Abstract
The scale invariance of geological phenomena is one of the first concepts taught to a student of geology. It is pointed out that an object with a scale, i.e., a coin, a rock hammer, a person, must be included whenever a photograph of a geological feature is taken. Without the scale, it is often impossible to determine whether the photograph covers 10 cm or 10 km. A specific example is folded, layered sedimentary rocks that occur over this range of scales. Another example is an aerial photograph of a rocky coastline. Without an object with a characteristic dimension, such as a tree or house, the elevation of the photograph cannot be determined. In this context, Mandelbrot (1967) introduced the concept of fractals. Because of scale invariance, the length of a coastline increases as the length of the measuring rod decreases according to a power law; the power determines the fractal dimension of the coastline.
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Turcotte, D.L., Huang, J. (1995). Fractal Distributions in Geology, Scale Invariance, and Deterministic Chaos. In: Barton, C.C., La Pointe, P.R. (eds) Fractals in the Earth Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1397-5_1
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