limiting the region of the strong basins and the black dashed curves represent the sutures. Uplift histories of <bold>(D)</bold> point C <bold>(E)</bold> point A1, and <bold>(F)</bold> point A2 in different models. Red curves show the elevation history of model-1, blue curves show the elevation history of model-2, and green curves show the elevation history of model-3.</p>
</caption>
<graphic xlink:href="feart-10-845126-g007.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>Effects of the Strong Basin&#x2019;s Width</title>
<p>Considering the fact that the hinterland basins inside the Tibetan Plateau vary in size, we designed a model (model-4, <xref ref-type="table" rid="T2">Table 2</xref>), in which the width of the strong basin is half that in the reference model, to investigate the effects of the strong basin&#x2019;s width on the topographic evolution of the plateau. <xref ref-type="fig" rid="F8">Figure 8</xref> shows the topographic evolution and the lowland uplift history of model-4. The topographic growth pattern of model-4 is similar to that of the reference model, except that the lowland in model-4 vanishes nearly 10&#xa0;Myr earlier than that in the reference model (<xref ref-type="fig" rid="F8">Figure 8A&#x2013;D</xref>). As a result, it takes only 40&#xa0;Myr to form a large uniform plateau in model-4 (<xref ref-type="fig" rid="F8">Figure 8E</xref>), instead of &#x3e;45&#xa0;Myr in the reference model.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Topographic evolution of the model-4 (<xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography at <bold>(A)</bold> 8.5&#xa0;Myr <bold>(B)</bold> 18.5&#xa0;Myr <bold>(C)</bold> 25.0&#xa0;Myr, and <bold>(D)</bold> 40.0&#xa0;Myr <bold>(E)</bold> exhibit the topographic evolution with time along section x &#x3d; 2,000&#xa0;km <bold>(F)</bold> showing the difference of the uplift history of center point C between the reference model (red curve) and model-4 (blue curve).</p>
</caption>
<graphic xlink:href="feart-10-845126-g008.tif"/>
</fig>
<p>The topographic features and uplift history of the lowland in model-4 are dramatically different from those observed in the reference model. The lowland center region in model-4 was elevated soon after the convergence started, rather than maintaining constant in the reference model (<xref ref-type="fig" rid="F8">Figure 8F</xref>). To be specific, after 10&#xa0;Myr of convergence, the lowland center (Point C) in model-4 had increased to a height of 3,000&#xa0;m and then kept unchanged until 20 Myr. Then, the height dropped by more than 2,500&#xa0;m, close to sea level after 30&#xa0;Myr of convergence (<xref ref-type="fig" rid="F8">Figure 8F</xref>). In contrast, the elevation of the lowland center in the reference model was nearly constant during the first 30&#xa0;Myr. The elevation fall of the lowland center in model-4 exceeds 2,500&#xa0;m, whereas this value in the reference model is less than 1,000&#xa0;m.</p>
</sec>
<sec id="s3-4">
<title>Effects of the Basin&#x2019;s Strength</title>
<p>In this section, we designed a model with a less strong basin (f &#x3d; 2, model-5 in <xref ref-type="table" rid="T2">Table 2</xref>) and a weak basin (f &#x3d; 0.5, model-6 in <xref ref-type="table" rid="T2">Table 2</xref>) to test the effects of the basin&#x2019;s strength on the topographic expressions of the plateau. The model results showed that the less strong basin had similar effects on the topographic growth of the plateau to that produced in the reference model (<xref ref-type="fig" rid="F9">Figure 9A&#x2013;E</xref>). The lowland basin also survives in the interior of the plateau for approximately 30&#xa0;Myr. However, the basin&#x2019;s uplift history is quite different to that in the reference model. The lowland center does not experience an elevation drop at a late stage, but keeps rising until reaching the height of the surrounding plateau (<xref ref-type="fig" rid="F9">Figure 9F</xref>).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Topographic evolution of the model-5 (<xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography at <bold>(A)</bold>8.7&#xa0;Myr <bold>(B)</bold> 20.2&#xa0;Myr <bold>(C)</bold> 30.0&#xa0;Myr, and <bold>(D)</bold>40.0&#xa0;Myr <bold>(E)</bold> display the topographic evolution with time along section x &#x3d; 2,000&#xa0;km <bold>(F)</bold> showing the difference of uplift history of center point C between the reference model (red line) and model-5.</p>
