On Mechanistic Explanation of the Shape of the Universal Curve of Earthquake Recurrence Time Distributions

This paper outlines an idea for an explanation of a mechanism underlying the shape of the universal curve of the Earthquake Recurrence Time Distributions. The proposed simple stochastic cellular automaton model is reproducing the gamma distribution fit with the proper value of parameter γ characterizing the Earth’s seismicity and also imitates a deviation from the fit at short interevent times, as observed in real data.Thus the model suggests an explanation of the universal pattern of rescaled Earthquake Recurrence Time Distributions in terms of combinatorial rules for accumulation and abrupt release of seismic energy.     

Testing a scaling law for the earthquake recurrence time distributions

The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.     

Statistical Properties of the Immediate Aftershocks of the 15 October 2013 Magnitude 7.1 Earthquake in Bohol,Philippines

The aftershock records of the magnitude 7.1 earthquake that hit the island of Bohol in central Philippines on 15 October 2013 is investigated in the light of previous results for the Philippines using historical earthquakes. Statistics of interevent distances and interevent times between successive aftershocks recorded for the whole month of October 2013 show marked differences from those of historical earthquakes from two Philippine catalogues of varying periods and completeness levels. In particular, the distributions closely follow only the regimes of the historical distributions that were previously attributed to the strong spatio-temporal correlations. The results therefore suggest that these correlated regimes which emerged naturally from the analyses are strongly dominated by the clustering of aftershock events.     

Clustering of mining-induced seismic events in equivalent dimension spaces

High energy release during seismic events induced by mining operation is one of the major dangers perturbing production in underground mines. In this work, temporal changes of seismic event parameters for one of the Rudna Mine (Poland) panels are investigated. The study aim was to find whether the temporal clustering of smaller events in different parameters can be observed before and after the high energy events (M_l?≥?3) in the mining panel. The method chosen for analysis was the study of temporal variation of fractal dimension of the seismic events parameter sets composed from: the interevent epicentral distance (dr), logarithm of seismic energy (lE), and interevent energy coefficient (dlE), which is the absolute difference between logarithms of energy of two consecutive events. Temporal variations study was performed in equivalent dimension (ED) space. The transformation of the seismic source parameters into ED space allowed to estimate and compare the temporal changes of the fractal dimension of different parameter spaces using the same method—correlation fractal dimension, and then easily compare the obtained temporal changes of fractal dimension of different parameter sets. The effect of grouping is expressed by decrease of fractal dimension, which is connected with the similarity of events parameter values. The temporal changes of the fractal dimension of seismicity before the strong induced events would indicate some initiation phase of the process leading to the high energy release. In the case of the studied Rudna Mine panel, the temporal behavior of the fractal dimension values in different parameter spaces before seismic events showed significant changes before three out of four events with CLVD dominant source mechanisms.     

Spatial variability and interdependence of rain event characteristics in the Czech Republic

Rain event characteristics are assessed in a 10‐year (1991–2000) record for 122 stations in the Czech Republic. Individual rain events are identified using the minimum interevent time (mit) concept. For each station, the optimal mit value is estimated by examining the distribution of interevent times. In addition, various mit values are considered to account for the effect of mit on rain event characteristics and their interrelationships. The interdependence between rain event characteristics and altitude, average rainfall depth, and geographic location are explored using simple linear models. Most rain event characteristics can be to some extent explained by average total rainfall or altitude, although models including the former significantly outperformed models using the latter. Significant correlation was found among several pairs of monthly mean characteristics often including event rain rate (with event duration, depth, maximum intensity, and fraction of intraevent rainless periods). Moreover, strong correlation was revealed between number of events, interevent time, event depth, and duration. In general, correlation decreases in absolute value with mit. Strong spatial correlation was found for the mean monthly interevent time and number of events. Spatial correlation was considerably smaller for other characteristics. In general, spatial dependence was smaller for larger mit values. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of the Temporal Occurrence of Seismicity at Deception Island (Antarctica). A Nonlinear Approach

—Deception Island is characterized by small magnitude local events with constant energy flux and very low stress drop. To obtain information about its origin, an interevent time series of 546 events, corresponding to an observational period of two month, has been analyzed. From a statistical point of view, data satisfies a Weibull distribution and presents clustering. A rescaled range analysis reveals that data are not independent, i.e. have memory, and the correlation dimension saturates at 2.2; as a consequence, the system can be modeled as a nonlinear iterative equation with three degrees of freedom that presents chaotic behavior. Taking into account that the average interevent time is of the order of 130 minutes, too short to be only due to tectonic activity, the above results indicate that some other mechanism may coexist with the regional tectonic one. According to several geological and geophysical observations, we suggest that most of the local events may be originated by pressure waves generated by a sudden change of phase, of sea and fresh water infiltrated into the main fractures and faults and also from shallow and confined water-saturated layers.     

