Conditioning bounds for traveltime tomography in layered media
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Demanet_Conditioning bounds.pdf
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445.32 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Baek, Hyoung Su
Demanet, Laurent
Date Issued
April 2012
Journal
Inverse Problems
Publisher
IOP Publishing
Citation
Baek, H, and L Demanet. “Conditioning bounds for traveltime tomography in layered media.” Inverse Problems 28, no. 5 (May 1, 2012): 055008.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1088/0266-5611/28/5/055008
