We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The practical measurement of the phase is discussed and the main pitfalls are underlined. For large values, the experimental distributions of the phase first, second and third derivatives obey universal power-law decays whose exponents are remarkably well predicted by circular Gaussian statistics. For small values, these distributions are flat. The details of the transition between the plateau and the power-law behavior are governed by the wavelength. The correlation function of the first phase derivative along the array shows a simple algebro-exponential decay with the mean free path as the only length scale. Although only loose bounds are provided in this study, our work suggests a new method to estimate the degree of heterogeneity of the cr
Attenuation study of a province is considered as a basic quantity for seismic hazard assessment, ground motion simulation process and source parameter studies. It is already established that the study of two physical processes, first, the seismic sources and second, propagation of the waves, is essential for seismic-hazard mapping, attenuation being one of the properties paying importance to the latter. Here, a computational tool entitled CodaQback is presented. Based on back scattering model, this versatile software is equipped with user friendly graphical user interface. It also allows quick…
We have studied the partition of shear, compressional and kinetic energies in the coda of ten earthquakes recorded on a dense array, located at Pinyon Flats Observatory (PFO), California. We observe a clear stabilization of the shear to compressional ($W^s/W^p$) energy ratio in the coda, with an average value of about 2.8. The ratio between the vertical and horizontal kinetic energies ($V^2/H^2$) can be measured from 5 to 25Hz and shows an abrupt transitionfrom 0.1 in the 5-10Hz band, to about 0.8 in the 15-25Hz band. These measured values are in sharp contrast with the theoretical prediction …
Coda in local earthquake exhibits resonance-like wave behaviour where the coda emerges as long-duration small-amplitude vibration with selective frequency, slow temporal decay, and uniform spatial energy distribution around the earthquake source. Coda is thought to be the incoherent waves scattered from random small-scale heterogeneity in the earth's lithosphere. Here I show that the coda is primarily attributed to the natural resonance in strong small-scale heterogeneity around the earthquake's hypocenter through seismic wave field modeling for 1D heterogeneity. The natural resonance is evolv…
The nominally incoherent coda of a scattered wavefield has been shown to be a remarkably sensitive quantitive monitoring tool. Its success is however often underpinned by the assumption of a moderate velocity perturbation, and in the absence of notable changes in material scattering properties. The deformation of a rock matrix, represents for a monitoring wavefield pronounced changes in scattering power. In this work we introduce a rolling reference wavefield when applying Coda-Wave Interferometry (CWI) and Coda-Wave-Decorrelation (CWD) in order to monitor relative velocity and material scatte…
We evaluated the body wave attenuation parameter in Kopili region of northeast India. Using the modified algorithm of coda normalization method, we delineated frequency-dependent attenuation for both P and S waves. Taking more than 300 seismograms as input, we comprehensively studied microearthquake spectra in the frequency range of 1.5 to 12 Hz. The estimated values of $Q_P^{-1}$ and $Q_S^{-1}$ show strong frequency dependence. The relationships emerge to be $Q_P^{-1}=(23.8\pm 6)\times10^{-3}f^{-1.2\pm 0.008}$ and $Q_S^{-1}=(10.2\pm 2)\times10^{-3}f^{-1.3\pm 0.02}$, respectively. The ratio $Q…
Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single scattering assumption. In heterogeneous areas such as volcanoes, the multiple scattering contribution limits the imaging-depth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof-of-c…
Extracting Empirical Green's Functions (EGFs) by cross-correlating ambient seismic noise or coda, considered as an efficient approach of retrieving new response inside the media of two receivers, has been developed well in the past two decades. However, EGFs emerge with high Signal-to-Noise Ratios (SNRs), which needs us to stack a large number of cross-correlations. Here, we retrieve EGFs with high SNRs from ambient seismic noise released by hurricane Dorian moving along the eastern coast of the United States during 3 days in Sept 2019. We systematically analyze the energy sources of seismic n…
Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maxim…
We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual va…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches: The non homogeneous Poissonian and the non Poissonian one. In all cases we obtain either a power law or a power law damped by an exponential factor behaviour. This feature of the distribution makes impossible any prediction of earthquakes occurrence. Nevertheless it suggests the interpretation of the earthquake occurrence phenomenon as due to some non-linear d…
