Broad-band power-law spectra of well-log data in Japan

Abstract

SUMMARY For the purpose of revealing the statistical characteristics of P-wave velocity, S-wave velocity and density in the uppermost part of the crust, we analysed well-log data obtained from five deep wells in different tectonic regions in Japan: three wells through the mainly sedimentary rocks in the Kanto plain and two wells in the Kuju volcano group in Kyushu Island. In the Kanto plain, the power spectral density of fractional fluctuation of P-wave velocity and that of density are proportional to a power of the spatial wavelength from a few metres to 100 m. where the power index (slope of the power spectral density at double logarithmic scale) is 1.1-1.3. At the Kuju volcano group, that of P- and S-wave velocity and density also obey a power law, with a power index of 1.3-1.6 for wavelengths from a few metres to few hundred metres. Correcting the effect of the moving box-car observation window which corresponds to the separation of two receivers of the logging tool, we find that the power-law characteristics hold for wavelengths down to a few tens of centimetres. The 1-D sections of the elastic inhomogeneities follow a kind of band-limited self-affine random process. Comparing the power spectral densities, we find smaller values of the power index in stable areas and larger values in tectonically active areas. The difference in the power index arises from long-wavelength components.