Theory of fractal sets is broadly used in structural geology for investigating such self-similar processes as faulting (Hirata, 1989) and cracking in rocks (Hirata et al, 1987; Sammis and Biegel, 1989) because it provides the simplest nontrivial description of scale invariance of physical systems. Computer simulation of quasi-static fracture in solids that incorporates lattice models (Louis and Guinea, 1989; Hassold and Srolovitz, 1989) also generates fractal patterns. In geophysical applications, however, multifractal measures are more relevant than fractal sets because geophysical quantities are best described as measures (or fields). This paper presents a multifractal method for describing crack and fault patterns in rocks using computer images of crack (fault) clusters and fault systems as depicted on geologic maps.
Fractal Dimension Basement Rock MULTIFRACTAL Analysis Bond Rupture Singularity Spectrum
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Chhabra A.B., Meneveau C., Jensen V., and Streenivasan K.R. (1989) Direct determination of the f(a) singularity spectrum and its application to fully developed turbulence. Phys.Rev.A, 40, 5284–5294.CrossRefGoogle Scholar
Gilman J.J. and Tong H.C. (1971) Quantum tunneling as elementary fracture process. J.Appl.Phys., 42, 3479–3486.CrossRefGoogle Scholar
Hassold G.N. and Srolovitz D.J. (1989) Brittle fracture in materials with random defects. Phys.Rev.B, 39, 9273–9281.CrossRefGoogle Scholar
Hirata T., Satoh T., and Ito K. (1987) Fractal structures of spatial distribution of microfracturing in rocks. Geophys.J.R.astr.Soc., 90, 369–374.Google Scholar
Hirata T. (1989) Fractal dimension of fault systems in Japan: fractal structure in rock fracture geometry at various scales, PAGEOPH, 131, 157–170.CrossRefGoogle Scholar