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Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere: Preliminary Result for the 2D Case

Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA,volume 151)

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 large-scale 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

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Acknowledgements

We appreciate valuable comments from two anonymous reviewers. This work was initiated when YT was visiting the GFZ German research center, and he acknowledges the hospitality of the institute, and, through VK, contributes to the Helmholtz project, “Advanced Earth system Modelling Capacity (ESM)”. This study was partly supported by JSPS KAKENHI Grant Numbers JP15K17746, JP16H02219 and JP16H06474.

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Correspondence to Yoshiyuki Tanaka .

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Tanaka, Y., Klemann, V., Martinec, Z. (2019). Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere: Preliminary Result for the 2D Case. In: Novák, P., Crespi, M., Sneeuw, N., Sansò, F. (eds) IX Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 151. Springer, Cham. https://doi.org/10.1007/1345_2019_62

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