Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity

Matteo Taroni,Jiancang Zhuang,Jacopo Selva

doi:10.3390/app112412166

Abstract

The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region.

Highlights

The Gutenberg-Richter law [1] is the most widely applied magnitude frequency distribution for earthquakes
If we look only to the distribution of the magnitudes, independently from the rate of events, this law corresponds to an exponential distribution [2]
We find instead that the corner magnitude for both normal and strike-slip events is well constrained, and incompatible with an unbounded Guttenberg-Richter distribution

Summary

Introduction

The Gutenberg-Richter law [1] is the most widely applied magnitude frequency distribution for earthquakes. If we look only to the distribution of the magnitudes, independently from the rate of events, this law corresponds to an exponential distribution [2]. In this case, it depends on only one parameter (the so-called b-value), controlling the slope of the distribution, and does not have an upper bound for the magnitude. In order to have a more physical behavior for the right tail of the magnitude distribution, two other formulations of this law are usually applied: the truncated and the tapered Gutenberg-Richter distributions [3]. The tapered version applies a soft bound, i.e., a corner magnitude (C M ): the probability of an earthquake bigger than the corner magnitude decreases very rapidly asymptotically reaching zero (see Figure 1)

Methods

Discussion

Conclusion