The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state of the art rate-and-state models for the prediction of seismic …
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 evaluates quantitatively the deviations of the distribution of scalar seismic moments from a power-like (Pareto) law. This statistic is close to zero for the Pareto law with arbitrary power index, and deviates from zero for any non-Pareto distribution. A version of this statistic for discrete distribution of quantified magnitudes is also given. A methodolog…
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…
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 with two statistical models that incorporate an exponential tail: the so-called tapered Gutenberg-Richter and the truncated gamma, when fitted to the global CMT earthquake catalog. The outcome is that the truncated gamma model outperforms the other two models. If simulated samples of the truncated gamma are reshuffled in order to mimic the time occurrence of …
Geodetic earthquake early warning (EEW) algorithms complement point-source seismic systems by estimating fault-finiteness and unsaturated moment magnitude for the largest, most damaging earthquakes. Because such earthquakes are rare, it has been difficult to demonstrate that geodetic warnings improve ground motion estimation significantly. Here, we quantify and compare timeliness and accuracy of magnitude and ground motion estimates in simulated real time from seismic and geodetic observations for a suite of globally-distributed, large earthquakes. Magnitude solutions saturate for the seismic …
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a spatially independent, time-homogenized version of Bak et al's procedure, which seems to …
We introduce the first fully self-consistent model combining the seismic micro-ruptures occurring within a generalized Burridge-Knopoff spring-block model with the nucleation and propagation of electric charge pulses within a coupled mechano-electrokinetic system. This model provides a general theoretical framework for modeling and analyzing geoelectric precursors to earthquakes. In particular, it can reproduce the unipolar pulses that have often been reported before large seismic events, as well as various observed anomalies in the statistical moments of the ambient electric fields and the po…
The distribution of the magnitudes of seismic events is generally assumed to be independent on past seismicity. However, by considering events in causal relation, for example mother-daughter, it seems natural to assume that the magnitude of a daughter event is conditionally dependent on the one of the corresponding mother event. In order to find experimental evidence supporting this hypothesis, we analyze different catalogs, both real and simulated, in two different ways. From each catalog, we obtain the law of triggered events' magnitude by kernel density. The results obtained show that the d…
The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physically-based models of earthquake recurrence (t…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (…
Statistical properties of earthquakes are studied both by the analysis of real earthquake catalog of Japan and by numerical computer simulations of the spring-block model in both one and two dimensions. Particular attention is paid to the spatiotemporal correlations of earthquakes, e.g., the recurrence-time distribution or the time evolution before and after the mainshock of seismic distribution functions, including the magnitude distribution and the spatial seismic distribution. Certain eminent features of the spatiotemporal correlations, e.g., foreshocks, aftershocks, swarms and doughnut-lik…
We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and Generalized Extreme Value distribution (GEV). We obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration tau. This distribution can be characterized by its quantile Qq(tau) at an…
Based on the Irkutsk fast monostatic chirp ionosonde data we made a statistical analysis of ionospheric effects for 28 earthquakes which appeared in 2011-2016 years. These effects are related with surface (Rayleigh) seismic waves far from epicenter. The analysis has shown that nine of these earthquakes were accompanied by vertical midscale ionospheric irregularities (multicusp). To estimate the ionospheric efficiency of the seismic waves we proposed new index $K_{W}$. The index estimates the maximal amplitude of the acoustic shock wave generated by given spatial distribution of seismic vibrati…
Based on several empirical evidence, a series of papers has advocated the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative Benioff strain (BS) increases as a power-law time-to-failure before the final event. This power law reflects a kind of scale invariance with respect to the distance to the critical point. A few years ago, on the basis of a fit of the cumulative BS released prior to the 1989 Loma Prieta earthquake, Sornette and Sammis [1995] proposed that this scale invaria…
Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）；Observatoire de la Côte d’Azur, Université Côte d’Azur（蔚蓝海岸天文台，蔚蓝海岸大学）；CNRS, IRD, Géoazur（法国国家科学研究中心、海外发展研究院、Géoazur）；University of California, Riverside（加州大学河滨分校）
