Isogeometric analysis of the lithosphere under topographic loading: Igalith v1.0.0

Abstract

This paper presents methods from isogeometric finite-element analysis for numerically solving problems in geoscience involving partial differential equations. In particular, we consider the numerical simulation of shells and plates in the context of isostasy. Earth’s lithosphere is modeled as a thin elastic shell or plate floating on the asthenosphere and subject to topographic loads. We demonstrate the computational methods on the isostatic boundary value problem posed on selected geographic locations. For Europe, the computed lithospheric depression is compared with available Mohorovičić depth data. We also perform parameter identification for the effective elastic thickness of the lithosphere, the rock density, and the topographic load that are most plausible to explain the measured depths. An example of simulating the entire lithosphere of the Earth as a spherical shell using multi-patch isogeometric analysis is presented, providing an alternative to spherical harmonics for solving partial differential equations on a spherical domain. The numerical results serve to showcase the features and capabilities of isogeometric methods rather than to provide insightful predictions since a fairly simple model is used for the loading of the lithosphere.