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Scale invariance

Contents

Idea

Defined as (from Wikipedia):

Scale invariance or self-similarity is a feature of objects or laws that does not change if scales of length, energy, or other variables, are multiplied by a common factor.

wiener processexample

Details

According to Donald Turcotte:

Many geological phenomena are scale invariant. Examples include frequency size distribution of rock fragments, faults, earthquakes, volcanic eruptions, mineral deposits and oil fields. A fractal distribution requires that the number of objects larger than a specified size has a power law dependency.

So it is critical to be aware of which geological phenomena are scale invariant or not, to be able to make for example predictions and models

References