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Fractures significantly impact the elastic and hydraulic properties of geological structures, influencing fields like geothermal energy, hydrocarbon exploration, nuclear waste disposal and |$\mathrm{ \mathrm{CO}}_2$| storage. Characterizing these formations is challenging due to the scale disparity between seismic wavelengths and fracture sizes. This study leverages decades of analytical and numerical advancements to evaluate the effective mechanical properties of fractured solids at the mesoscopic scale. A novel numerical method for modelling quasi-static Biot's poroelastic equations using graphics processing units (GPUs) is introduced for simulating hydromechanically coupled systems. Capable of handling up to 133 million voxel elements on a single GPU, this method offers unprecedented spatial resolution to model complex fracture networks. The GPU-accelerated solver, FastBiot_QS, delivers exceptional performance, achieving a computational speedup of approximately 520 times compared to central processing unit-based methods. The solver's accuracy is rigorously validated in 1-D and 3-D setups. Simulations reveal that fracture clustering and spatial distribution significantly affect seismic attenuation and modulus dispersion. Clusters of interconnected fractures lead to higher attenuation at higher frequencies, while sparsely distributed fractures result in higher attenuation at lower frequencies. Simulations with log-normal and uniform distributions present intermediate behaviours between densely clustered and sparsely distributed fractures. The study can improve interpretations of seismic data and hydraulic properties in fractured media. [ABSTRACT FROM AUTHOR]

The Accelerated Pseudo-Transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization. With the advent of the memory-wall phenomenon around 2005, where memory access speed overtook floating-point operations as the bottleneck in high-performance computing, the APT method has gained prominence as a powerful tool for tackling various PDEs in geosciences. Recent advancements have demonstrated the APT method's computational efficiency, particularly when applied to quasi-static nonlinear problems using Graphical Processing Units (GPUs). This manuscript presents a comprehensive analysis of the APT method, focusing on its application to quasi-static elastic, viscoelastic, and coupled hydro-mechanical problems, specifically those governed by quasi-static Biot's poroelastic equations, across 1D, 2D, and 3D domains. We systematically investigate the optimal numerical parameters required to achieve rapid convergence, offering valuable insights into the method's applicability and efficiency for a range of physical models. Our findings are validated against analytical solutions, underscoring the robustness and accuracy of the APT method in both homogeneous and heterogeneous media. We explore the influence of boundary conditions, non-linearities, and coupling on the optimal convergence parameters, highlighting the method's adaptability in addressing complex and realistic scenarios. To demonstrate the flexibility of the APT method, we apply it to the nonlinear mechanical problem of strain localization using a poro-elasto-viscoplastic rheological model, achieving extremely high resolutions – 10,0002 voxels in 2D and 5123 voxels in 3D – that, to our knowledge, have not been previously explored for such models. Our study contributes significantly to the field by providing a robust framework for the effective implementation of the APT method in solving challenging geophysical problems. Importantly, the results presented in this paper are fully reproducible, with Matlab, symbolic Maple scripts, and CUDA C codes made available in a permanent repository. [ABSTRACT FROM AUTHOR]

The interplay between compaction‐driven fluid flow and plastic yielding within porous media is investigated through numerical modeling. We establish a framework for understanding the dynamics of fluid flow in deforming porous materials that corresponds to the equations describing solitary porosity wave propagation. A concise derivation of the coupled fluid flow and poro‐viscoelastoplastic matrix behavior is presented, revealing a connection to Biot's equations of poroelasticity and Gassmann's theory in the elastic limit. Our findings demonstrate that fluid overpressure resulting from channelized fluid flow initiates the formation of new shear zones. Through three‐dimensional simulations, we observe that the newly formed shear zones exhibit a parabolic shape. Furthermore, plasticity exerts a significant influence on both the velocity of fluid flow and the shape of fluid channels. Importantly, our study highlights the potential of spontaneous channeling of porous fluids to trigger seismic events by activating both new and pre‐existing faults. Plain Language Summary: In this study, we looked at how fluids move through porous rocks and how they interact with the solid frame of the rocks. The physics was explored in two‐ and three‐dimensions by leveraging the power of high‐performance computing (HPC) based on graphical processing units (GPU). We found that two key processes occur at the same time: fluid flow gets concentrated into channels due to the changing pressure and interaction with the solid material, and it also forms dike‐like structures as it pushes into newly formed shear zones. Importantly, our study highlights the potential of spontaneous channeling of porous fluids to trigger seismic events by activating both new and pre‐existing faults. This research underscores the complex relationship between fluid flow dynamics and geomechanical processes, offering insights into the mechanisms underlying earthquake initiation. Key Points: We present the numerical modeling of fully coupled fluid flow and poro‐viscoelastoplastic matrix flow with decompaction weakeningWe show that fluid overpressure at the tip of the fluid flow channel triggers the development of non‐symmetric shear bandsWe discover that plastic yielding accelerates the fluid flow and modifies the fluid flow pattern [ABSTRACT FROM AUTHOR]

Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and concrete. In the Earth's crust, irreversible deformation can occur in brittle as well as in ductile regimes. Modeling of shear zones is essential in the geodynamic framework. Numerical modeling of strain localization remains challenging due to the non‐linearity and multi‐scale nature of the problem. We develop a numerical approach based on graphical processing units (GPU) to resolve the strain localization in two and three dimensions of a (visco)‐hypoelastic‐perfectly plastic medium. Our approach allows modeling both the compressible and incompressible visco‐elasto‐plastic flows. In contrast to symmetric shear bands frequently observed in the literature, we demonstrate that using sufficiently small strain or strain rate increments, a non‐symmetric strain localization pattern is resolved in two‐ and three‐dimensions, highlighting the importance of high spatial and temporal resolution. We show that elasto‐plastic and visco‐plastic models yield similar strain localization patterns for material properties relevant to applications in geodynamics. We achieve fast computations using three‐dimensional high‐resolution models involving more than 1.3 billion degrees of freedom. We propose a new physics‐based approach explaining spontaneous stress drops in a deforming medium. Plain Language Summary: Strain localization is the accumulation of strain in narrow regions of rocks and other materials like metals, soils, and concrete, occurring at different scales. The strength of most geomaterials, particularly rocks, is strongly pressure‐dependent, with strength increasing with increasing pressure. We developed efficient numerical algorithms using High‐Performance Computing (HPC) and graphical processing units (GPUs) to model strain localization in 2D and 3D for applications in geodynamics and earthquake physics. Unlike previous models, our method reveals non‐symmetrical patterns by using very small strain increments, highlighting the need for high‐detail modeling. We found that elasto‐plastic and visco‐plastic models show similar strain patterns for relevant materials. Our method also achieves fast, detailed computations with over 1.3 billion variables and offers a new explanation for sudden stress drops in deforming materials. Key Points: We resolve material instability during deformation resulting in a non‐symmetric pattern of strain localizationWe demonstrate the similarity in patterns of strain localization between frictional and time‐dependent plasticity modelsWe achieve fast numerical simulations in high‐resolution model setups in three dimensions involving more than 500 million degrees of freedom [ABSTRACT FROM AUTHOR]

Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing noninvasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries, appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid–solid deformation at the pore scale based on coupled Lamé–Navier and Navier–Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. Furthermore, the overall anisotropy of a medium mainly increases due to squirt flow, but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface. [ABSTRACT FROM AUTHOR]

Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing non-invasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid-solid deformation at the pore scale based on coupled Lame-Navier and Navier-Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. We show that the overall anisotropy of a medium mainly increases due to squirt flow but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface. [ABSTRACT FROM AUTHOR]

Biot's theory describes the coupled solid-fluid interaction in a porous medium. In the earth sciences, poroelasticity is essential in many applications, for example, in hydrogeology, in seismic monitoring of CO2 reservoirs, etc. In the present work, we solve Biot's equations for particle velocity and stress in the time domain with a finite difference approach on a staggered grid. Depending on the medium's properties, besides the elastic compressional and shear waves, one may observe the propagating slow wave or the diffusive static slow mode. In such a case, when the diffusive slow mode is present, the time-stepping should be very small in order to reach a stable simulation of Biot's equations. We present a new treatment of this problem based on the so-called pseudo-transient method. The idea is that at each time step, another pseudo iteration causes the slow mode to attenuate quickly. As a result, very fine time-stepping is unnecessary and the time-stepping is controlled by a standard Courant stability condition for the fast P-wave. Furthermore, we accelerate a finite-difference code using an NVIDIA graphics card with the CUDA programming language. [ABSTRACT FROM AUTHOR]