An optimal frequency-domain finite-difference operator with a flexible stencil and its application in discontinuous-grid modeling

Abstract

We develop an optimal method to determine expansion parameters for flexible stencils in 2D scalar wave finite-difference frequency-domain (FDFD) simulation. The proposed stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, where the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. The proposed method can work in FDFD discontinuous-grid with arbitrary integer coarse-to-fine gird spacing ratios. Numerical examples are presented to demonstrate how to apply this optimal method for the discontinuous-grid FDFD schemes with spacing ratios 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, while the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, the proposed discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging and full waveform inversion.