## Estimating the correlation function of a self-affine random medium

**Ludek Klimes**
### Summary

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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### Related full papers

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)].

Expanded Abstracts of 71st Annual Meeting (San Antonio),
pp. 740-743, Soc. Explor. Geophysicists, Tulsa, 2001.

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