Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators

TL;DR

This paper develops a nonlinear method to recover wave speeds and density across curved interfaces using reflected wave amplitudes, extending seismic analysis beyond flat interfaces with rigorous microlocal analysis.

Contribution

It introduces a nonlinear approach for curved interfaces, establishing uniqueness and providing a reconstruction method based on microlocal analysis.

Findings

Proves uniqueness of the inverse problem for curved interfaces.

Provides a reconstruction procedure for wave speeds and density.

Extends seismic reflection analysis to nonlinear, curved interface scenarios.

Abstract

We revisit the problem of recovering wave speeds and density across a curved interface from reflected wave amplitudes. Such amplitudes have been exploited for decades in (exploration) seismology in this context. However, the analysis in seismology has been based on linearization and mostly flat interfaces. Here, we present a nonlinear analysis allowing curved interfaces, establish uniqueness and provide a reconstruction, while making the notion of amplitude precise through a procedure rooted in microlocal analysis.