2D finite-difference viscoelastic wave modelling including surface topography

We have pursued two-dimensional (2D) finite-difference (FD) modelling of seismic scattering from free-surface topography. Exact free-surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity-stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free-surface topography. The wave equations are numerically discretized by an eighth-order FD method on a staggered grid in space, and a leap-frog technique and the Crank-Nicholson method in time. In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Karman realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities.