Relating the attenuation and velocity dispersion of seismic waves to fluid pressure diffusion (FDP) by means of numerical simulations is essential for constraining the mechanical and hydraulic properties of heterogeneous porous rocks. This, in turn, is of significant importance for a wide range of prominent applications throughout the Earth, environmental, and engineering sciences, such as, for example, geothermal energy production, hydrocarbon exploration, nuclear waste disposal, and CO₂ storage. In order to assess the effects of wave-induced FDP in heterogeneous porous rocks, we simulate time-harmonic oscillatory tests based on a finite element (FE) discretization of Biot’s equations in the time-frequency domain for representative elementary volumes (REVs) of the considered rock masses. The major challenge for these types of simulations is the creation of adequate computational meshes, which resolve the numerous and complex interfaces between the heterogeneities and the embedding background. To this end, we have developed a novel method based on adaptive mesh refinement (AMR), which allows for the fully automatic creation of meshes for strongly heterogenous media. The key concept of the proposed method is to start from an initially uniform coarse mesh and then to gradually refine elements which have non-empty overlaps with the embedded heterogeneities. This results in a hierarchy of non-uniform meshes with a large number of elements close to the interfaces, which do, however, not need to be explicitly resolved. This dramatically simplifies and accelerates the laborious and time-consuming process of meshing strongly heterogeneous poroelastic media, thus enabling the efficient simulation of REVs containing heterogeneities of quasi-arbitrary complexity. After a detailed description of the methodological foundations, we proceed to demonstrate that the FE discretization with low-order FE has a unique solution and hence does not present spurious modes. We assess the practical effectiveness and accuracy of the proposed method by means of four case studies of increasing complexity.

中文翻译：

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用于介质嵌入复杂异质性的全自动自适应网格细化：在孔隙弹性流体压力扩散中的应用

通过数值模拟将地震波的衰减和速度色散与流体压力扩散（FDP）相关联对于限制非均质多孔岩石的力学和水力特性至关重要。反过来，这对于整个地球，环境和工程科学的各种重要应用都具有重要意义，例如地热能生产，碳氢化合物勘探，核废料处置和CO ₂存储。为了评估波浪诱导的FDP在非均质多孔岩石中的影响，我们基于时频域中Biot方程的有限元（FE）离散化来模拟时谐振动测试，以代表该时空中代表性的基本体积（REV）。被认为是岩体。这些类型的仿真的主要挑战是创建适当的计算网格，该网格可以解决异构性和嵌入背景之间的众多复杂接口。为此，我们开发了一种基于自适应网格细化（AMR）的新颖方法，该方法可以针对强异构介质完全自动创建网格。所提出方法的关键概念是从最初均匀的粗网格开始，然后逐步细化与嵌入的异质性具有非空重叠的元素。这导致不均匀网格的层次结构，其中大量元素靠近界面，但是并不需要明确解决。这极大地简化并加快了将强异质多孔弹性介质网格化的费力且耗时的过程，从而使包含准任意复杂度异质性的REV的有效模拟成为可能。在详细描述了方法学基础之后，我们继续证明低阶有限元离散化具有独特的解决方案，因此不会出现虚假模式。