Conditioning bounds for traveltime tomography in layered media
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Publication:2888756
DOI10.1088/0266-5611/28/5/055008zbMATH Open1251.78007arXiv1110.3370OpenAlexW2007548320MaRDI QIDQ2888756
Author name not available (Why is that?)
Publication date: 4 June 2012
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1110.3370
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