A tentative model for the explanation of Båth law using the order parameter of seismicity in natural time

Abstract

Using the order parameter of seismicity defined in natural time, we suggest a simple model for the explanation of Båth law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Båth law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock's magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.

Statistical Significance of Earth’s Electric and Magnetic Field Variations Preceding Earthquakes in Greece and Japan Revisited

“…Here, we employed the function of the package [ 52 ] for R [ 54 ] that implements ECA and selected the (default) Poisson test. The reason behind this selection, although it is known that EQs appear in sequences due to aftershocks, was that the magnitude range of the EQs (that define A type events) in most of the studies here barely exceeds one magnitude unit while according to Båth law [ 4 , 55 , 56 , 57 , 58 ] the difference in magnitude between the mainshock and its largest aftershock is approximately 1.2 magnitude units. In other words, in the data presented in Section 3 below, it is improbable that aftershocks are used for the determination of A type events (cf.…”

On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

“…For the first case, the significance test is based on an empirical cumulative distribution function of the coincidence rates estimated by a large number of randomly shuffled time series having the same number of events like the original time series-thus numerically simulating a Poisson process-whereas for the second case, the significance test is based on a similar calculation for a large number of surrogate time series having the same waiting time distributions as the original data). The Poisson test has been selected because the magnitude range of the EQs (that define the A type events) considered here (see the first column of Tables 1-5) is such that it barely exceeds one magnitude unit while according to Båth law [11,33,[68][69][70] the difference in magnitude between the mainshock and its largest aftershock is approximately 1.2 magnitude units. Therefore, there are no aftershocks considered in our study and such EQs are expected to follow a Poisson process [71].…”

“…NTA has found applications in a wide variety of fields ranging from cardiology (see, e.g., [12][13][14][15]) to statistical physics (see, e.g., [16][17][18][19][20][21]), and atmospheric science (see, e.g., [22][23][24]). One of the main applications of NTA, however, is the study of the physics of EQs (see, e.g., [25][26][27][28][29][30][31][32][33][34][35][36][37]). In addition, natural time is considered as the basis of the "nowcasting earthquakes" methodology that has been introduced recently [38][39][40][41][42][43][44][45][46].…”