Geological features such as lithologie beds, fractures, folds, sedimentary structures, and pore networks are evident at a variety of scales and require that a length scale be specified in order to establish a frame of reference. Recently, it has been demonstrated that such apparently self-similar, scaling objects and features could be described as stochastic natural fractals. These natural fractals exhibit structures and features whose distributions are exponential (i.e., they exhibit power-law behavior) and can be described in terms of apparent or effective fractal dimensions. This paper presents a sampling of geological data sets whose distributions can be described as natural fractals: reservoir rock/pore systems, sand layers in mixed-lithology sequences, sandstone grain-size, and fault systems. The Arun Limestone, San Andres Dolomite, Norphlet Sandstone, Lobo Sandstone, and Spraberry Sandstone all exhibit fractal rock/pore networks with fractal pore size-frequency distributions. An example of a Tertiary deep-water sand/shale sequence from off-shore Gulf of Mexico exhibits a fractal sand thickness, and both the sand and shale thickness-frequency distributions are fractal, as well. A carbonate sand/carbonate mud sequence from Saudi Arabia also exhibits a fractal sand thickness-frequency distribution. Samples of a Tertiary Gulf of Mexico deep-water sandstone and a West African deltaic sandstone exhibit fractal grain size-frequency distributions. The amplitude and residue thickness of styolites from a Limestone from Abu Dhabi illustrate an example of fractal data sets from structural geology. Most geological objects and features, common to petroleum and mineral exploration and production, can probably be described statistically in terms of fractal geometry, and their fragmentation and irregularity can be characterized by fractal dimensions.

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