Statistical interpretation of traveltime fluctuations

Physics

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Scientific paper

A ray-theoretical relation between the autocorrelation functions of traveltime and slowness fluctuations is established for recording profiles with arbitrary angles to the propagation direction of a plane wave. From this relation follows that the variance of traveltime fluctuations is independent of the profile orientation and proportional to the variance, ∈2, of slowness fluctuations, to the correlation distance, a, and to the propagation distance L. The halfwidth of the autocorrelation function of traveltime fluctuations is proportional to a and decreases with increasing profile angle. This relationship allows us to estimate the statistical parameters ∈ and a from observed traveltime fluctuations. Numerical experiments for spatial isotropic random media characterized by a Gaussian autocorrelation function show that the statistical parameters can be reproduced successfully if L/a <= 10. For larger L/a the correlation distance is overestimated and the standard deviation is underestimated. However, the results of the numerical experiments provide empirical factors to correct for these effects. The theory is applied to observed traveltime fluctuations of the Pg phase on a profile of the BABEL project. For the upper crust east of Øland (Sweden) slowness fluctuations with standard deviation ∈ = 2.2-5% and correlation distance a = 330-600 m are found.

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