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

Abstract

AbstractThis paper proposed a new kind of qP wave equation second‐order 9‐point scheme of two‐dimensional vertical transversely isotropic (VTI) media in the frequency‐space domain based on an average‐derivative optimal method (ADM for short). This scheme represents the finite‐difference approximations of the second‐order centered spatial‐derivative terms of two‐dimensional VTI media qP wave equation as the weighted average of 3 grid points in orthogonal directions and the acceleration term as the weighted average of all 9 grid points. Determining the optimal weighting coefficients of the second‐order centered spatial‐derivative terms and the acceleration term by using the least‐square optimal method to minimize numerical dispersion, the number of grid points per wavelength bounded by a phase velocity error range of ±1% is only 3.57. But the VTI conventional 9‐point scheme needs approximately 12 grid points per wavelength bounded by the same error range of ±1%, so the ADM method significantly increases the computational accuracy. The numerical example of the complex BP2007 2D VTI ocean standard model also proves the validity and precision of the VTI media ADM 9‐point scheme.