</caption>
<graphic xlink:href="feart-10-845126-g009.tif"/>
</fig>
<p>The topographic response to a weak basin differs significantly from that of a strong basin. In model-6, the weak basin undergoes intense deformation in the early stage of the collision and uplifts earlier than the surrounding areas, leading to the formation of a topography high in the interior of the upper plate (<xref ref-type="fig" rid="F10">Figure 10</xref>). The highland continues to rise and maintains its size until 20 Myr. After that, it propagates southward and northward. After 30&#xa0;Myr of convergence, the plateau develops a flat-surfaced morphology. This set of models illustrates that the strength of the hinterland basin is a key factor in controlling the uplift pattern of the plateau. A strong hinterland basin favors a later uplift of the plateau&#x2019;s interior, whereas a weak hinterland basin facilitates the formation of a topography high in the early stage of collision.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Topographic evolution of the model-6 (<xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography at <bold>(A)</bold>2.8&#xa0;Myr <bold>(B)</bold> 11.2&#xa0;Myr <bold>(C)</bold> 16.2&#xa0;Myr, and <bold>(D)</bold> 28.2&#xa0;Myr <bold>(E)</bold> display the topographic evolution with time along section x &#x3d; 2,000&#xa0;km.</p>
</caption>
<graphic xlink:href="feart-10-845126-g010.tif"/>
</fig>
</sec>
<sec id="s3-5">
<title>Effects of the Convergence Rate</title>
<p>Different to the aforementioned models that test the inherent properties of the basin, we perform an additional model (model-7 in <xref ref-type="table" rid="T2">Table 2</xref>) to test the influence of the convergence rate in the topographic response of a hinterland basin. Here, we choose the convergence rate reconstructed by <xref ref-type="bibr" rid="B6">Cande and Stegman (2011)</xref>, in which the velocity is 13&#xa0;cm/yr in the first 5 Myr and is then gradually reduces to a fixed value of 5&#xa0;cm/yr after 15 Myr, keeping the other parameters the same as the reference model. The model results show that the growth pattern of the plateau and the topographic features in the interior of the lowland are similar to that in the reference model (<xref ref-type="fig" rid="F11">Figure 11A&#x2013;E</xref>). The lowland basin develops soon after the initial collision and survives for &#x223c;35 Myrs in the interior of the plateau. The basin center also experiences an evident elevation drop and rapid uplift before merging into the plateau (<xref ref-type="fig" rid="F11">Figure 11F</xref>). It is necessary to mention that the lowland basin migrates northward and shrinks more quickly due to the increased convergence amount. Also, it is worth noting that the lowland center was elevated about 1,000&#xa0;m at an early stage of the basin&#x2019;s lifespan, which is not noticeable in the reference model (<xref ref-type="fig" rid="F11">Figure 11F</xref>). By comparing the faster convergence model with the reference model, we can conclude that the initial convergence velocity has little influence on the major characteristics of the basin&#x2019;s topographic evolution and plateau growth.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Topographic evolution of the model-7 (<xref ref-type="table" rid="T2">Table 2</xref>). Snapshots showing the surface topography at <bold>(A)</bold> 5.1&#xa0;Myr <bold>(B)</bold>20.1&#xa0;Myr <bold>(C)</bold> 30.1&#xa0;Myr, and <bold>(D)</bold> 40.1&#xa0;Myr <bold>(E)</bold> display the topographic evolution with time along section x &#x3d; 2,000&#xa0;km. <bold>(F)</bold> showing the difference of uplift history of center point C between the reference model (red line) and model-7 (blue line).</p>
</caption>
<graphic xlink:href="feart-10-845126-g011.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<sec id="s4-1">
<title>Topographic Evolution of the Hinterland Basins</title>
