Three-Dimensional Elastic Full-Waveform Inversion Using Temporal Fourth-Order Finite-Difference Approximation

Full-waveform inversion (FWI) serves as a useful tool to quantitatively investigate the properties of the subsurface. Presently, 3-D elastic FWI uses a finite-difference time-domain (FDTD) approach in numerical simulation. However, such an FDTD scheme often includes only second-order temporal approximations, causing errors in temporal dispersion in the case of a large time-stepping size. Such temporal dispersion will affect the inversion results and reduce the inversion quality. We introduce a unique 3-D elastic FWI using a temporal fourth-order finite-difference (FD) approximation. A new quasi-stress–velocity elastic equation is solved by the temporal fourth-order and spatial arbitrary even-order FDTD method, and a novel inversion procedure for the convolutional objective function based on this equation is derived. The multiscale strategy is used to enhance the robustness of our algorithm. The forward modeling and FWI examples presented here demonstrate that our method can achieve modeling and inversion with a high degree of accuracy.