Importance of direct and indirect triggered seismicity

Is Earthquake Triggering Driven by Small Earthquakes?

Using a catalog of seismicity for Southern California, we measure how the number of triggered earthquakes increases with the earthquake magnitude. The trade-off between this relation and the distribution of earthquake magnitudes controls the relative role of small compared to large earthquakes. We show that seismicity triggering is driven by the smallest earthquakes, which trigger fewer events than larger earthquakes, but which are much more numerous. We propose that the non-trivial scaling of the number of triggered earthquakes emerges from the fractal spatial distribution of seismicity.

Statistical Physics Approaches to Seismicity

This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We summarize the leading theoretical physical models of the space-time organization of earthquakes. We present a general discussion and several examples of the new metrics proposed by statistical physicists, underlining their strengths and weaknesses. The entry concludes by briefly outlining future directions. The presentation is organized as follows. I Glossary II…

Productivity within the ETAS seismicity model

The productivity of a magnitude $m$ event can be characterized in term of triggered events of magnitude above $m-Δ$: it is the number of direct "descendants" $ν_Δ$ and the number of all "descendants" $V_Δ$. There is evidence in favour of the discrete exponential distribution for both $ν_Δ$ and $V_Δ$ with a dominant magnitude $m$ (the case of aftershock cluster). We consider the general Epidemic Type Aftershock Sequence (ETAS) model adapted to any distribution of $ν_Δ$. It turns out that the branching structure of the model excludes the possibility of having exponential distributions for both p…

重新审视地震活动临界性：统计地震学模型校准偏差校正的新框架

Revisiting Seismicity Criticality: A New Framework for Bias Correction of Statistical Seismology Model Calibrations

针对ETAS模型校准中的边界、有限尺寸和审查偏差，提出基于可变背景率的校正方法，利用napp(Mco)函数准确恢复真实分支比，并应用于加州、新西兰和川滇地区，发现地震活动呈明显亚临界状态。

Delayed dynamic triggering of earthquakes: Evidences from a statistical model of seismicity

I study a recently proposed statistical model of earthquake dynamics that incorporates aging as a fundamental ingredient. The model is known to generate earthquake sequences that quantitatively reproduce the spatial and temporal clustering of events observed in actual seismic patterns. The aim of the present work is to investigate if this model can give support to the empirical evidence that earthquakes can be triggered by transient small perturbations, particularly by the passing of seismic waves originated in events occurring in far geographical locations. The effect of seismic waves is inco…

Correlation between tides and seismicity in Northwestern South America: the case of Colombia

We present the first systematic exploration of earth tides-seismicity correlation in northwestern South America, with a special emphasis in Colombia. For this purpose, we use a dataset of ~167,000 earthquakes, gathered by the Colombian Seismological Network between 1993 and 2017. Most of the events are intermediate-depth earthquakes from the Bucaramanga seismic nest and the Cauca seismic cluster. For this purpose, we implemented a novel approach for the calculation of tidal phases that considers the relative positions of the Earth-Moon-Sun system at the time of the events. After applying the s…

使用监督机器学习进行地震去聚类

Earthquake Declustering Using Supervised Machine Learning

本文提出一种基于监督机器学习的去聚类方法，利用ETAS模型生成合成数据并以最近邻距离为特征训练模型，在南加州和意大利地震目录上验证其优于传统NND和随机去聚类方法。

A physical model for aftershocks triggered by dislocation on a rectangular fault

We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the source. The time-dependent rate of triggered earthquakes is estimated by a rate-state model applied to a uniformly distributed population of faults whose equilibrium is perturbated by a stress change caused only by the first dislocation. The rate of triggered events in our simulations is exponentially proportional to the stress change, but the time at which the …

Magnitude Of Earthquakes Controls The Size Distribution Of Their Triggered Events

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 earthquakes. In nearly all generalizations of the ETAS model, the magnitudes of the background and the triggered earthquakes are assumed to follow Gutenberg-Richter law with the same exponent (\b{eta}-value). Furthermore, the magnitudes of the triggered earthquakes are always assumed to be independent of the magnitude of the triggering earthquake. Using an EM algor…

Importance of small earthquakes for stress transfers and earthquake triggering

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as \~10^(Dm/2). The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future e…

Objective Estimation of Spatially Variable Parameters of Epidemic Type Aftershock Sequence Model: Application to California

The ETAS model is widely employed to model the spatio-temporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the Expectation-Maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the Bayesian Information Criterion (BIC) to rank inverted models given their likelihood and complexity and select the best models to finally compute an ensemble model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the know…

Complex networks of earthquakes and aftershocks

We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no corr…

Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes

We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (``productivity'' or ``fertility''), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of f…