<p>Our models demonstrate that the strength of the hinterland basin exerts a first-order control over the topographic evolution. The basin with a rigid basement develops into a lowland surrounded by high mountains soon after the initial collision and survives in the interior of the plateau for a long period of time (30&#x2013;40&#xa0;Myrs). In contrast, the basin with a soft basement uplifts quickly and reaches its current elevation after 20&#xa0;Myr of the convergence. This provides an explanation to why some basins inside the Tibetan Plateau have long-term sedimentary records and keep a low elevation until the Late Oligocene, such as the Lunpola and Hoh Xil basins (<xref ref-type="bibr" rid="B73">Wang et al., 2008</xref>; <xref ref-type="bibr" rid="B69">Sun et al., 2014</xref>; <xref ref-type="bibr" rid="B68">Sun et al., 2015</xref>; <xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>; and <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>), while some other basins ceased to deposit and have uplifted during the Eocene, such as the Linzhou and Shuanghu basins (<xref ref-type="bibr" rid="B23">Ding et al., 2014</xref>; <xref ref-type="bibr" rid="B92">Currie et al., 2016</xref>). Depending on the locations and the widths, the rigid hinterland basins display quite different lifetimes in the interior of the plateau. The time required for the formation of a lowland basin in the north Tibetan Plateau (model-3, Dis &#x3d; 1000&#xa0;km) delays by 10&#xa0;Myr in comparison to the basin at central Tibet (model-1, Dis &#x3d; 500&#xa0;km). The time of merging into the plateau for the narrow basin (model-4, width &#x3d; 250&#xa0;km) is approximately 10&#xa0;Myrs earlier than a vast basin (model-1, width &#x3d; 500&#xa0;km).</p>
<p>The hinterland basins also exhibit a variety of topographic features and uplift histories, depending on their locations, widths, and strengths. When the strong basin is close to the collisional zone (model-2) or is narrow (model-4), the central region rises at the early stage and then experiences an evident elevation drop at the late stage (<xref ref-type="fig" rid="F12">Figure 12</xref>). However, when located further north (e.g., model-3), the lowland basin displays low-relief topography in the interior and the elevation keeps unchanged for a long period of time (<xref ref-type="fig" rid="F7">Figure 7D</xref>). The topographic feature of the basin is closely related to the deep tectonic structure. Depressions and uplifted belts formed owing to the underthrusting and bending of the strong lower crust. Therefore, due to a weak surface topographic response to the bending, the less strong basin (model-5, f &#x3d; 2) displays a less topographic relief in the interior (<xref ref-type="fig" rid="F12">Figure 12</xref>). In model-2 and mode-4, the uplifted belts occur in the lowland center owing to the more intense bending and the narrowness of the strong basin, and the elevation drop is actually the result of the marginal depressions merging as the basin gradually shrinks (<xref ref-type="fig" rid="F12">Figure 12</xref>).</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Topographic features of the lowlands and deep structures in <bold>(A)</bold> model-1 <bold>(B)</bold> model-2 <bold>(C)</bold> model-3 <bold>(D)</bold> model-4, and <bold>(E)</bold> model-6. The left column exhibits the detailed topographic features of the lowland in different models. Red dashed lines highlight the time snapshot of 20&#xa0;Myr. The right column shows the deep structures along section x &#x3d; 2,000&#xa0;km at the snapshot of 20&#xa0;Myr. SB represents the strong basement of the basins. Depressions formed at the edges and uplifted belts formed adjacently due to bending of the strong lower crust. Note that a vertical exaggeration of two is used in the cross-sections of the right column.</p>
</caption>
<graphic xlink:href="feart-10-845126-g012.tif"/>
</fig>
</sec>
<sec id="s4-2">
<title>Implications for the Uplift Histories of the Lunpola and Hoh Xil Basins</title>
<p>The Lunpola Basin is a narrow basin and is located in the northern Lhasa terrane (<xref ref-type="fig" rid="F1">Figure 1</xref>). Geophysical observation and geochemical data show that it is characterized by fast velocity anomalies in the crust (<xref ref-type="bibr" rid="B85">Yang et al., 2012</xref>) and negative Hf isotopic values of felsic igneous rocks (<xref ref-type="bibr" rid="B34">Hou et al., 2015</xref>; <xref ref-type="bibr" rid="B35">Hou et al., 2020</xref>) (<xref ref-type="fig" rid="F2">Figure 2</xref>), which indicate that the Luopala Basin has a strong and old basement. Therefore, the uplift history of the Lunpola Basin can be compared with that of the lowland in model-4, in which the strong basin is 250&#xa0;km in width and located 500&#xa0;km north of the convergent boundary. A topographic analysis of model-4 shows that the basin was elevated to a medium elevation after 10&#xa0;Myr of convergence and experienced a noticeable