Nonextensive Statistical Mechanics

244 7 Thermodynamical and Nonthermodynamical Applications7.1.9 Geophysics7.1.9.1 EarthquakesThe q-statistical theory and functional forms have been successfully applied toearthquakes in many occasions [287–291, 380, 381, 540–544].Successive earthquakes in a given geographic area occur with epicenters distributedin a region just below the Earth surface. We note r the successive distances(measured in three dimensions). It has been verified [540] that, in California andJapan, this distribution, p(r), happens to be well represented (see Fig. 7.29) by aq-exponential form. More precisely, the corresponding accumulated probability isgiven by the Abe–Suzuki distance lawP(> r) = e −r/r 0q (0 < q < 1; r 0 > 0) . (7.11)Fig. 7.29 Log–Log plots of the cumulative distribution of successive distances in California (top)and Japan (bottom). Dots from the California and Japan catalogs, respectively; continuous curvesfrom Eq. (7.11). Insets: Thesameinq-log vs. linear representation (California: q = 0.773, r 0 =179 Km, and the linear regression coefficient R =−0.9993; Japan: q = 0.747, r 0 = 595 Km,andR =−0.9990). For details see [540].