Fractals and chaos in geology and geophysics / Фракталы и хаос в геологии и геофизике

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 that defines the 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. For example, self-similar folds occur over this range of scales. Another example would be 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. It was in this context that Mandelbrot (1967) introduced the concept of fractals. The length of a rocky coastline is obtained using a measuring rod with a specified length. Because of scale invariance, the length of the coastline increases as the length of the measuring rod decreases according to a power law; the power determines the fractal dimension of the coastline. It is not possible to obtain a specific value for the length of a coastline, owing to all the small indentations down to a scale of millimeters or less. <...>