GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 2.1 GNGTS 2023 Understanding long-memory behavior in the seismic process S. Barani 1 , M. Taroni 2 , P. Artale Harris 2 1 Dipartimento di Scienze della Terra dell’Ambiente e della Vita, Università degli Studi di Genova, Genova, Italy 2 Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy Although the concept of long memory, or long-range dependence (LRD), in the seismic process dates back to the late 80s (e.g., Bak and Tang, 1989), the awareness of this has gained in recent years thanks to the increasing completeness of earthquake data, which allows the application of various statistical techniques aimed at evaluating the level of correlation among observations in earthquake time series (e.g., Cisternas et al., 2004; Barani et al., 2018; Barani et al., 2021). Most of these studies examine the long-memory feature through the rescaled range analysis (R/S analysis), which was originally proposed by Hurst (1951) and described rigorously by Mandelbrot and Wallis (1968). This technique estimates the so-called Hurst exponent ( H ), a parameter that measures the level of correlation in time series. It takes values between 0 and 1, and indicates long memory for values different from 0.5. Specifically, a value of H in the range 0.5-1 indicates a time series with long-term positive autocorrelation, meaning that regions of recent high seismic activity have a larger than usual chance of producing new strong earthquakes. This is in agreement with empirical observations on earthquake clustering (e.g., Kagan and Jackson, 1991; Kagan and Jackson, 1999; Kagan and Jackson, 2013), showing that periods of high release of seismic deformation tend to be followed by years of higher-than-average seismic strain release. In the present study, we present and apply a simple model to mimic the original Hurst problem (Hurst, 1951), which consists in evaluating the capacity of an ideal water reservoir based upon a record of observed discharges from a lake. In any given year t , the reservoir will accept the influx from the lake and a given volume per year (discharge), assumed equal to the average influx over the period of τ years, will be released from the reservoir. The capacity of the reservoir is given by the range R ( ) between the maximum and minimum amounts of water contained in the reservoir over the time span of interest. Thus, R ( ) represents the storage capacity required to maintain the mean discharge throughout the period τ . In the case of earthquakes, the problem is perfectly specular, as seismologists measure the energy released by a hypothetical reservoir (i.e., a