Multifractal Modeling and Analyses of Crustal Heterogeneity



Heterogeneity is a ubiquitous feature of both the sedimentary cover and the crystalline crust, present in most, if not all, physical properties. This is documented by borehole measurements of sonic velocities, neutron porosity, resistivity and many other physical properties. Borehole measurements provide the bulk of high-resolution data and have been exploited to demonstrate that small-to intermediate-scale variability, from centimeters to kilometers, is not simply random, uncorrelated noise. It is clear from such logs that variability is the norm and homogeneity the exception. As an example, Figure 8.1 shows the gamma log measured at the Cajon Pass borehole, exhibiting systematic fluctuations at all scales. Moreover, such variability is itself inhomogeneous (e.g., the variance at ~3200 m is greater than at ~2600 m). These measurements follow a heterogeneous, non-Gaussian distribution, with clusters of peaks departing from the mean well past the standard deviation.


Fractional Brownian Motion Hurst Exponent Multifractal Analysis Spectral Slope Crystalline Crust 
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© Springer Science+Business Media New York 2003

Authors and Affiliations

  1. 1.Laboratoire de Géophysique Interne et TectonophysiqueUniversité de SavoieLe Bourget du LacFrance
  2. 2.Geology DepartmentUniversity College DublinBelfield, Dublin 4Ireland

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