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.
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
Donald Turcotte Cambridge Press 1997 Fractals and Chaos in Geology and Geophysics 2e.
Scale invariance, Wikipedia.