An introduction to multifractals and scale symmetry groups

The complexity of geosciences has inspired the development of many innovative concepts and techniques. For instance, the extreme variability of geophysical fields over wide ranges of space-time scales, particularly their intermittency, has been a key driver towards the development of multifractals. In turn, this development has significantly improved our understanding and modeling capacities of our complex environment as a whole, i.e. not only its physico-ecological component from its smallest scales (e.g. micro-turbulence) to its largest scales (e.g. climate (Lovejoy and Schertzer 2013), astrophysics (Sylos Labini et al. 1998)), but also its socio-economical component (e.g. city dynamics (Murcio et al. 2015, Dupuy 2016)). This introduction intends to demonstrate that recent theoretical developments on multifractals, particularly on their formalism, will make them even more useful and indispensable for geophysics.