Solving 3D anisotropic elastic wave equations on parallel GPU devices

Abstract

Efficiently modeling seismic datasets in complex 3D anisotropic media by solving the 3D elastic wave equation is an important challenge in computational geophysics. Using a stress-stiffness formulation on a regular grid, we present a 3D finite-difference time-domain (FDTD) solver using a 2 nd-order temporal and 8 thorder spatial accuracy stencil that leverages the massively parallel architecture of graphics processing units (GPUs) to accelerate the computation of key kernels. The relatively small memory of an individual GPU limits the model domain sizes that can be computed on a single device. To circumvent this constraint and move toward modeling industry-sized 3D anisotropic elastic data sets, we parallelize computation across multiple GPU devices by using domain decomposition and, for each time step, employing an inter-device communication protocol to exchange data values falling within interior boundaries of each sub-domain. For two or more GPU devices within a single compute node, we use direct peer-topeer (i.e., GPU-to-GPU) communication, while for networked nodes we employ message-passing interface (MPI) directives to route data over the network. Our 2D GPU-based anisotropic elastic modeling tests achieved a 10× speedup relative to an OpenMP CPU implementation run on an eight-core machine, while our 3D tests using dual GPU devices produced up to a 28× speedup. The performance boost afforded by the GPU architecture allows us to model seismic data for 3D anisotropic elastic models at lower hardware cost and in less time than previously possible.

Time-lapse image-domain tomography using adjoint-state theory

“…We use a 2D elastic finitedifference modelling code to generate baseline and monitor datasets using the P-wave slowness models shown in Figure 2. We use six equally spaced, horizontal density reflectors to introduce reflectivity (Weiss and Shragge, 2013). Figure 3a presents the one-way wave-equation migration baseline image using s 0 = 0.5 s/km migration slowness model.…”

Fast GPU-Based Seismogram Simulation From Microseismic Events in Marine Environments Using Heterogeneous Velocity Models

“…finite difference [15] [16][17] [18], finite element [19] [20][21] [22], spectral element [23] [24], discontinuous Galerkin method [25] [26], and on multi-GPU clusters [27] [28][29] [30]. Computational efficiency of such models are compared on three different NVIDIA GPUs (C1060, C2050, M2090) in Zhou et al [31] and in different size of models in Danek [32].…”

Time-domain 3D Wave Propagation Modeling and Memory Management Using Graphics Processing Units

“…기존 연구에서도 3차 원 파동 방정식 모델링을 구현한 사례들이 있으나, 주로 연산 을 위한 공유 메모리 사용이나 영역 분해를 위한 통신 등에만 초점을 맞추고 CPU 메모리와 GPU 메모리 사이의 효율적인 통신에 관한 언급은 거의 없었다 (Micikevicius, 2009;Komatitsch et al, 2009;Michéa and Komatitsch, 2010;Komatitsch et al, 2010a, b;Mu et al, 2013;Weiss and Shragge, 2013) …”