基于波形相似特征的微地震事件初至拾取及全局校正

微地震事件初至拾取是井下微地震监测数据处理的关键步骤之一.初至误差的存在会使微地震震源定位结果产生较大偏差,进而影响后续的压裂裂缝解释.通常初至拾取过程对所有的微地震事件选择相同的特征函数并采用一致的拾取参数进行统一处理,然而当事件的能量、震源机制、传播路径以及背景噪声等存在明显差异时,所得初至拾取结果差别显著.为了提高微地震事件初至拾取标准一致性,本文提出基于波形相似特征的初至拾取及全局校正方法.该方法首先利用互相关函数对每个事件内的各道记录进行时差校正,得到初始初至信息并形成叠加道,再对所有事件的叠加道进行全局互相关得到事件间初至相对校正量,最终初至结果可以通过各个事件的初始初至信息与其相对校正量相加得到.方法将所有微地震事件初至结果作为一个整体处理,从而能够克服常规方法初至拾取标准一致性差的缺陷.实际资料处理结果表明,相比于常规方法,该方法可以有效提高事件初至拾取和定位结果的一致性.     

Critical rainfall statistics for predicting watershed flood responses: rethinking the design storm concept

Recent advances have been made to modernize estimates of probable precipitation scenarios; however, researchers and engineers often continue to assume that rainfall events can be described by a small set of event statistics, typically average intensity and event duration. Given the easy availability of precipitation data and advances in desk‐top computational tools, we suggest that it is time to rethink the ‘design storm’ concept. Design storms should include more holistic characteristics of flood‐inducing rain events, which, in addition to describing specific hydrologic responses, may also be watershed or regionally specific. We present a sensitivity analysis of nine precipitation event statistics from observed precipitation events within a 60‐year record for Tompkins County, NY, USA. We perform a two‐sample Kolmogorov–Smirnov (KS) test to objectively identify precipitation event statistics of importance for two related hydrologic responses: (1) peak outflow from the Six Mile Creek watershed and (2) peak depth within the reservoir behind the Six Mile Creek Dam. We identify the total precipitation depth, peak hourly intensity, average intensity, event duration, interevent duration, and several statistics defining the temporal distribution of precipitation events to be important rainfall statistics to consider for predicting the watershed flood responses. We found that the two hydrologic responses had different sets of statistically significant parameters. We demonstrate through a stochastic precipitation generation analysis the effects of starting from a constrained parameter set (intensity and duration) when predicting hydrologic responses as opposed to utilizing an expanded suite of rainfall statistics. In particular, we note that the reduced precipitation parameter set may underestimate the probability of high stream flows and therefore underestimate flood hazard. Copyright © 2016 John Wiley & Sons, Ltd.     

Spatial distribution of aftershocks and background seismicity in central California

We examine the spatial distribution of earthquake hypocenters in four central California areas: the aftershock zones of the (1) 1984 Morgan Hill (2) 1979 Coyote Lake, and (3) 1983 Coalinga earthquakes, as well as (4) the aseismically creeping area around Hollister. The basic tool we use to analyze these data are frequency distributions of interevent distances between earthquakes. These distributions are evaluated on the basis of their deviation from what would be expected if earthquakes occurred randomly in the study areas. We find that both background seismic activity and aftershocks in the study areas exhibit nonrandom spatial distribution. Two major spatial patterns, clustering at small distances and anomalies at larger distances, are observed depending on tectonic setting. While both patterns are seen in the strike-slip environments along the Calaveras fault (Morgan Hill, Coyote Lake, and Hollister), aftershocks of the Coalinga event (a thrust earthquake) seem to be characterized by clustering only. The spatial distribution of earthquakes in areas gradually decreasing in size does not seem to support the hypothesis of a self-similar distribution over the range of scales studied here, regardless of tectonic setting. Spatial distributions are independent of magnitude for the Coalinga aftershocks, but events in strike-slip environments show increasing clustering with increasing magnitude. Finally, earthquake spatial distributions vary in time showing different patterns before, during, and following the end of aftershock sequences.     

Ground-motion intensity measure correlations observed in Italian strong-motion records

Ground-motion models (GMMs) are widely used in probabilistic seismic hazard analysis (PSHA) to estimate the probability distributions of earthquake-induced ground-motion intensity measures (IMs) at a site, given an earthquake of a certain magnitude occurring at a nearby location. Accounting for spatial and cross-IM correlations in earthquake-induced ground motions has important implications on probabilistic seismic hazard and loss estimates. This study first develops a new Italian GMM with spatial correlation for 31 amplitude-related IMs, including peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped elastic pseudo-spectral accelerations (PSAs) at 29 periods ranging from 0.01 to 4 seconds. The model estimation is performed through a recently developed one-stage nonlinear regression algorithm proposed by the authors, known as the Scoring estimation approach. In fact, current state-of-practice approaches estimate spatial correlation separately from the GMM estimation, resulting in inconsistent and statistically inefficient estimators of interevent and intraevent variances and parameters in the spatial correlation model. We test whether this affects the subsequent cross-IM correlation analysis. To this aim, based on the newly developed GMM, the empirical correlation coefficients from interevent and intraevent residuals are investigated. Finally, a set of analytical correlation models between the selected IMs are proposed. This is of special interest as several correlation models between different IMs have been calibrated and validated based on advanced GMMs and global datasets, lacking earthquakes in extensional regions; however, modeling the correlation between different IM types has not been adequately addressed by current, state-of-the-art GMMs and recent ground-motion records for Italy.     

Studies of short and long memory in mining-induced seismic processes

Memory of a stochastic process implies its predictability, understood as a possibility to gain information on the future above the random guess level. Here we search for memory in the mining-induced seismic process (MIS), that is, a process induced or triggered by mining operations. Long memory is investigated by means of the Hurst rescaled range analysis, and the autocorrelation function estimate is used to test for short memory. Both methods are complemented with result uncertainty analyses based on different resampling techniques. The analyzed data comprise event series from Rudna copper mine in Poland. The studies show that the interevent time and interevent distance processes have both long and short memory. MIS occurrences and locations are internally interrelated. Internal relations among the sizes of MIS events are apparently weaker than those of other two studied parameterizations and are limited to long term interactions.     

Interevent Time Distribution in Seismicity: A Theoretical Approach

This paper presents an analysis of the distribution of the time τ between two consecutive events in a stationary point process. The study is motivated by the discovery of unified scaling laws for τ for the case of seismic events. We demonstrate that these laws cannot exist simultaneously in a seismogenic area. Under very natural assumptions we show that if, after rescaling to ensure Eτ =1, the interevent time has a universal distribution F, then F must be exponential. In other words, Corral’s unified scaling law cannot exist in the whole range of time. In the framework of a general cluster model we discuss the parameterization of an empirical unified law and the physical meaning of the parameters involved. An erratum to this article is available at .     

A mixed model for earthquake interevent times

A mixed model is proposed to fit earthquake interevent time distribution. In this model, the whole distribution is constructed by mixing the distribution of clustered seismicity, with a suitable distribution of background seismicity. Namely, the fit is tested assuming a clustered seismicity component modeled by a non-homogeneous Poisson process and a background component modeled using different hypothetical models (exponential, gamma and Weibull). For southern California, Japan, and Turkey, the best fit is found when a Weibull distribution is implemented as a model for background seismicity. Our study uses earthquake random sampling method we introduced recently. It is performed here to account for space–time clustering of earthquakes at different distances from a given source and to increase the number of samples used to estimate earthquake interevent time distribution and its power law scaling. For Japan, the contribution of clustered pairs of events to the whole distribution is analyzed for different magnitude cutoffs, m _c, and different time periods. The results show that power laws are mainly produced by the dominance of correlated pairs at small and long time ranges. In particular, both power laws, observed at short and long time ranges, can be attributed to time–space clustering revealed by the standard Gardner and Knopoff’s declustering windows.     

Analysis of Temporal Structures of Seismic Events on Different Scale Levels

A statistical model for describing the energy scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) on different scale (energy/magnitude) levels the self-similarity of the distribution has been determined. A comparison between the distribution of inter-event times on different scale levels and the most popular distributions of reliability theory has been carried out. The distribution of inter-event times for different scale levels is well approximated by the Weibull distribution. The Weibull distribution, with parameters which obey the scaling model and the Gutenberg-Richter law, has been tested.     

Statistical analysis of the 2012–2013 Torreperogil–Sabiote seismic series,Spain

The study of earthquake swarms and their characteristics can improve our understanding of the transient processes that provoke seismic crises. The spatio-temporal process of the energy release is often linked with changes of statistical properties, and thus, seismicity parameters can help to reveal the underlying mechanism in time and space domains. Here, we study the Torreperogil–Sabiote 2012–2013 seismic series (southern Spain), which was relatively long lasting, and it was composed by more than 2000 events. The largest event was a magnitude 3.9 event which occurred on February 5, 2013. It caused slight damages, but it cannot explain the occurrence of the whole seismic crises which was not a typical mainshock–aftershock sequence. To shed some light on this swarm occurrence, we analyze the change of statistical properties during the evolution of the sequence, in particular, related to the magnitude and interevent time distributions. Furthermore, we fit a modified version of the epidemic type aftershock sequence (ETAS) model in order to investigate changes of the background rates and the trigger potential. Our results indicate that the sequence was driven by an aseismic transient stressing rate and that the system passes after the swarm occurrence to a new forcing regime with more typical tectonic characteristics.     

Recurrence Interval Statistics of Cellular Automaton Seismicity Models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.     

A diffusion approach to the statistical analysis of Kamchatka Seismicity

A diffusion approach was used to develop a statistical model of seismicity and to analyze Kamchatka earthquakes in order to detect features in the changes that are typical of random walk processes. We proposed a hypothesis of relationships among events and used an energy criterion to decompose the earth-quake catalog into a set of sequences, with each being a Brownian process with definite spatial, temporal, and energy scales. We constructed statistical distributions for these sequences over the number of their terms and total energies, as well as distributions of the sequences over distance, time, and flight times between events. We discuss non-local properties and memory effects in the random walk under different conditions.     

基于背向散射脉冲传播时间统计特性的随机界面参数反演研究

研究了利用背向散射脉冲传播时间统计特性反演随机界面参数的问题.首先扩展了Fuks & Godin关于随机界面背向散射脉冲传播时间统计特性理论,给出了当随机界面高度-斜率统计相关情形下,最早返回的两个脉冲传播时间及其时延的概率密度函数（PDF）表达式.进而提出了一种基于背向散射脉冲传播时间统计特性的随机界面参数反演算法：采用遗传算法匹配前两个背向散射脉冲传播时间及其时延的PDF实现随机界面高度—斜率相关系数的绝对值|ρ|和无量纲参数T的反演.最后利用参数的后验概率分析反演结果的不确定性.数值模拟结果表明：该算法可有效反演随机界面的参数,参数|ρ|相对于T反演精度较高;|ρ|和T之间存在较强的参数耦合.与前人认为可忽略高度—斜率相关性（|ρ|）的观点不同：此类反演问题中应同时考虑|ρ|和T.     

Earthquakes: Recurrence and Interoccurrence Times

The purpose of this paper is to discuss the statistical distributions of recurrence times of earthquakes. Recurrence times are the time intervals between successive earthquakes at a specified location on a specified fault. Although a number of statistical distributions have been proposed for recurrence times, we argue in favor of the Weibull distribution. The Weibull distribution is the only distribution that has a scale-invariant hazard function. We consider three sets of characteristic earthquakes on the San Andreas fault: (1) The Parkfield earthquakes, (2) the sequence of earthquakes identified by paleoseismic studies at the Wrightwood site, and (3) an example of a sequence of micro-repeating earthquakes at a site near San Juan Bautista. In each case we make a comparison with the applicable Weibull distribution. The number of earthquakes in each of these sequences is too small to make definitive conclusions. To overcome this difficulty we consider a sequence of earthquakes obtained from a one million year “Virtual California” simulation of San Andreas earthquakes. Very good agreement with a Weibull distribution is found. We also obtain recurrence statistics for two other model studies. The first is a modified forest-fire model and the second is a slider-block model. In both cases good agreements with Weibull distributions are obtained. Our conclusion is that the Weibull distribution is the preferred distribution for estimating the risk of future earthquakes on the San Andreas fault and elsewhere.     

A procedure to estimate the probability distribution of recurrence times in the west-northwestern Hellenic arc

The determination of the probability distribution of recurrence times is the most important problem in the calculation of long-term conditional probabilities for the recurrence of large and great earthquakes.The principle of maximum entropy in conjunction with a goodness-of-fit test (chi-square or Kolmogorov-Smirnov test) may be employed to obtain estimates of these densities using recurrence data for some seismic regions.Four different distributions are characterized by the property of maximum entropy, as possible laws for recurrence times of the largest earthquakes: uniform, exponential, Gaussian and log-normal. To discriminate among these different probability distributions we use the probability theory and the chi-square test to check the goodness-of-fit to the distribution of recurrence time of shocks of magnitude 6.5 and largest occurred in the west-northwestern zone of the Hellenic arc from 1791 to 1983.It is found that the recurrence times data for the west-northwestern zone of the Hellenic arc cannot be represented by the uniform and the Gaussian probability densities. The recurrence times data for the west-northwestern zone of the Hellenic arc can be described accurately by the exponential and log-normal probability densities, which were predicted from the principle of maximum entropy. In other words, the principle of maximum entropy does not necessarily lead to a unique solution. In turn, the mathematical properties of these distributions could be used to derive different physical properties of the earthquake process in the west-northwestern zone of the Hellenic arc.