3-D finite-difference elastic wave modeling including surface topography

Three-dimensional finite-difference (FD) modeling of seismic scattering from free surface topography has been pursued. We have developed exact 3-D free surface topography boundary conditions for the particle velocities. A velocity-stress formulation of the full elastic wave equations together with the boundary conditions has been numerically modeled by an eighth-order FD method on a staggered grid. We give a numerical stability criterion for combining the boundary conditions with curved-grid wave equations, where a curved grid represents the physical medium with topography. Implementation of this stability criterion stops instabilities from arising in areas of steep and rough topographies. We have simulated scattering from teleseismic P-waves using a plane, vertically incident wavefront and real topography from a 40 x 40 km area centered at the NORESS array of seismic receiver stations in southeastern Norway. Synthetic snapshots and seismograms of the wavefield show clear conversion from P-waves to Rg (short period fundamental mode Rayleigh) waves in an area of rough topography approximately 10 km east of NORESS. This result is consistent with numerous observations.