Statistical Complexity Analysis of Spatiotemporal Dynamics

Knowledge about structural aspects of spatiotemporal dynamics can be obtained, among other approaches, in terms of a variety of information-theoretic related measures. In this context, multifractal analysis tools such as generalized dimensions and multifractal spectrum are useful to study different aspects of scaling behaviour. Recent research has been focused on statistical complexity measures. Conceptual connections between multifractality and complexity, generally understood from intuitive interpretation, can be established based on limiting behaviour according to scale, in terms of variational properties of generalized dimension curves. Complexity and multifractality analysis, in combination with suitable transformations of the data space-time coordinates, allows to identify and assess dimensional interaction and evolutionary changes, two important issues in structural analysis of dependence and heterogeneity. These aspects are investigated and illustrated with application to seismic data.