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 is then derived. Travel-time variances are thus proportional to a power of ray lengths. A method designed to estimate the medium correlation function using field travel-times is proposed.
Travel times, self-affine random medium, correlation function, scaling geology, fractal geology.
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Klimes, L.: Estimating the correlation function of a self-affine random medium. In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 111-131, Dep. Geophys., Charles Univ., Prague, 2001 [to appear in Pure and Applied Geophysics, 159 (2002)].