An Overset Virieux-Lebedev FDTD Scheme for Efficient Seismic Wave Modeling in Complex Topography

Abstract

Accurate finite-difference modeling of seismic wave propagation with irregular free surfaces remains challenging. The standard staggered-grid (SSG) finite-difference method exhibits significant numerical dispersion when simulating surface waves, necessitating dense spatial sampling to maintain accuracy. In contrast, the Fully Staggered Grid (FSG) or Lebedev scheme, enhanced with Mimetic Finite Difference (MFD) operators, enables high-precision modeling with relatively few grid points (approximately eight points per minimum wavelength). However, FSG requires simultaneous computations on multiple staggered layouts, resulting in a substantial increase in computational cost. In many seismic imaging applications, using an FSG everywhere in the model domain is unnecessary and often inefficient. Motivated by this observation and inspired by overset grid techniques, we propose a hybrid-grid strategy to balance accuracy and efficiency. Near irregular free-surface boundaries, FSG is applied in general curvilinear coordinates to ensure accurate surface wave simulation. In deeper regions where topographic effects diminish, a more efficient SSG scheme is used. An overset grid strategy is introduced to ensure smooth wavefield transitions between the two regions. Numerical experiments demonstrate that the proposed method preserves computational accuracy while significantly reducing runtime, achieving a nearly 50% reduction in computation time. Furthermore, the use of a staggered grid eliminates source injection errors in the transition zone that typically arise when applying the MacCormack scheme in collocated grids, thereby simplifying the source implementation strategy.