Antoine Tonnoir , Cyrille Fauchard , Yannick Fargier , Vincent Guilbert , Raphael Antoine
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引用次数: 0
摘要
电阻率成像(ERI)是地球物理学中最常用的技术之一。与许多成像方法一样,数字高程模型(DEM)需要考虑复杂的地形条件。在本文中,我们介绍了在此背景下优化的新型 3D-ERI 软件的一些开发成果。文章重点关注前向问题,并讨论了:(i) 在处理过程中直接考虑 DEM 的网格划分方法,以及电极不一定对齐的几个剖面;(ii) 考虑无边界域的新方面。事实上,定义数值建模问题的边界条件是求解偏微分方程(PDE)的最重要问题之一。为了解决 3D-ERI 前向问题,我们提出了一种无限元素与传统有限元素相结合的新方法。我们首先在重现悬崖的合成案例中验证了这一方法,然后又在呈现类似荒地悬崖的真实案例研究中验证了这一方法。结果表明,网格划分程序和无限元素的使用都提高了正向问题的效率和反向问题的准确性。特别是,与传统的二维方法相比,这种方法能够更准确地再现复杂环境中的局部地质情况。
PyLGRIM: Modelling 3D-ERI with infinite elements in complex topography context
Electrical Resistivity Imaging (ERI) is one of the most used techniques in geophysics. As for many imaging methods, Digital Elevation Models (DEMs) are required to consider complex topography conditions. In this paper, we present some developments implemented into a new 3D-ERI software optimized in this context. The article focuses on the forward problem and discusses (i) the meshing methodology that directly consider DEMs in the processing and several profiles where electrodes are not necessarily aligned and (ii) new aspects for taking into account the unbounded domain. Indeed, defining boundary conditions of a numerical modelling problem arises as one of the most important issues into solving Partial Differential Equations (PDE). In order to solve the 3D-ERI forward problem, we propose an original implementation of the infinite elements, together with conventional finite elements. This methodology is first validated on synthetic case reproducing cliffs and, then, on a real case study presenting Badlands-like cliffs. Our results show that both the meshing procedure as well as the use of infinite elements enhance the efficiency of the forward problem as well as the accuracy of the inverse problem. In particular, this allows to reproduce more closely the local geology in complex environments than with a conventional 2D approach.
期刊介绍:
Computers & Geosciences publishes high impact, original research at the interface between Computer Sciences and Geosciences. Publications should apply modern computer science paradigms, whether computational or informatics-based, to address problems in the geosciences.