Finite-difference Seismic Modeling on CPUs/GPUs Using Matrix-vector Products

Modern seismic imaging methods such as reverse time migration (RTM) or full-waveform inversion (FWI) require large high-performance computing (HPC) systems to provide enough computational power to solve a large number of forward problems based on the wave equation. These wavefield simulations are conventionally performed by explicit time-domain finite-difference (FD) methods on regular numerical grids, where the parallelization is often based on a fixed and rather inflexible decomposition of the computational domain. However, such parallelization cannot exploit the computing capacities of modern and especially future exascale HPC architectures, which are expected to become more and more hierarchical and non-uniform. For this purpose, we developed a matrix-vector formulation of the explicit time-domain FD method solving the 3D elastic wave equation. To implement the matrix-vector formalism, we chose the open-source framework LAMA, which allows the development of hardware-independent code. We found that the implementation of such a matrix-vector based 3D elastic forward solver is straightforward. In a strong and weak scaling benchmark, we subsequently explored the scaling behavior of our implementation. The overall scaling performance shows the large potential of our method, which can be improved even further by tuning on the application and framework level.