Institute of Geophysics
Ludwig-Maximilians-University
Munich
Germany
Email:
igel@geophysik.uni-muenchen.de
poster/oral: oral
| The calculation of synthetic seismograms for general three-dimensional spherical Earth models is one of the most important steps today to go beyond ray-based tomography and improve the structural resolution of the deep Earth imaging process. As the perturbation approach to normal-mode methods does not seem to be a viable approach, common numerical methods for the solution of time-dependent partial differential equations like the finite-difference method, the finite- (or spectral-) element method, the finite-volume method, or pseudospectral methods are now being applied to the problem of seismic wave propagation in a 3D spherical Earth. These grid-based methods can in general not directly be applied to the elastic wave equation in spherical coordinates. The reason is that a standard discretization of the spherical coordinate axes (r, q, f) lead to grid cells which decrease in size towards the rotational axis leading to stability problems. In addition, the axis q=0 is a singularity and the wave equation is not defined. We will present various algorithms aiming at complete solutions for spherical Earth models. First, an axisymmetric approach allows a reduction of the problem to two dimensions. When centering the source on the rotational axis, the 3D geometric spreading can be simulated correctly for zonal sources (e.g. explosions, toroidal sources, vertical forces), models, and wavefields. The advantage is that one can achieve high frequencies due to the two-dimensional computational domain. 3D spherical sections can be simulated in spherical coordinates when keeping away from the poles and geographical models are rotated accordingly. We will also present initial results from combining the axisymmetric approach with a 3D spherical section. This allows a teleseismic wavefield to flow into a 3D box (e.g. at the surface of the Earth containing a plume) with the options to have the correct scattering behavior for 3D objects near the surface. We will show results using these algorithms to problems of wave propagation in subduction zones, plumes and heterogeneous lower mantle models. |