Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere: Preliminary Result for the 2D Case
Advancements in the Global Geodetic Observing System (GGOS) have enabled us to investigate the effects of lateral heterogeneities in the internal Earth structure on long-term surface deformations caused by the Glacial Isostatic Adjustment (GIA). Many theo
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Abstract
Advancements in the Global Geodetic Observing System (GGOS) have enabled us to investigate the effects of lateral heterogeneities in the internal Earth structure on long-term surface deformations caused by the Glacial Isostatic Adjustment (GIA). Many theories have been developed so far to consider such effects based on analytical and numerical approaches, and 3D viscosity distributions have been inferred. On the other hand, fewer studies have been conducted to assess the effects of lateral heterogeneities on short-term, elastic deformations excited by surface fluids, with 1D laterally homogeneous theories being frequently used. In this paper, we show that a spectral finite-element method is applicable to calculate the elastic deformation of an axisymmetric spherical Earth. We demonstrate the effects of laterally heterogeneous moduli with horizontal scales of several hundred kilometers in the upper mantle on the vertical response to a relatively largescale surface load. We found that errors due to adopting a 1D Green’s function based on a local structure could amount to 2–3% when estimating the displacement outside the heterogeneity. Moreover, we confirmed that the mode coupling between higher-degree spherical harmonics needs to be considered for simulating smaller-scale heterogeneities, which agreed with results of previous studies. Keywords
Finite element method GGOS Lateral heterogeneity Mass redistribution Surface loading
1 Y. Tanaka () Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan e-mail: [email protected] V. Klemann Department 1: Geodesy, Helmholtz Centre Potsdam—GFZ German Research Centre for Geosciences, Potsdam, Germany Z. Martinec Faculty of Mathematics and Physics, Charles University in Prague, Praha 8, Czech Republic School of Cosmic Physics, Dublin Institute for Advanced Studies, Dublin 2, Ireland
Introduction
A surface-loading response is a geophysical process that describes deformation of the solid Earth due to variations in surface fluids including the atmosphere, ocean, continental water and ice sheets. Short-term responses to these loads are usually modeled by elastic deformation. Farrell (1972)’s theoretical framework based on Green’s function (GF) method is well known. Mathematically, it enables us to estimate local as well as global scale elastic deformations of a selfgravitating, layered sphere to a load applied at the surface of the Earth. On the other hand, long-term responses of the Earth caused by the GIA have been modeled by viscoelastic
International Association of Geodesy Symposia, https://doi.org/10.1007/1345_2019_62, © Springer Nature Switzerland AG 2019
Y. Tanaka et al.
relaxation. A number of authors have developed theoretical models for laterally homogeneous (e.g., Peltier 1974) and heterogeneous (e.g., D’Agostino et al. 1997; Kaufmann and Wolf 1999; Wu 2002) cases (see the review by Whitehouse (2018) for more details). The authors of this paper also developed a computational method in which 3D viscosity distrib
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