New Versus Conventional Approach for Modeling Flexure of Foreland Basins
Authors: Pirouz Mortaza , Avouac Jean-Philippe , Gualandi Adriano , Quddusi Muhammad Hassan , Huang Weitong 
Published: March 2020

&lt;p&gt;We constrain foreland basins geometry to assess the equivalent elastic thickness of the lithosphere and the loads that have originated due to the collisional process. Geometry of the foreland relates to the topography loading and hidden subsurface load based on simple 2D flexural models have been done for many foreland basins during 80 and 90s (for example for Zagros, Taiwan, and Colville foreland in Alaska) and most of them highlighted that present topographic and basin loads are not enough to provide such a deflection and extra buried loads are expected. Recent 3D flexure models using conventional approaches are used to estimate the elastic thickness of the lithosphere and may highlight a need for the buried loads. In the conventional approach, we apply topographic and basin loads and use the common assumption that the space created due to the deflection is filled with material of crustal density. This takes place in the deflection function by &amp;#916;&amp;#961;=&amp;#961;&lt;sub&gt;mantle&lt;/sub&gt;-&amp;#961;&lt;sub&gt;cruct&lt;/sub&gt;. The conventional approach thus includes the static subsurface load associated with the buoyancy of the crustal root. In the new approach, we assume that the deflection is filled with air &amp;#916;&amp;#961;=&amp;#961;&lt;sub&gt;mantle&lt;/sub&gt;-&amp;#961;&lt;sub&gt;air&lt;/sub&gt; and the sub-surface load is proportional to the topographic load. The load from topography and sub-surface loads is then simply &amp;#955; times the topographic load. This approach allows accounting for quantifying all sub-surface loads correlated with topography, including the effect of the crustal root. In the new approach the Moho depth, representing the ratio between the root and topographic height, can be considered and the results give more clue about recognizing and quantifying buried load or mantle dynamics loads. With the new approach, we investigated Zagros, Taiwan, and Colville basin-Alaska foreland basins and obtained very precise models with less than 5% misfit between observations and predictions. Previous studies highlight that the buried loads are needed to obtain comparable results to the observations. However, our results show that the best models do not need extra buried loads with a reasonable ratio between topographic relief and crustal root using the new modeling approach.&lt;/p&gt;&lt;p&gt;&lt;img 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&quot; alt=&quot;&quot;&gt;&lt;/p&gt;&lt;p&gt;Abbreviations: Tc, thickness of undeformed lithosphere; w&lt;sub&gt;t&lt;/sub&gt;, deflection due to topographic load; P&lt;sub&gt;t&lt;/sub&gt;, topographic load; &amp;#961;&lt;sub&gt;m&lt;/sub&gt;, density of Mantle; &amp;#961;&lt;sub&gt;c&lt;/sub&gt;, density of crust; &amp;#961;&lt;sub&gt;a&lt;/sub&gt;, density of air; g, gravity acceleration; &amp;#946;, flexural parameter; H&lt;sub&gt;r&lt;/sub&gt;, root thickness; H&lt;sub&gt;t&lt;/sub&gt;, topographic height, and &amp;#955;, ratio between root thickness and topographic height.&lt;/p&gt;