Resolving Wave Propagation in Anisotropic Poroelastic Media Using Graphical Processing Units (GPUs)

Biot'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.ISSN:2169-9313ISSN:0148-0227ISSN:2169-935

A time-domain finite element boundary integral approach for elastic wave scattering

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach

Advanced BEM-based methodologies to identify and simulate wave fields in complex geostructures

To enhance the applicability of BEM for geomechanical modeling numerically optimized BEM models, hybrid FEM-BEM models, and parallel computation of seismic Full Waveform Inversion (FWI) in GPU are implemented. Inverse modeling of seismic wave propagation in inhomogeneous and heterogeneous half-plane is implemented in Boundary Element Method (BEM) using Particle Swarm Optimization (PSO). The Boundary Integral Equations (BIE) based on the fundamental solutions for homogeneous elastic isotropic continuum are modified by introducing mesh-dependent variables. The variables are optimized to obtain the site-specific impedance functions. The PSO-optimized BEM models have significantly improved the efficiency of BEM for seismic wave propagation in arbitrarily inhomogeneous and heterogeneous media. Similarly, a hybrid BEM-FEM approach is developed to evaluate the seismic response of a complex poroelastic soil region containing underground structures. The far-field semi-infinite geological region is modeled via BEM, while the near-field finite geological region is modeled via FEM. The BEM region is integrated into the global FEM system using an equivalent macro-finite-element. The model describes the entire wave path from the seismic source to the local site in a single hybrid model. Additionally, the computational efficiency of time domain FWI algorithm is enhanced by parallel computation in CPU and GPU

Sdružené inverzní modelování koseismického a postseismického skluzu kalifornského zemětřesení South Napa 2014

Název: Sdružené inverzní modelování koseismického a postseismického skluzu kalifornského zemětřesení South Napa 2014 Autor: Jan Premus Katedra: Katedra geofyziky Vedoucí dizertační práce: prof. František Gallovič, Katedra geofyziky Abstrakt: Skluz na tektonických zlomech probíhá nejen krátkodobě v průběhu zemětřesení (tzv. koseismicky), ale i v dlouhodobějším měřítku ve formě postseis- mického dokluzu, jak dokumentují měření pomocí seismogramů a geodetických metod. Oba typy skluzu byly dosud modelovány většinou odděleně a navíc převážně kinematicky. Zde představujeme Bayesovskou metodu pro inverzní fyzikální modelování koseismického a postseismického skluzu, která využívá sjed- nocující zákon tření typu "rate-and-state". Vyvinuli jsme efektivní otevřený kód FD3D TSN pro simulaci šíření zemětřesné trhliny metodou konečných difer- encí. Využití GPU vede k až desetinásobnému zrychlení kódu oproti CPU, což umožňuje provést stovky tisíc simulací zemětřesení v rozumném čase. Im- plementovali jsme také kvazidynamickou simulaci dokluzu metodou hraničních prvků. Bayesovskou dynamickou inverzi jsme aplikovali na zemětřesení v kali- fornské Napě z roku 2014 (Mw 6,0). Získaný sdružený model vysvětluje dy-...Title: Joint inverse modeling of coseismic and postseismic slip of the 2014 South Napa, California, earthquake Author: Jan Premus Department: Department of Geophysics Supervisor: prof. František Gallovič, Department of Geophysics Abstract: Slip at tectonic faults spans a wide range of time scales, from tens of seconds of earthquake coseismic rupture to months of aseismic afterslip, recorded in seismograms and geodetic data. The two slip phenomena are often studied separately, focusing on kinematic aspects. We introduce a Bayesian method for physics-based joint inverse modeling of an earthquake slip and afterslip, employ- ing a unifying rate-and-state friction law. To simulate the rupture propagation, we develop an efficient finite-difference open-source code FD3D TSN. GPU ac- celeration of the code yields speed-up by a factor of 10 with respect to a CPU, enabling hundreds of thousands of earthquake simulations in a reasonable time. We also implement a quasi-dynamic afterslip simulation using a boundary inte- gral element method. We apply the Bayesian dynamic inversion to the 2014 Mw 6.0 Napa earthquake. We reveal the dynamics of coseismic and postseismic slip in terms of stress and friction in a unified model, reconciling previous disjunctive analyses of the event. We show that the two types of slip are mostly...Katedra geofyzikyDepartment of GeophysicsMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Theoretical and numerical modeling of Rayleigh wave scattering by an elastic inclusion

This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having arbitrary shape and crystallographic symmetry. The theoretical model is developed based on the reciprocity theorem using the far-field Green's function and the Born approximation, assuming a small acoustic impedance difference between the host and inclusion materials. The numerical finite element (FE) model is established to deliver relatively accurate simulation of the scattering problem and to evaluate the approximations of the theoretical model. Quantitative agreement is observed between the theoretical model and the FE results for arbitrarily-shaped surface/subsurface inclusions with isotropic/anisotropic properties. The agreement is excellent when the wavelength of the Rayleigh wave is larger than, or comparable to, the size of the inclusion, but it deteriorates as the wavelength gets smaller. Also, the agreement decreases with the anisotropy index for inclusions of anisotropic symmetry. The results lay the foundation for using Rayleigh waves for quantitative characterization of surface/subsurface inclusions, while also demonstrating its limitations.Comment: 25 pages, 8 figures. The article has been submitted to The Journal of the Acoustical Society of America. After it is published, it will be found at https://asa.scitation.org/journal/ja