A rectangular staggered-grid finite-difference scheme with fourth-order temporal accuracy for pseudo-acoustic VTI modelling

摘要

Current staggered-grid finite-difference (SFD) schemes for anisotropic wave equations can ensure only high-order spatial modelling accuracy, whereas the time discretisation accuracy is still of second-order. To improve temporal modelling accuracy, we develop a rectangular SFD scheme with fourth-order temporal accuracy to solve the first-order pseudo-acoustic wave equation in vertical transversely isotropic media. High-order temporal accuracy is achieved by applying the high-order temporal derivatives, which can be replaced with the high-order spatial derivatives to reduce the computational cost. The corresponding high-order finite-difference (FD) coefficients are generated by using Taylor-series expansion and least-squares. Dispersion and stability analyses indicate that our proposed method has higher accuracy and better stability than the conventional method. Several modelling examples confirm that our proposed scheme exhibits low temporal dispersion even for a large time step. Because of the high-order accuracy in time and space domains, our new SFD scheme allows for a larger time step and shorter operator length, which is more efficient.