Related papers: Unifying the Gutenberg-Richter Law with Probabilis…
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…
Without rigorous attention to the completeness of earthquake catalogs, claims of new discoveries or forecasting skills cannot be deemed credible. Therefore, estimating the completeness magnitude (Mc) is a critical step. Among various…
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…
The complete part of the earthquake frequency-magnitude distribution (FMD), above completeness magnitude mc, is well described by the Gutenberg-Richter law. The parameter mc however varies in space due to the seismic network configuration,…
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 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…
It is well accepted that, at the global scale, the Gutenberg-Richter (GR) law describing the distribution of earthquake magnitude or seismic moment has to be modified at the tail to properly account for the most extreme events. It is…
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 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…
In this study we address the question of the minimum sample size needed for distinguishing between Gutenberg-Richter distributions with varying b-values at different resolutions. In order to account for both the complete and incomplete…
Machine learning (ML) catalogs contain many more earthquakes than routine catalogs, but their performance in phase picking and earthquake detection has not been fully evaluated. We develop station-level detection probabilities using…
We have written a new equation to study the statistics of earthquake distributions. We call this equation "the generalized logistic equation". The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the…
We introduce a new model for an earthquake fault system that is composed of non-interacting simple lattice models with different levels of damage denoted by $q$. The undamaged lattice models ($q=0$) have Gutenberg-Richter scaling with a…
The $b$-value in earthquake magnitude-frequency distribution quantifies the relative frequency of large versus small earthquakes. Monitoring its evolution could provide fundamental insights into temporal variations of stress on different…
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…
We make an extensive numerical study of a two dimensional nonconservative model proposed by Olami-Feder-Christensen to describe earthquake behavior. By analyzing the distribution of earthquake sizes using a multiscaling method, we find…
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…
We propose two methods to calibrate the parameters of the epidemic-type aftershock sequence (ETAS) model based on expectation maximization (EM) while accounting for temporal variation of catalog completeness. The first method allows for…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
Machine learning regression can predict macroscopic fault properties such as shear stress, friction, and time to failure using continuous records of fault zone acoustic emissions. Here we show that a similar approach is successful using…