Elastic full-waveform inversion based on GPU accelerated temporal fourth-order finite-difference approximation

Elastic full-waveform inversion (FWI) estimates the subsurface velocity model by inverting multi-component seismic data. Most of the current elastic FWI solves the elastic wave equation by a temporal second-order finite-difference time-domain (FDTD) method. However, the traditional temporal second-order FDTD introduces large temporal dispersion in the case of a large time-stepping size. To suppress the temporal dispersion, a relatively small time step should be used, which increases the computational cost of FWI. We introduce a temporal fourth-order and spatial arbitrary even-order FDTD method for elastic wave modeling and inversion. The temporal fourth-order scheme can simulate a highly accurate wavefield, even when a large time step is used for temporal extrapolation. Compared with the traditional temporal second-order FDTD scheme, the temporal fourth-order FDTD enables a larger time step for its more relaxed stability condition and smaller dispersion. As a result, FWI with temporal fourth-order FDTD scheme can achieve high accuracy inversion without reducing much computational efficiency. We run our elastic FWI codes on a Graphic Processing Unit (GPU) computing platform, and to accelerate the GPU computing, we propose to use the GPU shared memory to reduce the data access delay. By transferring the data frequently accessed for the FDTD approximations, from the global memory to the shared memory, we realize the FDTD calculation in a more efficient way. Forward modeling and FWI examples are carried out to confirm the effectiveness of our elastic FWI.