A Three-dimensional Immersed Boundary Method for Accurate Simulation of Acoustic Wavefields with Complex Surface Topography

Abstract

Irregular topography of the free surface significantly affects seismic wavefield modelling, especially when employing finite-difference methods on rectangular grids. These methods represent the free surface as discrete points, resulting in a boundary that resembles a “staircase”. This approximation inaccurately represents surface topography, introducing errors in surface reflection traveltimes and generating artificial diffractions in wavefield simulation. We introduce a stable three-dimensional immersed boundary method (3DIBM) employing Cartesian coordinates to address these challenges. The 3DIBM enables the simulation of acoustic waves in media with complex topography through standard finite difference, extending the two-dimensional immersed boundary approach to compute spatial coordinates for ghost and mirror points in a three-dimensional space. Wavefield values at these points are obtained by three-dimensional spatial iterative symmetric interpolation, specifically through the Kaiser windowed sinc method. By implicitly implementing the free surface boundary condition in three dimensions, this method effectively reduces artificial diffractions and enhances the accuracy of reflection traveltime. The effectiveness and accuracy of 3DIBM are validated through numerical tests and pre-stack depth migration (PSDM) imaging with simulated data, demonstrating its superiority as a modelling engine for migration imaging and waveform inversion in three-dimensional land seismic analysis.