Earthquake Time Series Research Articles

Earthquake magnitude time series: scaling behavior of visibility networks

We present a statistical analysis of earthquake magnitude sequences in terms of the visibility graph method. Magnitude time series from Italy, Southern California, and Mexico are transformed into networks and some organizational graph properties are discussed. Connectivities are characterized by a scale-free distribution with a noticeable effect for large scales due to either the presence or the lack of large events. Also, a scaling behavior is observed between different node measures like betweenness centrality, clustering coefficient, nearest neighbor connectivity, and earthquake magnitude. Moreover, parameters which quantify the difference between forward and backward links, are proposed to evaluate the asymmetry of visibility attachment mechanism. Our results show an alternating average behavior of these parameters as earthquake magnitude changes. Finally, we evaluate the effects of reducing temporal and spatial windows of observation upon visibility network properties for main-shocks.

The atmospheric water as a triggering factor for earthquakes in the central Virginia seismic zone

Even though central Virginia is far from the nearest plate boundaries, the region is well-known for minor-to-moderate shocks, which have occurred frequently since at least the eighteenth century. Many of its people have experienced small earthquakes, while infrequent larger ones have caused damage. The largest destructive earthquake (magnitude 5.8) in this seismic zone was recorded in August 2011. Smaller earthquakes that cause little or no damage are felt each year or two. It is difficult to link the earthquakes of this zone to known small faults which are numerous, deeply buried and do not show up at the surface. The mean earthquake depth since 1960 is 6.7 km. On the other hand, central Virginia is a big collector and transporter of precipitation water, which flows to the Atlantic Ocean through the James River and its tributaries. There are about 2,000 abandoned mining sites in Virginia with underground openings that can facilitate the interception and conveyance of surface water. This paper presents evidence that seismic activity in certain zones can be associated clearly with the hydrological effects of abundant precipitation. Such effects can increase tectonic stress, which surpasses the marginal amount when an earthquake occurs. We analyze the cross-correlation between precipitation or water discharge in the rivers and earthquake occurrence in the central Virginia seismic zone. This correlation is examined both over a long-term span (57–92 years) and with regard to individual cases in which earthquakes have followed the occurrence of intense hydrological phenomena such as torrential rainfall or hurricanes. As we probe for a correlation between earthquake time series for central Virginia and the monthly precipitation series at hydrometeorological stations located in the zone, we observe that the best cross-correlation is obtained for a time period of 3 months. The same time period applies to certain historical earthquakes that were preceded by large amounts of precipitation. These results support the hydroseismicity hypothesis, which points to the role of water in the generation of intraplate seismicity.

Investigating the dynamical features of the time distribution of the reservoir-induced seismicity in Enguri area (Georgia)

We analyzed the fractal and multifractal properties of the earthquake time series occurred around the Enguri dam in West Georgia by applying the methods of detrended fluctuation analysis and multifractal detrended fluctuation analysis. We examined the interevent time series in two periods: (1) 1960–1980, in which the investigated area was characterized by the natural seismicity; and (2) 1981–2012, in which the quasi-periodic change of the reservoir water level affected the earthquake generation. Our findings show that the water level variation may influence the fractal properties of earthquake temporal distribution in the local area around the Enguri dam. In particular, it is observed that the time distribution features of seismicity occurred in the second period are more persistent than the natural seismicity occurred in the first period. Furthermore, the seismic process of the second period shows a lower multifractal degree than that of the first period, indicating that the influence of quasi-periodic fluctuation of water level features the seismicity as more regular compared to the natural seismicity.

Analysis of temporal variation of earthquake occurrences in Caucasus from 1960 to 2011

Abstract Frequency of earthquake occurrences in Caucasus is investigated on hourly and daily time scales. The observation period is 51 years, which is sufficiently long to perform a reliable statistics. Several methods (power spectrum, wavelet and Hilbert–Huang transformation) are applied to earthquake time series. Our findings show that earthquakes hourly and daily occurrence is not characterized by the dominant frequencies. However, many different oscillations with periods from hours to years and longer contribute to the frequency content of the earthquake time distribution, although their amplitude is rather low. The variation of the power of cyclic components in the temporal features of earthquakes occurrence is not uniform, but their amplification corresponds to the decrease of released local seismic energy.

A Test for Second-Order Stationarity and Approximate Confidence Intervals for Localized Autocovariances for Locally Stationary Time Series

SummaryMany time series are not second order stationary and it is not appropriate to analyse them by using methods designed for stationary series. The paper introduces a new test for second-order stationarity that detects kinds of departures from stationarity that are different from those based on Fourier methods. The new test is also computationally fast, designed to work with Gaussian and a wide range of non-Gaussian time series, and can locate non-stationarities in time and scale. The test is demonstrated on earthquake, explosion, infant electrocardiogram and simulated time series showing varying degrees of stationarity. The second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate. Our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series.

