Related papers: Estimating the maximum possible earthquake magnitu…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
In this paper, I introduce a novel approach to modelling the individual random component (also called the intra-event uncertainty) of a ground-motion relation (GMR), as well as a novel approach to estimating the corresponding parameters. In…
The statistical properties of avalanches in a dissipative particulate system under slow shear are investigated using molecular dynamics simulations. It is found that the magnitude-frequency distribution obeys the Gutenberg-Richter law only…
Geometrical complexities in natural fault zones, such as steps and gaps, pose a challenge in seismic hazard studies as they can act as obstacles to seismic ruptures. In this study, we propose a criterion, which is based on the…
We present an axiomatic approach to earthquake forecasting in terms of multi-component random fields on a lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…
A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence…
Let $X_0$ be a complete hyperbolic surface of infinite type that has a geodesic pants decomposition with cuff lengths bounded above. The length spectrum Teichm\"uller space $T_{ls}(X_0)$ consists of homotopy classes of hyperbolic metrics on…
Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a…
Due to the saturation of the body ($m_b$) and surface ($M_S$) earthquake magnitudes, the moment magnitude ($M_W$) is a more convenient parameter for representing earthquake energies. We use the HRVD data, including 18,569 earthquakes…
We report an exact analysis of a discrete form of the Chakrabarti-Stinchcombe model for earthquakes [Physica A \textbf{270}, 27 (1999)] which considers a pairof dynamically overlapping finite generations of the Cantor set as a prototype of…
The ranking problem of earthquake forecasts is considered. We formulate simple statistical requirements to forecasting quality measure R and analyze some R-ranking methods on this basis, in particular, the pari-mutuel gambling method by…
Slope stability description through mechanical laws has important implication for Earth morphology understanding and risk assessment. Previous researches have showed that shear, tensile, and hybrid fractures can be observed experimentally…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…