Examples of nonuniqueness for an inverse problems of geophysics

TL;DR

This paper presents explicit examples demonstrating the significant non-uniqueness in solving the inverse problem of determining velocity profiles from surface acoustic measurements, highlighting challenges in geophysical inverse problems.

Contribution

It provides analytical explicit examples that illustrate the extensive non-uniqueness in the inverse problem of velocity profile reconstruction in geophysics.

Findings

Explicit examples show vast non-uniqueness in solutions.

Dimensionality of data and unknown are both 3.

Highlights challenges in inverse problem uniqueness.

Abstract

The inverse problem of finding the velocity profile from the surface measurements of acoustic field is considered. The dimensionalities of the data and of the unknown velocity profile are equal, both are equal 3. Analytical explicit examples are given showing vast non-uniqueness of the solution to this inverse problem.