Optimal 3-D traveltime tomography

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Abstract
We propose a practical new method for 3-D traveltime tomography. The method combines an efficient approximation to the extended Kalman filter for rapid, accurate, nonlinear tomography, with the concept of data‐driven zonation, in which the dimensionality and geometry of the parameterization are dynamically determined using cluster analysis and region merging by random field union. The Bayesian filter uses geostatistics as it recursively incorporates measurements in an optimal (minimum‐variance) manner. Geologic knowledge is introduced through a priori estimates of the parameter field and its spatial covariance. Conditional estimates of the parameter number, geometry, value, and covariance are evolved. An initial decomposition of the 3-D domain into 2-D slices, the simplified filter design, and the data‐driven reduction in parameter dimensionality, all contribute to make the method computationally feasible for large 3-D domains. The method is verified by the inversion of crosswell seismic traveltimes to 3-D estimates of seismic slowness in four synthetic heterogeneous domains. Starting with homogeneous, fully distributed slowness fields, and no knowledge of the true covariance structure, the method is able to accurately and efficiently resolve the structure and values of markedly different domains.