Wave propagation in three-dimensional spherical sections by the Chebyshev spectral method

The elastic wave equation in spherical coordinates is solved by a Chebyshev spectral method. In the algorithm presented the singularities in the governing equations are avoided by centring the physical domain around the equator. The highly accurate pseudospectral (PS) derivative operators reduce the required grid size compared to finite difference (FD) algorithms. The non-staggered grid scheme allows easy extension to general material anisotropy without additional interpolations being required as in staggered FD schemes. The boundary conditions previously derived for curvilinear coordinate systems can be applied directly to the velocity vector and stress tensor in the spherical basis. The algorithm is applied to the problem of a double-couple source located in a high-velocity region at the top of the mantle (slab). The synthetic seismograms show azimuth-dependent traveltime and waveform effects which are likely to be observable in regions where subduction takes place. Such techniques are important in modelling the full-wave characteristics of the Earth's 3-D structure and in providing accurate reference solutions for 3-D global models.