Wave Propagation in 3 - D

The elastic wave equation in spherical coordinates is solved on a spherical section by a Chebyshev spectral method. In the presented algorithm the singularities in the governing equations are avoided by centering the physical domain around the equator. The highly accurate pseudo-spectral (PS) derivative operators reduce the required grid size compared to nite-diierence (FD) algorithms. The non-staggered grid scheme allows easy extension to general material anisotropy without the additional interpolations required in staggered FD schemes. The boundary conditions previously derived for curvi-linear coordinate systems can directly be applied to the velocity vector and stress tensor in the spherical basis. Such techniques will be important to model the full 3-D characteristics of upper mantle structure and to provide accurate reference solutions for 3-D global models.