Correlation functions of random media

Contents

1 Correlation functions of material parameters

1.1 Material parameters

1.2 Mean value of the material parameter

1.3 Correlation function of the material parameter

1.4 Synthetic realizations of a statistically homogeneous random medium

2 Isotropic homogeneous correlation functions

3 Examples of isotropic homogeneous correlation functions

3.1 Gaussian correlation function (N=-d/2, a=+infinity)

3.2 Von Karman correlation functions (a_G=0)

3.2.1 Exponential correlation function (N=1/2, a_G=0)

3.2.2 Zeroth Von Karman correlation function (N=0, a_G=0)

3.3 Self-affine random medium (a_G=0, a=+infinity)

3.4 Laguerr correlation functions (a=+infinity)

3.5 Low-pass filtered self-affine random medium

3.5.1 Low-pass filtered self-affine medium: N=-1

3.5.2 Low-pass filtered white noise

Acknowledgements

References

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Revised versions

Klimes, L.: Correlation functions of random media. In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 91-109, Dep. Geophys., Charles Univ., Prague, 2001.

Klimes, L.: Correlation functions of random media. Pure and Applied Geophysics, 159 (2002), 1811-1831.

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