Uniqueness for a seismic inverse source problem modeling a subsonic rupture

TL;DR

This paper investigates the uniqueness and reconstruction of source locations, times, and the smooth part of seismic sources in an inhomogeneous wave equation with subsonic rupture, based on data collected over time.

Contribution

It provides new results on the uniqueness and microlocal recovery of source parameters in seismic inverse source problems with subsonic rupture.

Findings

Proved uniqueness for source location and timing.

Developed microlocal reconstruction methods.

Reconstructed the smooth source component assuming uniformity.

Abstract

We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some detection surface. We explore the question of uniqueness for these problems, show how to recover the times and locations of sources microlocally, and then reconstruct the smooth part of the source assuming that it is the same at each source location.