elevation drop of &#x223c;3,000&#xa0;m from 20 to 30&#xa0;Myr of convergence, then followed by a rapid uplift (<xref ref-type="fig" rid="F8">Figure 8F</xref>). We compiled the paleoelevation data published over the past 2&#xa0;decades in the Lunpola Basin, including oxygen isotope, hydrogen isotope, and paleontology (<xref ref-type="bibr" rid="B58">Rowley and Currie, 2006</xref>; <xref ref-type="bibr" rid="B56">Polissar et al., 2009</xref>; <xref ref-type="bibr" rid="B69">Sun et al., 2014</xref>; <xref ref-type="bibr" rid="B40">Jia et al., 2015</xref>; <xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>; <xref ref-type="bibr" rid="B26">Farnsworth et al., 2018</xref>; and <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>) (<xref ref-type="fig" rid="F13">Figure 13A</xref>). The estimates based on isotope data tend to predict a higher elevation, whereas fossil-based data tend to reflect lowland elevations (<xref ref-type="bibr" rid="B65">Spicer et al., 2021</xref>). Fossil-based data indicate that the Lunpola Basin was elevated to a medium elevation during the Eocene (50&#x2013;38&#xa0;Ma) and suffered an evident elevation drop during the Oligocene (38&#x2013;25&#xa0;Ma), and then followed by a rapid uplift in the Early Miocene (23&#xa0;Ma) (<xref ref-type="fig" rid="F11">Figure 11</xref>). The elevation fluctuation of the Lunpola Basin, as revealed by fossils, is in agreement with the uplift history of the lowland center predicted by our model-4 (<xref ref-type="fig" rid="F13">Figure 13A</xref>). In addition, the isotopic data also suggest that the Lunpola Basin had a high elevation during the Eocene and suffered a rapid uplift during the Early Miocene. Therefore, the Lunpola Basin was likely to be elevated to 2,500&#x2013;3,000&#xa0;m in the Middle Eocene and suffered an evident elevation fall of &#x223c;2,000&#xa0;m during the Oligocene, and then experienced a rapid uplift to achieve its present height in the Early Miocene.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Compilation of paleolevations data of the Lunpola Basin <bold>(A)</bold> Red circles are the paleoelevations of the Lunpola Basin obtained from fossils of plant, animal, and pollen (<xref ref-type="bibr" rid="B93">Deng et al., 2011</xref>; <xref ref-type="bibr" rid="B69">Sun et al., 2014</xref>; <xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>; <xref ref-type="bibr" rid="B94">Liu et al., 2019</xref>; <xref ref-type="bibr" rid="B26">Farnsworth et al., 2018</xref>, <xref ref-type="bibr" rid="B67">Su et al., 2020</xref>; <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>; and <xref ref-type="bibr" rid="B81">Xie et al., 2021</xref>). Gray circles represent the paleoelevations based on the oxygen isotope (<xref ref-type="bibr" rid="B56">Polissar et al., 2009</xref>; <xref ref-type="bibr" rid="B40">Jia et al., 2015</xref>) and hydrogen isotope (<xref ref-type="bibr" rid="B58">Rowley and Currie, 2006</xref>; <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>). The red dashed curve draws the expected uplift history of the Lunpola Basin based on fossils. The black curve displays the uplift history of the lowland center in model-4 <bold>(B)</bold> Red circles are the paleoelevations of the Hoh Xil Basin obtained from fossils (<xref ref-type="bibr" rid="B68">Sun et al., 2015</xref>; <xref ref-type="bibr" rid="B51">Miao et al., 2016</xref>; <xref ref-type="bibr" rid="B64">Song et al., 2021</xref>). Gray circles represent the paleoelevations based on the oxygen isotope (<xref ref-type="bibr" rid="B15">Cyr et al., 2005</xref>; <xref ref-type="bibr" rid="B95">Quade et al., 2011</xref>; <xref ref-type="bibr" rid="B46">Li et al., 2020</xref>) and the hydrogen isotope (<xref ref-type="bibr" rid="B56">Polissar et al., 2009</xref>). Dashed curves depict the expected uplift histories of the two sub-basins in the Hoh Xil Basin based on paleoelevations. The black curve shows the tendency of the uplift history of the lowland center in model-3.</p>
</caption>
<graphic xlink:href="feart-10-845126-g013.tif"/>
</fig>
