Conditioning bounds for traveltime tomography in layered media
Abstract
This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the medium in a well-posed manner, regardless of the discretization. The counterpart of the Abel transform in the case of reflected rays is a Fredholm kernel of the first kind which is shown to have singular values that decay at least root-exponentially. Kinematically equivalent media are characterized in terms of a sequence of matching moments. This severe conditioning issue comes on top of the well-known rearrangement ambiguity due to low velocity zones. Numerical experiments in an ideal scenario show that a waveform-based model inversion code fits data accurately while converging to the wrong wave speed profile.
Keywords
Cite
@article{arxiv.1110.3370,
title = {Conditioning bounds for traveltime tomography in layered media},
author = {Hyoungsu Baek and Laurent Demanet},
journal= {arXiv preprint arXiv:1110.3370},
year = {2015}
}