Detection of wave front set perturbations via correlation: Foundation for wave-equation tomography

TL;DR

This paper explores the mathematical basis for detecting wave front set perturbations in seismic data, proposing a correlation-based detection method and analyzing its theoretical foundation through simple case studies.

Contribution

It provides a rigorous mathematical analysis of a correlation-based detection method for wave front set perturbations in seismic wave fields.

Findings

The detection method is grounded in distribution theory and oscillatory integrals.

Theoretical case studies support the validity of the correlation approach.

Foundation for wave-equation tomography is established.

Abstract

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals.