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Thursday, March 16 • 4:00pm - 5:30pm
Poster: Robust Computation of Seismic Normal Modes using Rayleigh-Ritz Galerkin Method in a Spherically Symmetric Earth

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The most popular software package Mineos is widely used in computing synthetic seismograms in a spherically symmetric non-rotating Earth. However, it fails to handle the catastrophic eigenvalue clustering. The eigenfunctions of different modes with very close eigenvalues are not orthogonal. On the contrast, our package can get the pure eigenfunctions verified by the classification theory.

Instead of introducing the minor vectors and shooting method used by Mineos, we choose the generalized Rayleigh-Ritz-Galerkin finite element method based on Buland's approach, which leads to a generalized eigenvalue problem. Buland's method works perfectly fine for toroidal modes, and however, it suffers from the ``extraneous" eigenfrequencies throughout the eigenspectrum. The eigenfunctions of these non-seismic modes have energies concentrated in the fluid outer core, which indicates that we need a novel technique to deal with the fluid region. Our method creatively projects out these non-seismic outer core modes by introducing the pressure besides the normal and tangential displacements. Based on Lehoucq's shift-invert strategy, we utilize a sparse, direct solver to speed up the algorithm.

Our package has a number of advantages over the finite difference and shooting method. The utilization of generalized Rayleigh-Ritz technique can handle the artificial sigularity at the center of the Earth. Therefore we can abandon the shooting method, which makes our approach more stable, mode independent, more efficient for the high accuracy requirement. Moreover, the Finite Element Method preserves the high accuracy across the boundary compared to Finite Difference Method. Most importantly, our successful projection in the fluid region can properly handle near degeneracy in eigenfrequency. We are also working on a parallel package to compute the non-symmetric three-dimensional seismic normal modes.

Thursday March 16, 2017 4:00pm - 5:30pm
Exhibit Hall BRC