A non-perturbative approach to computing seismic normal modes in rotating planets

作     者：Shi, Jia Li, Ruipeng Xi, Yuanzhe Saad, Yousef de Hoop, Maarten V. 

作者机构：Department of Earth Environmental and Planetary Sciences Rice University TX United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory CA United States Department of Mathematics Emory University AtlantaGA United States Department of Computer Science and Engineering University of Minnesota MN United States Department of Computational and Applied Mathematics Rice University TX United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2019年

核心收录：

主　　题：Seismology 

摘      要：MSC Codes 86-08, 86-04, 85-04, 85-08, 85-10, 15A18, 65N25, 65N30A Continuous Galerkin method based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial filtering eigensolver. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method. Our discretization utilizes fully unstructured tetrahedral meshes for both solid and fluid regions. The relevant eigenvalue problem is solved by a combination of several highly parallel and computationally efficient methods. We validate our three-dimensional results in the non-rotating case using analytical results for constant elastic balls, as well as numerical results for an isotropic Earth model from standard radial algorithms. We also validate the computations in the rotating case, but only in the slowly-rotating regime where perturbation theory applies, because no other independent algorithms are available in the general case. The algorithm and code are used to compute the point spectra of eigenfrequencies in several Earth and Mars models studying the effects of heterogeneity on a large range of scales. Copyright © 2019, The Authors. All rights reserved.