## Correlation function of a self-affine random medium

**Ludek Klimes**
### Summary

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.

### Keywords

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

### Whole paper

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### Revised version

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)].

In: Seismic Waves in Complex 3-D Structures, Report 4, pp. 25-38,
Dep. Geophys., Charles Univ., Prague 1996.

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