Trapezoid-grid finite difference frequency domain method for seismic wave simulation

Abstract

Abstract The large computational cost and memory requirement for the finite difference frequency domain (FDFD) method limit its applications in seismic wave simulation, especially for large models. For conventional FDFD methods, the discretisation based on minimum model velocity leads to oversampling in high-velocity regions. To reduce the oversampling of the conventional FDFD method, we propose a trapezoid-grid FDFD scheme to improve the efficiency of wave modeling. To alleviate the difficulty of processing irregular grids, we transform trapezoid grids in the Cartesian coordinate system to square grids in the trapezoid coordinate system. The regular grid sizes in the trapezoid coordinate system correspond to physical grid sizes increasing with depth, which is consistent with the increasing trend of seismic velocity. We derive the trapezoid coordinate system Helmholtz equation and the corresponding absorbing boundary condition, then get the FDFD stencil by combining the central difference method and the average-derivative method (ADM). Dispersion analysis indicates that our method can satisfy the requirement of maximum phase velocity error less than $1\%$ with appropriate parameters. Numerical tests on the Marmousi model show that, compared with the regular-grid ADM 9-point FDFD scheme, our method can achieve about $80\%$ computation efficiency improvement and $80\%$ memory reduction for comparable accuracy.