Related papers: Estimating the maximum possible earthquake magnitu…
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 upper bound earthquake magnitude (maximum possible magnitude) of a truncated Gutenberg-Richter relation is the right truncation point (right end-point) of a truncated exponential distribution and is important in the probabilistic…
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 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…
Earthquake prediction has been a challenging research area for many decades, where the future occurrence of this highly uncertain calamity is predicted. In this paper, several parametric and non-parametric features were calculated, where…
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…
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…
The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cut-off exponential…
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…
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…
In this short note, I comment on the research of Pisarenko et al. (2014) regarding the extreme value theory and statistics in case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic…
Earthquake occurrence is notoriously difficult to predict. While some aspects of their spatiotemporal statistics can be relatively well captured by point-process models, very little is known regarding the magnitude of future events, and it…
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…
This paper focuses on the problem of anticipating the local occurrence of future large earthquakes. "Local" is defined as the probability of a large earthquake occurring with a defined circle of arbitrary radius surrounding a point of…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered…
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…
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…
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…