Fourier integral operators with open umbrellas and seismic inversion for cusp caustics

TL;DR

This paper studies a special class of Fourier integral operators with cusp degeneracies, revealing their compositions form wave-front relations combining diagonals and open umbrellas, aiding seismic inversion near cusp caustics.

Contribution

It introduces a new class of Fourier integral operators with cusp degeneracies and analyzes their composition, expanding understanding of wave-front relations in seismic imaging.

Findings

Compositions have wave-front relations in union of diagonal and open umbrella

Provides a framework for seismic inversion near cusp caustics

Extends FIO theory to include cusp degeneracies

Abstract

In general the composition of Fourier integral operators (FIOs) need not be an FIO. Motivated by the problem of linearized seismic inversion in the presence of cusp caustics for the background sound speed, we consider FIOs whose canonical relations have certain two-sided cusp degeneracies, and show that the resulting compositions have wave-front relations in the union of the diagonal and an open umbrella, the simplest type of singular Lagrangian manifold.