<p>The Hoh Xil Basin is a large basin far from the Indus&#x2013;Yarlung suture zone (IYS). Weak crustal deformation (<xref ref-type="bibr" rid="B66">Staisch et al., 2016</xref>) and the negative Hf isotopic feature of felsic igneous rocks (<xref ref-type="bibr" rid="B35">Hou et al., 2020</xref>) imply a mechanically strong basement beneath the Hoh Xil Basin. Therefore, the topographic evolution of the Hoh Xil Basin can be compared with the lowland in model-3, where the strong basin is wide and far from the collisional zone. Our results show that the lowland center in model-3 keeps a constant elevation for &#x223c;30&#xa0;Myr and then experiences a slight elevation drop before the rapid uplift (<xref ref-type="fig" rid="F7">Figure 7D</xref>). In the Hoh Xil Basin, a compilation of paleoelevation data indicates that the elevation did not change significantly throughout the Eocene (<xref ref-type="bibr" rid="B15">Cyr et al., 2005</xref>; <xref ref-type="bibr" rid="B56">Polissar et al., 2009</xref>; <xref ref-type="bibr" rid="B51">Miao et al., 2016</xref>; and <xref ref-type="bibr" rid="B64">Song et al., 2021</xref>) (<xref ref-type="fig" rid="F13">Figure 13B</xref>). This is in accordance with the long-term unchanged elevation of the lowland center in model-3. As expected by the uplift histories of two sub-basins within the Hoh Xil Basin (<xref ref-type="bibr" rid="B48">Liu et al., 2016</xref>) (<xref ref-type="fig" rid="F13">Figure 13B</xref>), the Hoh Xil Basin experienced a slight elevation drop during Oligocene followed by a fast uplift in the Early Miocene. This is consistent with the late-stage elevation variation of the lowland center in model-3.</p>
</sec>
<sec id="s4-3">
<title>Cenozoic Uplift Process of the Tibetan Plateau</title>
<p>How the Tibetan Plateau uplifted is a subject of intense debate. Several hypotheses for the growth pattern of the Tibetan Plateau have been proposed, including: 1) northward stepwise uplift model (<xref ref-type="bibr" rid="B70">Tapponnier et al., 2001</xref>; <xref ref-type="bibr" rid="B53">Mulch and Chamberlain, 2006</xref>), 2) a central proto-Tibetan Plateau model (<xref ref-type="bibr" rid="B73">Wang et al., 2008</xref>; <xref ref-type="bibr" rid="B72">Wang et al., 2014</xref>), and 3) the &#x201c;Central Tibetan Valley&#x201d; model (<xref ref-type="bibr" rid="B19">Deng and Ding, 2015</xref>; <xref ref-type="bibr" rid="B26">Farnsworth et al., 2018</xref>; and <xref ref-type="bibr" rid="B82">Xiong et al., 2022</xref>). According to the stepwise uplift model, the Tibetan Plateau rises gradually from the south to the north, with the Lhasa rising by Eocene, the Qiangtang rising during the Oligocene, the Songpan&#x2013;Ganzi rising during the Miocene, and the Qilian rising during the Pliocene to Quaternary (<xref ref-type="bibr" rid="B53">Mulch and Chamberlain, 2006</xref>). The proto-Tibetan Plateau model argues that the Lhasa and southern Qiangtang terranes were elevated into a central Tibetan highland during the Middle Eocene, and then the highland expanded to the Himalayas during the mid-Miocene, and to the Hoh Xil Basin during the Early Miocene (<xref ref-type="bibr" rid="B73">Wang et al., 2008</xref>; <xref ref-type="bibr" rid="B72">Wang et al., 2014</xref>). However, the &#x201c;Central Tibetan Valley&#x201d; model supports a lowland central Tibetan along the Bangong&#x2013;Nujiang suture zone (BNS) sandwiched between the Gangdese and the Tanggula mountains (or central watershed) during the Early Eocene to the Late Oligocene, and then uplifted in the early Miocene (<xref ref-type="bibr" rid="B26">Farnsworth et al., 2018</xref>; <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>; <xref ref-type="bibr" rid="B82">Xiong et al., 2022</xref>).</p>
<p>Based on the predicted uplift histories of the Lunpola and Hoh Xil basins in this study and previous paleoelevation data, we propose a revised Cenozoic uplift model for the Tibetan Plateau south of the Kunlun Mountain (<xref ref-type="fig" rid="F14">Figure 14</xref>). We subdivide the Tibetan Plateau&#x2019;s growth into four stages according to the surface topographic evolution. At the first stage (50&#x2013;38&#xa0;Ma), the Tibetan Plateau is characterized by two highlands separated by three lowlands (<xref ref-type="fig" rid="F14">Figure 14A</xref>). Paleoelevation data from the Linzhou and Namling&#x2013;Qiyug basins suggest that a high Andean-type Gangdese mountain range (&#x223c;5000&#xa0;m) developed in the southern Lhasa during the Early Eocene (<xref ref-type="bibr" rid="B23">Ding et al., 2014</xref>; <xref ref-type="bibr" rid="B39">Ingalls et al., 2017</xref>). Also, the central watershed highlands were contemporaneously elevated to 4,000&#x2013;5,000&#xa0;m in central Qiangtang, according to the paleoelevation data of the Heihuling and Gonjo basins (<xref ref-type="bibr" rid="B84">Xu et al., 