Ph.D. student LAN Haiqiang and his teacher ZHANG Zhongjie simulate the three dimensional wave-field with irregular free surface.

They use a stable and explicit second-order accurate finite-difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 3D heterogeneous transversely isotropic medium. The free-surface boundary conditions are accurately applied by introducing a discretization that uses boundary modified difference operators for the mixed derivatives in the governing equations.

The accuracy of the proposed method is checked by comparing the numerical results obtained by the trial algorithm with the analytical solutions of the Lamb’s problem, for an isotropic medium and a transversely isotropic medium with a vertical symmetry axis, respectively. Efficiency tests performed by different numerical experiments illustrate clearly the influence of an irregular (nonflat) free surface on seismic-wave propagation

Lan and Zhang. Three-Dimensional Wave-Field Simulation in Heterogeneous Transversely Isotropic Medium with Irregular Free Surface. Bulletin of the Seismological Society of America, 2011, 101(3): 1354-1370 （Download Here）

Figure. Model of a half-space with Gaussian shape hill topography. (Image by LAN)

Figure Snapshots of the vertical component of the wave field at the surface (xy plane) at 2.3s propagation time for the Gaussian shape hill topography model. (Image by LAN)