Correlation Functions of Random Media

In geophysics, the correlation functions of random media are of principal importance for understanding and inverting the properties of seismic waves propagating in geological structures. Unfortunately, the kinds of correlation functions inappropriate for the description of geological structures are often assumed and applied. The most frequentlyused types of correlation functions are thus summarized and reviewed in this paper, together with an explanation of the physical meaning of their parameters. A stationaryrandom medium is assumed to be realized in terms of a white noise filtered by a spectral filter. The spectral filter is considered isotropic, in a simple general form enabling the random media used in geophysics to be specified. The medium correlation functions, corresponding to the individual special cases of the general random medium (Gaussian, exponential, von Ka´rma´ n, self-affine, Kummer), are then derived and brieflydiscussed. The corresponding ellipticallyanisotrop ic correlation functions can simply be obtained bylinear coordinate transforms.