Seismic-wave traveltimes in random media

SUMMARY A ray-theoretical relation is established between the autocorrelation function of the slowness fluctuations of a random medium and the autocorrelation function of the traveltime fluctuations on a profile perpendicular to the general propagation direction of an originally plane wave. Although this relation can be inverted exactly, it is preferable for applications to use the results of a forward calculation for a modified exponential autocorrelation function which represents slowness fluctuations with zero mean. The essential parameters of this autocorrelation function, standard deviation E and correlation distance a, follow by simple relations from the maximum and the zero crossing of the corresponding autocorrelation function of the traveltime fluctuations. The traveltime analysis of 2-D finite-difference seismograms shows that E and a can be reconstructed successfully, if the wavelength-tocorrelation-distance ratio is 0.5 or less. Otherwise, E is underestimated and a overestimated; however, both effects can be compensated for. The average traveltime, as determined from the finite-difference seismograms, is slightly, but systematically shorter than the traveltime according to the average slowness, i.e. the wave prefers fast paths through the medium. This is in agreement with results of Wielandt (1987) for a spherical low-velocity inclusion in a full-space and with results of Soviet authors, summarized by Petersen (1990). The velocity shift is proportional to E*, it has dispersion similar to the dispersion related to anelasticity, and it increases with the pathlength of the wave.

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