Spectral analyses of the KTB sonic and density logs using robust nonparametric methods

Abstract

We use robust techniques to estimate power spectra, coherences and transfer functions of the German Continental Deep Drilling Program (KTB) sonic and density logs and lithologically defined subsets thereof. Our results confirm the overall 1/wavelength‐decay of the power spectra inferred by parametric analyses, but provide superior resolution and nonparametric estimates of errors and statistical significance. We demonstrate the absence of any statistically meaningful coherence between the velocity logs from the main and pilot holes, suggesting a spatially quasi‐isotropic upper crustal velocity structure. Also, there is little coherence between the physical and caliper logs, indicating that disturbances introduced by breakouts and uneven relief of the borehole wall mostly contribute to the uncorrelated portions of the velocity logs. Coherence between the gamma and physical logs is weak to absent, indicating that the observed velocity and density fluctuations are dominated by the physical state of the rocks rather than by their petrological composition. Attempts to derive Poisson's ratio, and its variation with wavelength, from the relationship between the shear and compressional velocity logs met with limited success, but imply that caution should be exercised when comparing Poisson's ratio derived from laboratory studies on samples representative of a region to crustal‐scale seismic determinations. Our preferred interpretation is that fluctuations in the physical logs in the intermediate wavelength range (∼10–150 m) are dominated by cracks and their level of fluid saturation. At larger wavelengths (>50–150 m) the effects of the petrology becomes more significant as shown by changes in slope of the power spectra and the emerging coherence between the Vp and the gamma logs.