S U M M A R YAn efficient algorithm of the network shortest path calculation of rays and traveltimes of the first arrivals is described. The traveltime error of such computations is estimated. The rough estimate of t h e relative traveltime error is evaluated locally a t all network nodes prior t o network ray tracing, and is minimized by m e a n s of a proper choice of t h e sizes of forward stars. In this way, t h e structure of the network is adjusted f o r a particular m o d e l and f o r a particular c o m p u t e r memory. A f t e r network ray tracing, t h e error estimate is refined and t h e absolute error bounds of t h e calculated traveltimes are evaluated. The m e t h o d and its accuracy are demonstrated on numerical examples.

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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 frequently used types of correlation functions are thus summarized and reviewed in this paper, together with an explanation of the physical meaning of their parameters.A stationary random 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 briefly discussed. The corresponding elliptically anisotropic correlation functions can simply be obtained by linear coordinate transforms.