THE STATISTICAL NATURE OF THE UPPER CONTINENTAL CRYSTALLINE CRUST DERIVED FROM IN-SITU SEISMIC MEASUREMENTS

In situ measurements in the main borehole of the German continental deep drilling project (KTB) point to the statistical nature of the continental crystalline crust between 286 and 6000 m depth. P-wave, S-wave and density logs display deviations from Gaussian distribution functions that may be partly due to the approximately bimodal nature of the lithology, because the crust consists mainly of metabasites and paragneisses. The autocovariance functions and power spectra of the logs indicate that the velocity and density perturbations have a complex statistical nature, but the autocovariance functions can be approximated by a superposition of two exponential functions with correlation lengths of 1 m and 20 m. The associated relative standard deviations for each exponential function are about 3 per cent of the mean for the sonic logs, and nearly 6 per cent of the mean for the density. A vertical seismic profile measured between 3000 and 6000 m depth shows small traveltime fluctuations, which can be explained by a generalization of a recently published scattering theory for transverse wavefield fluctuations to include the case of longitudinal fluctuations. The theory is valid for harmonic scalar plane-wave propagation in random media with isotropic statistics, and scattering mainly in the forward direction. One important theoretical result is that, although longitudinal and transverse autocovariance functions of amplitudes and phases differ, the expectations of their respective autovariances are the same. The observed traveltime fluctuations agree with theoretical predictions based on normally distributed velocity perturbations that are described by the average of the autocovariance functions of the two P-wave logs measured from 286 to 3000 m and between 3000 and 6000 m depth. Owing to the lack of traveltime information that can be averaged, and because the traveltime fluctuations predicted by the theory do not differ sufficiently for 2-D and 3-D random perturbations, no statement can be made on how anisotropic the observed random velocity perturbations are. The observed heterogeneities are, however, consistent with the fact that reflection seismic profiles reveal a nearly transparent upper crystalline crust.