Natural time chi enables the distinction of two origins of self-similarity, i.e., the process memory and the process increments infinite variance. Employing multiplicative cascades in natural time, the most probable value of the variance kappa(1)(is identical to chi(2)-chi(2))is explicitly related with the parameter b of the Gutenberg-Richter law of randomly shuffled earthquake data. Moreover, the existence of temporal and magnitude correlations is studied in the original earthquake data. Magnitude correlations are larger for closer in time earthquakes, when the maximum interoccurrence time varies from half a day to 1 min.
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Sarlis et al. (2009) studied this question.
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