What Is a Fractal, and Why Fractals Should Matter to the Petroleum Geologist

MANDELBROT, BENOIT B., IBM, T. J. Watson Research Center, Yorktown Heights, NY, and Mathematics Department, Yale University, New Haven, CT

The following statements are obviously quite wrong: oil fields are circular; they are the same size and are distributed uniformly throughout the world; soil is of uniform porosity and permeability; after water has been pumped into a field it seeps through as an underground sphere. The preceding statements are so grossly incorrect that they do not even provide useful first approximations that one could improve upon by adding so-called corrective terms. For example, one gains little by starting with the notion of a uniform distribution of oil fields and then assuming it is perturbed by small Gaussian scatter. The flow of water in a porous medium often fingers out in a pattern so diffuse that a sphere is not a useful point of departure in describing

it. In summary, even the simplest data underlying petroleum geology exhibit very gross irregularity and unevenness.

Fractal geometry is the proper geometry of manageable irregularity, fragmentation, and unevenness. It is the only workable alternative between the excessive order of the Euclidean geometry and unmanageable disorder. The main features of fractal geometry will be described and several techniques will be pointed out that show promise for the petroleum geologist.

AAPG Search and Discovery Article #91004 © 1991 AAPG Annual Convention Dallas, Texas, April 7-10, 1991 (2009)