Multifractal complexity analysis in space-time based on the generalized dimensions derivatives

In this work, the formulation of some parametric families of complexity measures in the multifractal domain, from the scaling limiting behaviour of generalized Rényi-entropy-based 'product complexity measures', is proposed. These families are related to incremental functionals of the curve of generalized Rényi dimensions. In particular, the significance in this context of the first derivative of the generalized dimensions curve, and specifically the indicators given by its minimum value and the corresponding value of the deformation parameter, is justified. The practical usefulness of the multifractal complexity measures proposed, for characterization and assessment of structural dynamical changes in a spatiotemporal system with multifractal behaviour, is illustrated with the study of real data from a seismic series involving a central period of high activity within a regular regime.