Curvature, a mechanical link between the geometrical complexities of a fault

TL;DR

This paper introduces a new interpretation of how fault geometry, specifically curvature and torsion, influences stress distribution and earthquake mechanics, providing insights into complex fault surface behaviors.

Contribution

It presents a regularized boundary-element approach that isolates the effects of geometric complexities on fault stress from slip gradients, advancing understanding of fault mechanics.

Findings

Geometry influences fault stress through curvature and torsion.

The approach clarifies the impact of fault roughness and bends.

It explains the paradox of smooth versus abrupt fault bends.

Abstract

Many recent studies have tried to determine the influence of geometry of faults in earthquake mechanics. In this paper, we suggest a new interpretation of the effect of geometry on the stress on a fault. Starting from the representation theorem, which links the displacement in a medium to the slip distribution on its boundary, and assuming homogeneous infinite medium, a regularized boundary-element equation can be obtained. Using this equation, it is possible to separate the influence of geometry, as expressed by the curvatures and torsions of the field line of a dislocation on the fault surface, which multiply the slip, from the effect of the gradient of slip. This allows us to shed new light on the mechanical effects of geometrical complexities on the fault surface, with the key parameters being the curvatures and torsions of the slip field on the fault surface. We have used this new approach to explain further the false paradox between smooth-and-abrupt-bends (see Sato et al. (2019)) as well as to re-interpret the effect of roughness on a fault.