Some remarks on the estimation of fractal scaling parameters from borehole wire-line logs

Well-logging provides a direct means of assessing fluctuations in petrophysical properties with depth, and thus allows for the statistical characterisation of crustal heterogeneity. Using records from three super-deep boreholes (KTB and Cajon Pass) and synthetic data, we assess three different techniques for estimating fractal dimension and correlation length. Inaccurate correlation lengths may result from the way in which the autocorrelation is calculated for well-logs, leading to an incorrect application of the von Karman function. Analysis of the rescaled range, power spectra and autocorrelation allow us to model the data as k(-beta) (where k = wavenumber and exponent beta = 5 - 2D, for fractal dimension D) process with values of fractal dimension displaying anti-persistence.