Seismic Electric Signals: An additional fact showing their physical interconnection with seismicity

Natural time analysis reveals novel dynamical features hidden behind time series in complex systems. By applying it to the time series of earthquakes, we find that the order parameter of seismicity exhibits a unique change approximately at the date(s) at which Seismic Electric Signals (SES) activities have been reported to initiate. In particular, we show that the fluctuations of the order parameter of seismicity in Japan exhibits a clearly detectable minimum approximately at the time of the initiation of the SES activity observed by Uyeda and coworkers almost two months before the onset of the volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan. To the best of our knowledge, this is the first time that, well before the occurrence of major earthquakes, anomalous changes are found to appear almost simultaneously in two independent datasets of different geophysical observables (geoelectrical measurements, seismicity). In addition, we show that these two phenomena are also linked closely in space.

Employing Cantor sets for earthquake time series analysis in two zones of western Turkey

In this study, a fractal approach is employed to analyze the seismic history of Fethiye and Simav zones in the West of Turkey. In this scope, a database, including the set of earthquakes in two seismogenic zones, is compiled. Applying fractal dimension and probability concepts, it is aimed to find out the occurrence probability of earthquakes having magnitudes equal to or greater than a threshold level. The results are analyzed in detail and relationships among the fractal dimension, threshold magnitude, probability intercept, and critical time scale are presented. The analyses revealed that activities in the Fethiye Zone are more frequent and continuous than those in the Simav Zone. As mentioned in previous studies, the critical time scales at certain magnitude thresholds can be referred to as the lower limit of the recurrence period of earthquakes in these zones.

Scale-specific order parameter fluctuations of seismicity before mainshocks: Natural time and Detrended Fluctuation Analysis

The order parameter fluctuations of seismicity are investigated upon considering a natural time window of fixed length sliding through the consecutive earthquakes that occurred in California. We previously found that when this length corresponds to a time period of the order of a few months, the fluctuations exhibit a global minimum before the strongest mainshock. Here, we show that in California, during the twenty five year period 1979–2003, minima of the fluctuations are identified 1 to 5 months before four out of five mainshocks with magnitude M = 7.0 or larger as well as before the M = 6.9 Northridge earthquake. These minima are accompanied by minima of the exponent α of the Detrended Fluctuation Analysis (DFA) of the earthquake magnitude time series, which since α < 0.5 indicate anticorrelated behavior. These results of DFA alone cannot serve for prediction purposes, but do so when combined with the aforementioned minima in the fluctuations of the order parameter of seismicity identified in natural time analysis.

Changes in representativity of the earthquake catalogue for Greece in time and space

The representativity of the earthquake catalogue for Greece for the period of 1964–2010 was studied. The studies were aimed at finding the homogeneous event groups and obtaining the homogeneous earthquake time series. Representative magnitude values were estimated in various parts of the region in different time intervals. The investigated catalogue was revealed to be characterized by significant space and time heterogeneity that should be taken into account when making studies of seismicity regularities. A wrong earthquake representativity threshold can crucially distort the estimations of seismicity parameters. Underestimation of the representativity threshold by 0.3–0.5 units of magnitude relative to a real value can result in understatement of most earthquakes included in a selected group.

Universal relation between skewness and kurtosis in complex dynamics

We identify an important correlation between skewness and kurtosis for a broad class of complex dynamic systems and present a specific analysis of earthquake and financial time series. Two regimes of non-Gaussianity can be identified: a parabolic one, which is common in various fields of physics, and a power law one, with exponent 4/3, which at the moment appears to be specific of earthquakes and financial markets. For this property we propose a model and an interpretation in terms of very rare events dominating the statistics independently on the nature of the events considered. The predicted scaling relation between skewness and kurtosis matches very well the experimental pattern of the second regime. Regarding price fluctuations, this situation characterizes a universal stylized fact.

The Frequency Distribution of Inter-Event Times of M ≥ 3 Earthquakes in the Taipei Metropolitan Area: 1973 - 2010

