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De Groot-Hedlin, CD, Vernon FL.  1998.  An evolutionary programming method for estimating layered velocity structure. Bulletin of the Seismological Society of America. 88:1023-1035. AbstractWebsite

For most geophysical inverse problems, one solves for an Earth model that minimizes the misfit between the observed data and observational predications determined from forward modeling. However, the solutions to such problems are almost always nonunique, as some of the model parameters are poorly resolved by the data. We have developed a novel form of evolutionary programming (EP) that solves directly for a broad cluster of models that adequately fit the data. We obtain improved performance of the EP algorithm by rotating the model parameter axes at each generation so that the axes are aligned perpendicular and parallel to long valleys in the misfit surface. The rotated axes are defined by the eigenvectors of the covariance matrix of the set of models; the mutation rate in each new direction varies with the square root of the corresponding eigenvalue, This modified EP method finds a wide range of models satisfying the data, allowing one to determine the uncertainty in the model parameters. We illustrate this EP method by applying it to the problem of determining velocity structure from regional travel-time data. Application of this method to a travel-time data set generated from a model that includes a low-velocity zone (LVZ) illustrates that it successfully finds a wide range of models within the broad minimum that includes the initial solution. We apply the method to regional travel-time data recorded at the Kyrgyz broadband network (KNET) and find that velocities are well resolved, except at depths of 25 to 50 km.

Donner, S, Lin CJ, Hadziioannou C, Gebauer A, Vernon F, Agnew DC, Igel H, Schreiber U, Wassermann J.  2017.  Comparing direct observation of strain, rotation, and displacement with array estimates at Pinon Flat Observatory, California. Seismological Research Letters. 88:1107-1116.   10.1785/0220160216   AbstractWebsite

The unique instrument setting at the Pinon Flat Observatory in California is used to simultaneously measure 10 out of the 12 components, completely describing the seismic-wave field. We compare the direct measurements of rotation and strain for the 13 September 2015 M-w 6.7 Gulf of California earthquake with array-derived observations using this configuration for the first time. In general, we find a very good fit between the observations of the two measurements with cross-correlation coefficients up to 0.99. These promising results indicate that the direct and array-derived measurements of rotation and strain are consistent. For the array-based measurement, we derived a relation to estimate the frequency range within which the array-derived observations provide reliable results. This relation depends on the phase velocity of the study area and the calibration error, as well as on the size of the array.