The governing equations for the elastic-gravitational deformation of an Earth model involve a perturbed gravitational potential. The gravitational potential is governed by Poisson’s equation inside the Earth and by Laplace’s equation in the rest of space. The infinite domain and large-scale nature of the problem poses difficult challenges for numerical simulations in 3D Earth models. In order to tackle these challenges, we introduce a spectral-infinite-element method by combining the spectral-element method with the mapped infinite-element method. Spectral elements are used to represent internal fields, and infinite elements represent the external gravitational field. Infinite elements naturally couple with spectral elements, thereby avoiding an iterative procedure which is necessary if the Poisson/Laplace equation has to be solved independently. Potential applications of new method include long-period seismic wave propagation, as well as quasistatic problems, such as post-earthquake relaxation and glacial isostatic adjustment.
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