Estimating the correlation function of a self-affine random medium

Ludek Klimes


The self-affine random medium is assumed to be realized in terms of a white noise filtered by the power-law spectral filter of amplitude proportional to a reasonable power of the wavenumber. The power-law medium correlation function and corresponding geometrical travel-time covariances are then derived. The geometrical travel-time variances are proportional to the power of ray lengths. A method designed to estimate the medium correlation function using field travel times is proposed, and applied to data from the Western Bohemia region.


Travel times, self-affine random medium, correlation function, scaling geology, fractal geology.

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Pure and appl. Geophys., 159 (2002), 1833-1853.
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