Nonuniqueness in traveltime tomography: Ensemble inference and cluster analysis

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Abstract
We examine the nonlinear aspects of seismic traveltime tomography. This is accomplished by completing an extensive set of conjugate gradient inversions on a parallel virtual machine, with each initiated by a different starting model. The goal is an exploratory analysis of a set of conjugate gradient solutions to the traveltime tomography problem. We find that distinct local minima are generated when prior constraints are imposed on traveltime tomographic inverse problems. Methods from cluster analysis determine the number and location of the isolated solutions to the traveltime tomography problem. We apply the cluster analysis techniques to a cross‐borehole traveltime data set gathered at the Gypsy Pilot Site in Pawnee County, Oklahoma. We find that the 1075 final models, satisfying the traveltime data and a model norm penalty, form up to 61 separate solutions. All solutions appear to contain a central low velocity zone bounded above and below by higher velocity layers. Such a structure agrees with well‐logs, hydrological well tests, and a previous seismic inversion.

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