Calculation of the a priori geometrical covariances of travel times in a self-affine random medium

Ludek Klimes


To perform the stochastic inversion of travel times, we need the geometrical covariances of travel times, represented by the integrals of the medium covariance function over corresponding pairs of rays. These covariances are also essential for estimating the deviations of synthetic travel times calculated in the velocity model from correct travel times. The medium covariance function describing the deviation of the medium from the mean model is expressed in terms of the velocity-scaled ellipsoidally anisotropic power-law correlation function of a self-affine random medium. The geometrical covariances of travel times are semianalytically expressed in terms of the hypergeometric functions which can efficiently be calculated.


Stochastic inversion of travel times, velocity model, heterogeneous medium, self-affine random medium, medium covariance function, travel-time covariance.

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In: Seismic Waves in Complex 3-D Structures, Report 18, pp. 27-70, Dep. Geophys., Charles Univ., Prague, 2008.
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