Geophysical Journal zyxwvutsrq (1989) zyxwvutsrq 96, 185-188 zyxwvutsrq RESEARCH NOTE Use of non-parametric correlation tests for the study of seismic interrelations zyxwv Dario Albarello Marco Mucciarelli Istituto Nazionale di Geofisica, Dipartimento di Fisica, Universitd di Bologna, 40127 Bologna, Italy Dipartimento di Scienze della Terra, Universitd di Siena 53100 Siena, Italy and Dipartimento di Fisica, Universitd di Bologna, 40127 Bologna, Italy Enzo Mantovani Dipartimento di Scienze deffaTerra, Universird di Siena, 53100 Siena, Italy Accepted 1988 June 20. Received 1988 June 20; in original form 1987 July 2 SUMMARY The use of non-parametric correlation tests (Kendall rank correlation coefficient) is proposed to analyse the interrelation between seismic energy release time series. This approach overcomes the difficulties encountered using parametric techniques (Pearson product-moment correlation coefficient) and, furthermore, it provides a statistically correct estimate of the interrelations significance level. The proposed technique has been used to re-examine four seismic interrelations reported in the literature. Key words: non-parametric statistics, seismic interrelations INTRODUCTION Recognizing the interrelation between seismic zones may provide constraints to possible tectonic models and also indications useful for middle and long-term prediction of earthquakes. Recent works (Bkh 1984a,b; Mantovani, Albarello zyxwvutsrqp & Mucciarelli; 1986, 1987a,b) used techniques based on the Pearson product-moment correlation coefficient for the study of correlations between seismic energy release time series. This approach, however, allows the estimate of the interrelation significance level only in the case when the statistical distribution of seismic energy release is the normal one (Fisher 1958), whereas this condition is not fulfilled by experimental data. To stress this fact we applied the Kolmogorov-Smirnov test (see, e.g. Siege1 1956) to evaluate whether the data used by BHth and Mantovani et al. do or do not depart significantly from normality. This test has given a very low probability (<0.01) that the parent distributions are normal (Table 1). Another problem is due to the fact that Pearson’s coefficient is strongly conditioned by the maxima of each series. This effect becomes very important in the cases examined where the time series show variations of several orders of magnitude. The use of pth root of energy, as proposed by Mantovani et zyxwvut af. (1986, 1987a,b), reduces this effect but introduces, on the other hand, a new arbitrary quantity (p) and makes less clear the physical meaning of the considered quantity. Table 1. Comparison between the observed distributions of seismic energy release and the normal one. D, indicates the maximum deviation between the normal distribution and the empirical one obtained by the time series used for parametrical analysis (BBth 1984a,b, Mantovani et al. 1986, 1987a,b). D, is the theoretical threshold value in the Kolmogorov-Smirnov test. When D, is greater than Dt the hypothesis that the parent distribution is the normal one may be rejected with a confidence level of 99 per cent. 0, 0, Whole Earth (M 37.0, 1917-1976) 0.667 0.210 Sweden (M 93.0, 1917-1976) 0.485 0.210 Greece (M 3 5.3, 1928-1977) 0.661 0.231 North Aegean (M P 5.0, 1600-1980) 0.601 0.084 Calabrian Arc (M 3 5.0, 1600-1980) 0.399 0.084 Southern Apennines (M 3 5.0, 1800-1980) 0.680 0.121 Southern Dinarides (M 95.0, 1800-1980) 0.525 0.121 Notwithstanding these problems, the use of energy release seems to be necessary because it represents a dynamic measure depending on both the frequency of occurrence and the magnitude of earthquakes (Bkh 1984a). In this work, a new approach based on the Kendall’s rank correlation coefficient (Kendall 1938) is proposed in order to overcome the described difficulties. KENDALL’S RANK CORRELATION COEFFICIENT Let us suppose to have N bivariate observations (Xi, zy x). We want to test the hypothesis HO (X and Y are unrelated) 185 by guest on September 25, 2016 http://gji.oxfordjournals.org/ Downloaded from