2013</xref>; <xref ref-type="bibr" rid="B83">Xiong et al., 2020</xref>). The fossil evidence indicates the existence of a lowland with an elevation of &#x3c;2,000 m south of the Gangdese Mountains (<xref ref-type="bibr" rid="B22">Ding et al., 2017</xref>), a lowland region with an elevation of 2,500&#x2013;3,000&#xa0;m between the Gangdese and the central watershed highlands (<xref ref-type="bibr" rid="B75">Wei et al., 2016</xref>; <xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>; <xref ref-type="bibr" rid="B67">Su et al., 2020</xref>), and a broad lowland region with an elevation of &#x223c;2,000 m north of the central watershed highlands during the Eocene (<xref ref-type="bibr" rid="B51">Miao et al., 2016</xref>; <xref ref-type="bibr" rid="B64">Song et al., 2021</xref>).</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Schematic surface uplift of the Tibetan Plateau, which can be subdivided into four stages: <bold>(A)</bold> two highlands, the Gangdese and central watershed mountains, were separated by three lowlands <bold>(B)</bold> the central Tibetan lowland along BNS experienced an elevation drop of &#x223c;2,000&#xa0;m during the Oligocene <bold>(C)</bold> the central Tibetan lowland suffered an rapid uplift and merged into the Tibetan Plateau during the Early Miocene <bold>(D)</bold> the south and north lowlands were elevated and merged into the Tibetan Plateau since the Middle Miocene, forming a flat-surfaced topography similar to the modern Tibetan Plateau. GT, Gangdese Thrust; GST, Gaize-Siling Tso Thrust; SGAT, Shiquanhe-Gaize-Amdo Thrust; TGLT, Tanggula Thrust; MFT, Main Frontal Thrust; MCT, Main Central Thrust; and STD, South Tibetan Detachment.</p>
</caption>
<graphic xlink:href="feart-10-845126-g014.tif"/>
</fig>
<p>At the second stage (35&#x2013;25&#xa0;Ma), the central Tibetan lowland along the Bangong&#x2013;Nujiang suture (BNS) experienced an elevation drop of &#x223c;2,000&#xa0;m, forming a central Tibetan deep valley (<xref ref-type="fig" rid="F14">Figure 14B</xref>). Plant and foraminifera fossils indicate that the elevation of the Lunpola, Nima, and Gerze basins were no more than 1,000&#xa0;m during the Late Oligocene (<xref ref-type="bibr" rid="B75">Wei et al., 2016</xref>; <xref ref-type="bibr" rid="B79">Wu et al., 2017</xref>). Sedimentary records show a noticeable facie transition from lacustrine mudstones to fluvial and alluvial conglomerates and a threefold increase of the sedimentary rate in the Lunpola Basin during the Late Oligocene (<xref ref-type="bibr" rid="B25">Fang et al., 2020</xref>). This consolidates our prediction that the central Tibetan lowland suffered an evident subsidence during the Oligocene. However, paleoelevation data reveal that the lowland south of the Gangdese Mountains and the lowland north of the central watershed mountains remained at an elevation of &#x223c;2,000 m at this stage (<xref ref-type="bibr" rid="B22">Ding et al., 2017</xref>; <xref ref-type="bibr" rid="B16">Dai et al., 2019</xref>). The elevation drop of the central Tibetan lowland occurred soon after the reduction of the India&#x2013;Asia convergence rate (<xref ref-type="bibr" rid="B52">Molnar and Stock, 2009</xref>; <xref ref-type="bibr" rid="B13">Copley et al., 2010</xref>; and <xref ref-type="bibr" rid="B6">Cande and Stegman, 2011</xref>). Thus, we suggest that the slow convergence rate may result in a relaxation of the lithospheric compression bending, thereby sinking the surface.</p>
<p>At the third stage (25&#x2013;18&#xa0;Ma), the central Tibetan valley suffered a rapid uplift and merged into the plateau (<xref ref-type="fig" rid="F14">Figure 14C</xref>). Fossil evidences from plants, mammals, and fish indicate that the ecosystem of the Lunpola and Nima basins experienced a significant turnover from a warm tropical environment in the Late Oligocene to a cool climate since the Early Miocene (<xref ref-type="bibr" rid="B20">Deng et al., 2019</xref>; <xref ref-type="bibr" rid="B21">Deng et al., 2021</xref>), whereas the lowland south of the Gangdese Mountains and the lowland north of the central watershed mountains remained at a low elevation according to carbon isotopic and palaeobotanical evidences (<xref ref-type="bibr" rid="B74">Wang et al., 2006</xref>; <xref ref-type="bibr" rid="B68">Sun et al., 2015</xref>; and <xref ref-type="bibr" rid="B46">Li et al., 2020</xref>). Seismic evidence suggests the convective removal of thickened lithosphere under