Application of Fractal Geometry to Geological Site Characterization

  • Michael D. Impey
  • Peter Grindrod
Conference paper


In this paper we apply fractal geometry to a problem of practical significance in geosciences, that of generating a rock transmissivity field with realistic detail over a range of length scales from a relatively small number of measured values. We discuss a conceptual rock-property model based on statistically self-affine fractals. Then we demonstrate a methodology based on this model for generating realizations of the transmissivity field with spatial variability over a range of scales. We estimate a fractal dimension directly from the measured data, and assess, in a quantitative manner, the ‘goodness-of-fit’ of the fractal model to the measured data. The goodness-of-fit test indicates that it is realistic to interpret the measured data in terms of a fractal model. Thus, we can be confident that the model can be used to generate physically realistic transmissivity fields. The Intera code AFFINITY is applied to measured field data to generate fractal transmissivity fields that have the correct dimension and interpolate the field data. AFFINITY is also used to compute flow and tracer transport through the fractal transmissivity fields. These computations exhibit channelling and dispersive phenomena. These phenomena are of significant practical interest in the assessment of the geological properties of a rock formation.


Fractal Dimension Fractal Model Fractal Geometry Tracer Transport Transmissivity Field 
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    Mood, A.M., Graybill, F.A., and Boes, D.C., Introduction to the Theory of Statistics, London: McGraw-Hill, 1988.Google Scholar
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    Grindrod, P., Robinson, P.C., and Williams, M.J., The art of noise: self-affinity, flow and transport, Intera Sciences internal report, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Michael D. Impey
  • Peter Grindrod

There are no affiliations available

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