Abstract
AbstractBiot's equations describe the physics of hydromechanically coupled systems establishing the widely recognized theory of poroelasticity. This theory has a broad range of applications in Earth and biological sciences as well as in engineering. The numerical solution of Biot's equations is challenging because wave propagation and fluid pressure diffusion processes occur simultaneously but feature very different characteristic time scales. Analogous to geophysical data acquisition, high resolution and three dimensional numerical experiments lately redefined state of the art. Tackling high spatial and temporal resolution requires a high‐performance computing approach. We developed a multi‐ graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells. We present a comprehensive dimensional analysis reducing the number of material parameters needed for the numerical experiments from ten to four. Furthermore, the dimensional analysis emphasizes the key material parameters governing the physics of wave propagation in poroelastic media. We perform a dispersion analysis as function of dimensionless parameters leading to simple and transparent dispersion relations. We then benchmark our numerical solution against an analytical plane wave solution. Finally, we present several numerical modeling experiments, including a three‐dimensional simulation of fluid injection into a poroelastic medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results. The high efficiency of our numerical implementation makes it readily usable to investigate three‐dimensional and high‐resolution scenarios of practical applications.
Highlights
Majority of the most powerful supercomputers on the world host hardware accelerators to sustain calculations at the petascale level and beyond
We developed a multi- graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells
We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results
Summary
Majority of the most powerful supercomputers on the world host hardware accelerators to sustain calculations at the petascale level and beyond. One of the main application of Biot's equations in Earth sciences is the estimation of seismic dispersion and attenuation in porous media due to wave-induced fluid flow. Different methods have been used, based on combined finite-volumes/differences on structured grids (Blanc et al, 2013; Carcione & Quiroga-Goode, 1995; Chiavassa et al, 2010; Chiavassa & Lombard, 2011; Dai et al, 1995; Masson et al, 2006; Özdenvar & McMechan, 1997; Wenzlau & Müller, 2009; Zeng et al, 2001; Zhu & McMechan, 1991), pseudo-spectral methods (Özdenvar & McMechan, 1997), discontinuous Galerkin methods (de la Puente et al, 2008; Dupuy et al, 2011; Shukla et al, 2019, 2020; Ward et al, 2017; Zhan et al, 2019), spectral element methods (Morency & Tromp, 2008), and finite-volume methods (Lemoine, 2016; Lemoine et al, 2013) Most of these studies implemented the corresponding equations as a first-order hyperbolic system and used explicit time integration schemes as it is convenient for the elastic wave propagation, except for (Morency & Tromp, 2008; Özdenvar & McMechan, 1997), where a. We achieve a very fast execution time (seconds) using high-resolution models involving more than 1.5 billion grid cells
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