the central Tibet during the Early Miocene (<xref ref-type="bibr" rid="B8">Chen M. et al., 2017</xref>), implying that the lithospheric delamination and mantle upwelling may have played important roles in the uplifting of the central Tibetan valley (<xref ref-type="bibr" rid="B82">Xiong et al., 2022</xref>). A recent study reveals an Early Miocene transition from a cold and strong middle-lower crust to a hot and weak middle-lower crust in the Qiangtang Block (<xref ref-type="bibr" rid="B89">Zhang et al., 2022</xref>). This supports that the Early Miocene uplift of the central Tibetan valley was driven by the crustal flow from surrounding highlands. Thus, we suggest that the lateral crustal flow and the vertical lithospheric delamination and mantle upwelling are the primary drivers of the central Tibetan valley&#x2019;s rapid uplift.</p>
<p>At the last stage (18&#x2013;0&#xa0;Ma), the lowland south of the Gangdese Mountains and the lowland north of the central watershed mountains were uplifted and merged into the plateau since the Middle Miocene, forming the topography similar to the present Tibetan Plateau (<xref ref-type="fig" rid="F14">Figure 14D</xref>). Oxygen isotopic data from the Gyirong Basin and the Thakkhola graben indicate that the Tethyan Himalaya was elevated to its current elevation by the Middle Miocene (<xref ref-type="bibr" rid="B27">Garzione et al., 2000</xref>; <xref ref-type="bibr" rid="B59">Rowley et al., 2001</xref>). Oxygen and hydrogen isotopes-based paleoelevations show that the Hoh Xil Basin was elevated to a height of &#x3e;4,000&#xa0;m after the Early Miocene (<xref ref-type="bibr" rid="B56">Polissar et al., 2009</xref>). The small degree of shortening and the Late Oligocene cessation of deformation in the Hoh Xil Basin imply that the north Tibetan lowland may have been uplifted as a result of the crustal flow and lithospheric removal (<xref ref-type="bibr" rid="B66">Staisch et al., 2016</xref>; <xref ref-type="bibr" rid="B47">Li et al., 2017</xref>).</p>
</sec>
</sec>
<sec id="s5">
<title>Model Limitations</title>
<p>The numerical models conducted in this study are incomplete in that they do not consider the surface processes, such as erosion and sedimentation. There have been a number of investigations on the coupling and feedback between tectonics and erosion for orogens (<xref ref-type="bibr" rid="B77">Willett, 1999</xref>; <xref ref-type="bibr" rid="B76">Whipple and Meade, 2004</xref>; <xref ref-type="bibr" rid="B29">Graveleau et al., 2012</xref>). The climate-driven erosion generally leads to a narrowing of the orogenic belts, a temporary increase in sedimentary deposition, and a persistent increase in the rate of rock exhumation (<xref ref-type="bibr" rid="B50">Marques and Cobbold, 2002</xref>; <xref ref-type="bibr" rid="B54">Persson et al., 2004</xref>; <xref ref-type="bibr" rid="B76">Whipple and Meade, 2004</xref>; and <xref ref-type="bibr" rid="B14">Cruz et al., 2010</xref>). In our simulations, ignoring the erosion process results in an abnormally high elevation of the plateau. Neglecting the sedimentation process enlarges the topographic relief between the lowland basins and their surrounding topographic highs. However, the erosion and sedimentation processes are not significant in the interior of the Tibetan Plateau, exerting limited impact on the topographic evolution of the hinterland basins.</p>
<p>For simplification, we set a single basin in the upper plate in the model. Yet, it is noteworthy that there are a number of basins inside Tibet before merging into the Tibetan Plateau. These basins may have an interactive impact on each other&#x2019;s topographic evolution. We will conduct further exploration on the basins&#x2019; interaction effects in the future.</p>
<p>Because of the large amount of computation in the 3D numerical simulation, we did not test the influences of plastic softening and high radiogenic crust on the basin&#x2019;s topographic response to the continental collision. The plastic softening promotes the strain localization (<xref ref-type="bibr" rid="B38">Huismans and Beaumont, 2011</xref>). <xref ref-type="bibr" rid="B10">Chen et al. (2019)</xref> demonstrated that radioactive heating plays an important role in crustal melting, which promotes plateau expansion and crustal flow.</p>
<p>Despite the aforementioned simplifications, the presented 3D models can depict the first-order topographic response of the hinterland basins to the India&#x2013;Asia collision.</p>
