IBFD for seismic wave modeling -A regular grid method handling arbitrary topography

Abstract

To accurately simulate seismic wave propagation for the purpose of land data acquisition, processing, and interpretation, especially for land data full waveform inversion (FWI), we developed an efficient high-order finite-difference modeling algorithm with the capability of handling arbitrarily shaped surface topography. Unlike most of the existing modeling algorithms dealing with irregular surface topography, this finite-difference algorithm, based on an immersed boundary (IB) method, uses regular Cartesian staggered or collocated grid system without suffering from the well-known staircasing error. In this immersed boundary finite-difference (IBFD) algorithm, arbitrary surface topography is accounted for by imposing the free surface boundary conditions at the exact boundary locations instead of using body-conforming grids, thus greatly reducing the complexity of preprocessing procedures. Furthermore, local continuity and curvatures (including sub-cell curvatures) are represented precisely through the employment of a local cylindrical or a spherical coordinate system. Wavefield values in a ghost zone required for boundary condition enforcement are obtained using a special recursive interpolation technique, which simplifies the boundary treatment and further improves the accuracy, as validated by the numerical simulation. Another unique feature of this algorithm is that the stencil length for ghost zone wavefield interpolation is adaptively determined by the local curvature to maintain the accuracy and stability. This method is a general algorithm applicable to acoustic, elastic, 2D, 3D, and anisotropic cases. A numerical example is presented to show its excellent performances compared with the conventional finitedifference method.