CORRELATION IN AFTERSHOCK MAGNITUDES

Abstract

Cumulative integral Q(t) of magnitude over time for aftershock sequences was found to have a linear relationship with time by Bhattacharya et al. (2011). They also conjectured that constant of proportionality `S' could be controlled by the self-similar geometry of the fault surface on the basis of a simple, non-realistic model of earthquakes (P Bhattacharya (2007)). Using the Gutenberg-Richter law of aftershock statistics, they showed that `S' can be expressed as the sum of two terms, one of which is the completeness magnitude m. (the cut-off magnitude below which there is deviation from the power law) of the aftershock sequence and the other is inversely related to the b-value (a statistical parameter in GR law). The explicit assumption was that all aftershock magnitudes are independent of each other and that the time series is stationary. These assumptions are open to question as there is no conclusive evidence in existing literature. But what are the implications of deviations of the observed slope from its obtained relation with mc and b? Could it imply correlations in aftershock magnitudes? Is it indeed controlled by the self-similar geometry of the fault surface? A detailed verification of - this relation on real earthquake catalogs is therefore an important scientific exercise and the subject matter of our study. If the slope is not connected to the b-value by the simple formula as suggested, we probably can learn more about the temporal behavior of the aftershock magnitude time series. As aftershocks pose considerable seismic hazard, it is of central scientific and logistic interest to understand the feasibility of this claim and verify it independently. So a detailed verification of the slope function S on real earthquake catalogs is an important scientific exercise and the subject matter of my work.