A shape derivative algorithm for reconstructing elastic dislocations in geophysics

TL;DR

This paper introduces a shape derivative-based iterative algorithm to reconstruct elastic dislocations, modeling seismic faults, from surface displacement data in a simplified 2D geophysical setting.

Contribution

It develops both distributed and boundary shape derivatives for the inverse problem of seismic fault reconstruction, enabling improved iterative algorithms.

Findings

Successful numerical tests in 2D demonstrate the method's potential.

The shape derivative approach effectively captures dislocation changes.

The algorithm shows promise for more complex geophysical fault modeling.

Abstract

We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a distributed as well as a boundary shape derivative that encodes the change in a misfit functional between the measured and the computed surface displacement under infinitesimal movements of the dislocation and infinitesimal changes in the slip vector, which gives the displacement jump across the dislocation. We employ the shape derivative in an iterative reconstruction algorithm. We present some numerical test of the reconstruction algorithm in a simplified 2D setting.