Dispersion analysis of an average-derivative optimal scheme for Laplace-domain scalar wave equation

Abstract

Laplace-domain modeling is an important foundation of Laplace-domain full-waveform inversion. However, dispersion analysis for Laplace-domain numerical schemes has not been completely established. This hampers the construction and optimization of Laplace-domain modeling schemes. By defining a pseudowavelength as a scaled skin depth, I establish a method for Laplace-domain numerical dispersion analysis that is parallel to its frequency-domain counterpart. This method is then applied to an averagederivative nine-point scheme for Laplace-domain scalar wave equation. Within the relative error of 1%, the Laplace-domain average-derivative optimal scheme requires four grid points per smallest pseudowavelength, whereas the classic five-point scheme requires 13 grid points per smallest pseudowavelength for general directional sampling intervals. The average-derivative optimal scheme is more accurate than the classic five-point scheme for the same sampling intervals. By using much smaller sampling intervals, the classic fivepoint scheme can approach the accuracy of the averagederivative optimal scheme, but the corresponding cost is much higher in terms of storage requirement and computational time.

Forward Modeling of VTI Media in the Frequency‐Space Domain Based on an Average‐Derivative Optimal Method

“…Considering the geometrical symmetry of the VTI media ADM 9-point scheme in two cases of ∆x ≥ ∆z and ∆x < ∆z, as for the case of ∆x < ∆z, the only change is that the optimized coefficients corresponding to ∆x and ∆z are exchanged (Chen, 2012(Chen, , 2014. The solved optimized coefficients for different r = ∆z ∆x (∆x < ∆z) by the least-square optimal method are shown in Table 2 for r = 1.5, 2, 2.5, 3, 3.5, 4.…”