Solving 3D Anisotropic Elastic Wave Equations on Parallel GPU Devices

Conclusions

We present a GPU-based FDTD solution to the 3D elastic wave equation in a stress-stiffness formulation on a regular computational mesh that allows rapid modeling of data sets for 3D anisotropic TI media. We present a FD formulation of $2^{nd}$ -order temporal and $8^{th}$ -order spatial accuracy that leads to a compact stencil with a regular memory access pattern that is well-suited for running wavefield simulations on GPU devices. For the 3D algorithm we follow a loop unrolling approach over the slowest varying axis to minimize read redundancy from the GPU global memory. To circumvent the relatively limited memory on a GPU card, we use a domain decomposition strategy and employ CUDA's native P2P communications between multiple GPU devices housed within a single node. For situations involving a network of GPU-enabled compute nodes, we use the MPI instruction set to enable communication between GPUs.

For 2D elastic modeling we achieved a 10$\times$ GPU speedup relative to an eight-core CPU version, while 3D anisotropic elastic modeling tests indicate up to a 16$\times$ improvement for a single GPU and a maximum 28$\times$ speedup when using two GPU devices relative to CPU benchmarks. These GPU-based speedup improvements allow us to efficiently model 3D elastic anisotropic phenomena and compute data sets for velocity and anisotropic parameter estimation and migration at lower hardware cost and with fewer total compute resources than heretofore possible.

Solving 3D Anisotropic Elastic Wave Equations on Parallel GPU Devices