An FIO calculus for marine seismic imaging, II: Sobolev estimates

TL;DR

This paper develops precise Sobolev estimates for pseudodifferential operators with singular symbols, relevant to seismic imaging and operators with fold singularities, advancing mathematical understanding of wave propagation in complex media.

Contribution

It introduces sharp Sobolev estimates for classes of pseudodifferential operators with fold singularities, including applications to seismic imaging.

Findings

Sharp $L^2$-Sobolev estimates established

Operators include those with fold caustics in seismic imaging

Results applicable to operators with two-sided fold singularities

Abstract

We establish sharp $L^2$-Sobolev estimates for classes of pseudodifferential operators with singular symbols whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in $R^2$ with simple inflection points and normal operators arising in linearized seismic imaging in the presence of fold caustics.