On the implementation of faults in finite-element glacial isostatic adjustment models

Abstract

Stresses induced in the crust and mantle by continental-scale ice sheets during glaciation have triggered earthquakes along pre-existing faults, commencing near the end of the deglaciation. In order to get a better understanding of the relationship between glacial loading/unloading and fault movement due to the spatio-temporal evolution of stresses, a commonly used model for glacial isostatic adjustment (GIA) is extended by including a fault structure. Solving this problem is enabled by development of a workflow involving three cascaded finite-element simulations. Each step has identical lithospheric and mantle structure and properties, but evolving stress conditions along the fault.The purpose of the first simulation is to compute the spatio-temporal evolution of rebound stress when the fault is tied together. An ice load with a parabolic profile and simple ice history is applied to represent glacial loading of the Laurentide Ice Sheet. The results of the first step describe the evolution of the stress and displacement induced by the rebound process. The second step in the procedure augments the results of the first, by computing the spatio-temporal evolution of total stress (i.e. rebound stress plus tectonic background stress and overburden pressure) and displacement with reaction forces that can hold the model in equilibrium. The background stress is estimated by assuming that the fault is in frictional equilibrium before glaciation. The third step simulates fault movement induced by the spatio-temporal evolution of total stress by evaluating fault stability in a subroutine. If the fault remains stable, no movement occurs; in case of fault instability, the fault displacement is computed.We show an example of fault motion along a 45°-dipping fault at the ice-sheet centre for a two-dimensional model. Stable conditions along the fault are found during glaciation and the initial part of deglaciation. Before deglaciation ends, the fault starts to move, and fault offsets of up to 22m are obtained. A fault scarp at the surface of 19.74m is determined. The fault is stable in the following time steps with a high stress accumulation at the fault tip. Along the upper part of the fault, GIA stresses are released in one earthquake.