a Department of Earth Science, University of California Santa Barbara, Santa Barbara, CA, 93106-9630, USA b Institute for Geophysics and Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, University Station, C1160, Austin, TX 78712-0254, USA c Dept. of Geology and Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii...

The complexity of geophysics has been extremely stimulating for developing concepts and techniques to analyze, understand and simulate it. This is particularly true for multifractals and Generalized Scale Invariance. We review the fundamentals, introduced with the help of pedagogical examples, then their abstract generalization is considered. This includes the characterization of multifractals,...