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Much previous seismic and ground-penetrating radar (GPR) research has focused on investigating, theoretically and empirically, the relationship between the statistical characteristics of subsurface velocity heterogeneity and those of the associated surface-based reflection image. However, an effective and robust method for solving the corresponding inverse problem has not been presented. Assuming that waves are weakly scattered in the subsurface, a relatively simple relationship can be derived between the 2D autocorrelation of a geophysical reflection image and that of the underlying velocity field. A Monte Carlo inversion strategy based on this relationship can then be used to generate sets of parameters describing the autocorrelation of velocity that are consistent with recorded reflection data. Results of applying that strategy to realistic synthetic seismic and GPR data indicate that the inverse solution is inherently nonunique in that many combinations of the vertical and horizontal correlation lengths that describe the velocity heterogeneity can yield reflection images with the same 2D autocorrelation structure. However, the ratio of each of those combinations is approximately the same and corresponds to the aspect ratio of the velocity heterogeneity, which suggests that the aspect ratio is a quantity that can be recovered reliably from geophysical-reflection-survey data.

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