Unknown slowness distribution describing the geological structure is assumed to be composed of a smoothly heterogeneous mean value and a realization of a stationary self-affine random medium. The power-law correlation function of a stationary self-affine random medium is described by the Hurst exponent and "standard deviation" expressed at a chosen reference length. The geometrical travel-time variances are then proportional to the power of ray lengths. A method designed to estimate the two parameters of the power-law medium correlation function using field travel times is proposed, and applied to data from the Western Bohemia region.
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Klimes, L.: Correlation function of a self-affine random medium. In: Seismic Waves in Complex 3-D Structures, Report 4, pp. 25-38, Dep. Geophys., Charles Univ., Prague 1996.
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)].