</sec>
<sec sec-type="conclusion" id="s6">
<title>Conclusion</title>
<p>In this article, we use 3D thermo-mechanical models to investigate the topographic response of the strong hinterland basin imbedded in a relatively weak continental lithosphere under the horizontal compression condition. The conclusions are as follows:<list list-type="simple">
<list-item>
<p>(1) Deformation strongly localizes around the margins of the strong basin soon after the convergence begins, while the strong basin experiences little deformation, resulting in a lowland area surrounded by topographic highs in the interior of the plateau. The central lowland progressively shrinks as the convergence continues, and eventually merges into the high plateau after &#x223c;40&#x2013;50&#xa0;Myr of convergence.</p>
</list-item>
<list-item>
<p>(2) The central lowland does not rise monotonously during plateau growth, but experiences an unexpected elevation drop after &#x223c;20&#x2013;30&#xa0;Myr of convergence, followed by a rapid uplift to reach the height of the surrounding plateau.</p>
</list-item>
<list-item>
<p>(3) A strong hinterland basin uplifts later than its surrounding regions, whereas a weak hinterland basin uplifts earlier. Our model results provide a mechanism to link the spatial distribution of hinterland basins and a diachronous uplift of the Tibetan Plateau.</p>
</list-item>
<list-item>
<p>(4) Based on the modeling results and paleoelevation data, we propose a revised model for the Tibetan Plateau&#x2019;s uplift. During the Eocene (50&#x2013;38&#xa0;Ma), the Gangdese Mountains and central watershed mountains have developed and isolated three lowlands. The central lowland along the BNS experienced an elevation drop of &#x223c;2,000&#xa0;m during the Oligocene (35-25&#xa0;Ma), then suffered a rapid uplift and merged into the Tibetan Plateau in the Early Miocene (25&#x2013;18&#xa0;Ma). The south and north lowlands were uplifted and merged into the plateau since the Middle Miocene (18&#x2013;0&#xa0;Ma).</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec id="s7">
<title>Data Availability Statement</title>
<p>The geophysical and Hf isotopic values data are available from <xref ref-type="bibr" rid="B85">Yang et al. (2012)</xref> and <xref ref-type="bibr" rid="B34">Hou et al. (2015)</xref>, respectively. The paleoelevation data of the Lunpola and Hoh Xil Basin are available from <xref ref-type="bibr" rid="B48">Liu et al. (2016)</xref>.</p>
</sec>
<sec id="s8">
<title>Author Contributions</title>
<p>PZ conducted the work, analyzed the result data, and drafted the manuscript. LC made substantial contributions to the design of the work and revised the manuscript. WX made substantial contributions in guidance and discussion of the work and helped in revising the content. J&#x27;Z helped in analyzing the data of this work and revised the manuscript.</p>
</sec>
<sec id="s9">
<title>Funding</title>
<p>The National Natural Science of Foundation (41888101, 91955311, and 41974110) provided funds for calculating the numerical models on super computers. The Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB18030103) provided funds for participating in relatively academic meetings.</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The handling editor declared a past co-authorship with one of the authors LC at time of review.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ack>
<p>The authors sincerely thank Taras Gerya for providing the I3ELVIS code. They are grateful to Xi Xu, Zhiyong Yan, Renxian Xie, Jiaxuan Tang, Shunzhi Li, Xiaona Cui, and Xiao Xiang for discussions. <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref> were generated with the open-source software ParaView (<ext-link ext-link-type="uri" xlink:href="http://www.paraview.org/">http://www.paraview.org</ext-link>), and the rest of the figures were generated with the Generic Mapping Tools (GMT, <ext-link ext-link-type="uri" xlink:href="https://www.generic-mapping-tools.org">https://www.generic-mapping-tools.org</ext-link>). All the models were run on the Beijing Super Cloud Computing Center, Beijing, China (<ext-link ext-link-type="uri" xlink:href="http://www.blsc.cn/">http://www.blsc.cn/</ext-link>), on the TianHe-1A Cluster at the National Supercomputer Center, Tianjin, China, and on the Supercomputing Laboratory, IGGCAS, Beijing, China.</p>
</ack>
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