Structural complexity in space–time seismic event data

Different approaches and tools have been adopted for the analysis and characterization of regional seismicity based on spatio–temporal series of event occurrences. Two main aspects of interest in this context concern scaling properties and dimensional interaction. This paper is focused on the statistical use of information-theoretic concepts and measures in the analysis of structural complexity of seismic distributional patterns. First, contextual significance is motivated, and preliminary elements related to informational entropy, complexity and multifractal analysis are introduced. Next, several technical and methodological extensions are proposed. Specifically, limiting behaviour of some complexity measures in connection with generalized dimensions is established, justifying a concept of multifractal complexity. Under scaling behaviour, a mutual-information-related dependence coefficient for assessing spatio–temporal interaction is defined in terms of generalized dimensions. Also, an alternative form of generalized dimensions based on Tsallis entropy convergence rates is formulated. Further, possible incorporation of effects, such as earthquake magnitude, is achieved in terms of weighted box-counting distributions. Different aspects in relation to the above elements are analyzed and illustrated using two well-known series of seismic event data of an underlying different nature, occurred in the areas of Agrón (Granada, Spain) and El Hierro (Canary Islands, Spain). Finally, various related directions for continuing research are indicated.

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