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The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law distribution…
The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude…
The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…
The time dependence of the parameter of the Gutenberg-Richter (GR) magnitude distribution is computed for foreshock sequences of earthquakes, correlated with the main shock, by using the geometric-growth model of earthquake focus, the…
The area-characteristic, maximum possible earthquake magnitude $T_M$ is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg-Richter law predicts that earthquake magnitudes…
Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m…
We develop a new method for the statistical esitmation of the tail of the distribution of earthquake sizes recorded in the Worldwide Harvard catalog of seismic moments converted to mW-magnitudes (1977-2004 and 1977-2006). We show that using…
The identification of patterns in space, time, and magnitude, which could potentially encode the subsequent earthquake magnitude, represents a significant challenge in earthquake forecasting. A pivotal aspect of this endeavor involves the…
We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are…
The evaluation of the $b$ value of the Gutenberg-Richter (GR) law, for a sample composed of $n$ earthquakes, presents a systematic positive bias $\delta b$ which is proportional to $1/n$, as already observed by Ogata \& Yamashina (1986). In…
We propose a new version of the ETAS model, which we also analyze theoretically. As for the standard ETAS model, we assume the Gutenberg-Richter law as a probability density function for background events' magnitude. Instead, the magnitude…
Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on…
Investment in measuring a process more completely or accurately is only useful if these improvements can be utilised during modelling and inference. We consider how improvements to data quality over time can be incorporated when selecting a…
The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay…
Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult…
The Gutenberg-Richter law is a fundamental empirical law in seismology describing earthquake frequency-magnitude distributions, with one of its key parameters, the so-called b-value, quantifying the relative frequency of small versus large…
After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number…
We present a generic and powerful approach to study the statistics of extreme phenomena (meteorology, finance, biology...) that we apply to the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation…
It was conjectured for a long time that the tectonic plates are in a self-organized state of criticality and that the Gutenberg-Richter law is a manifestation of that. It was recently shown that for a system near criticality, the inequality…
We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two…