Discontinuities without discontinuity: The Weakly-enforced Slip Method

TL;DR

This paper introduces a novel finite-element method that efficiently models fault dislocations without geometric restrictions, facilitating inverse geophysical problems by enabling component reuse and reducing computational costs.

Contribution

The paper presents a weakly-enforced slip method that allows for flexible approximation spaces independent of fault geometry, improving computational efficiency in geophysical modeling.

Findings

Method achieves optimal approximation properties.

Numerical experiments validate the approach in 2D and 3D.

Enables efficient inverse problem analysis.

Abstract

Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.