M ≥ 3 earthquakes which occurred in the Taipei Metropolitan Area from 1973 through 2010 are used to study seismicity of the area. First, the epicentral distribution, depth distribution, and temporal sequences of earthquake magnitudes are described. The earthquakes can be divided into two groups: one for shallow events with focal depths ranging 0 - 40 km and the other with focal depths deeper than 60 km. Shallow earthquakes are mainly located in the depth range from 0 - 10 km north of 25.1°N, and down to 35 km for those south of 25.1°N. Deep events are located in the subduction zone, with a dip angle of about 70°. Three statistical models, the gamma, power-law, and exponential functions, are applied to describe the single frequency distribution of inter-occurrence times between two consecutive events for both shallow and deep earthquakes. Numerical tests suggest that the most appropriate time interval for counting the frequency of events for statistical analysis is 10 days. Results show that among the three functions, the power-law function is the most appropriate for describing the data points. While the exponential function is the least appropriate to describe the observations, thus, the time series of earthquakes in consideration are not Poissonian. The gamma function is less and more appropriate to describe the observations than the power-law function and the exponential function, respectively. The scaling exponent of the power-law function decreases linearly with an increasingly lower-bound magnitude. The slope value of the regression equation is smaller for shallow earthquakes than for deep events. Meanwhile, the power-law function cannot work when the lower-bound magnitude is 4.2 for shallow earthquakes and 4.3 for deep events.

Study on Techniques of Earthquake Prediction

An event called prediction in a time series is more important for geophysics and economy problems. The time series data mining is a combination field of time series and data mining techniques. The historical data are collected which has follow the time series methodology, combine the data mining for preprocessing and finally apply the fuzzy logic rules to predict the impact of earthquake. Earthquake prediction has done by historical earthquake time series to investigating the method at first step ago. Huge data sets are preprocessed using data mining techniques. Based on this process data prediction is possible. This paper is focused on statistics and soft computing techniques to analyze the earthquake data. 1. The Seasonal component 2. The Trend component and 3. The Irregular component The seasonal data are systematic or regular movements of data. The Trend data mean by Long-term fluctuations and the irregular data mean by unsystematic or short-term fluctuations. The major utility area of the time series model is statistical forecasting. The available prediction approaches are regression, time series and chaotic approaches. Each and every method has its own advantage and disadvantage. The historical sequences of data are to be used for forecasting purposes, because of this reason the time series models are used to predict the future values. The prediction will show what will happen but won't why it happens. Time series values are transformed to phase space by using a nonlinear method and then apply the fuzzy logic to predict optimum value. The time series data are derived from the time interval of any system. Traditional stationary time series models are Autoregressive Integrated Moving Average (ARIMA) and Minimum Mean Square Error forecasting methods. Data mining is used to extract useful and more relevant information from the huge database. The author Han describes an artificial intelligence and pattern recognition methods for prediction (7). The time series data mining is used for prediction of earthquake (5). Fuzzy logic methods are used to predict the earthquake, stock market changes, weather forecasting and gold price changes. The similarities of patterns are selected as a fuzzy set; these sets are specified in membership function. The fuzzy logic is accurately predicted the prediction event. The concepts of time series data mining had been used for clustering and natural event prediction. Povinelli, (8) suggested an application for the event prediction. In their study, they focus the different applications such as earthquake prediction, fall of stock price and gold price prediction. The major advantage of time series is possible to predict the future value based on the previous historical data. The study of the past sequence of historical data may be more valuable. The time series is helpful to predict the next sequence of future values. The utility of time series method is specifically for Trend analysis, Trade market, Finance, Climatologic and earthquake prediction.

Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures

We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activity.

The Gumbel hypothesis test for left censored observations using regional earthquake records as an example

Abstract. Annual maximum (AM) time series are incomplete (i.e., censored) when no events are included above the assumed censoring threshold (i.e., magnitude of completeness). We introduce a distrtibutional hypothesis test for left-censored Gumbel observations based on the probability plot correlation coefficient (PPCC). Critical values of the PPCC hypothesis test statistic are computed from Monte-Carlo simulations and are a function of sample size, censoring level, and significance level. When applied to a global catalog of earthquake observations, the left-censored Gumbel PPCC tests are unable to reject the Gumbel hypothesis for 45 of 46 seismic regions. We apply four different field significance tests for combining individual tests into a collective hypothesis test. None of the field significance tests are able to reject the global hypothesis that AM earthquake magnitudes arise from a Gumbel distribution. Because the field significance levels are not conclusive, we also compute the likelihood that these field significance tests are unable to reject the Gumbel model when the samples arise from a more complex distributional alternative. A power study documents that the censored Gumbel PPCC test is unable to reject some important and viable Generalized Extreme Value (GEV) alternatives. Thus, we cannot rule out the possibility that the global AM earthquake time series could arise from a GEV distribution with a finite upper bound, also known as a reverse Weibull distribution. Our power study also indicates that the binomial and uniform field significance tests are substantially more powerful than the more commonly used Bonferonni and false discovery rate multiple comparison procedures.

Search for Technogenic Effects in the Time Series of Earthquakes in Greece

A search for technogenic effects in the time series of earthquakes in Greece is carried out. The ine- quality of intra-week distributions of earthquakes including the events of M ≥ 3.7 is shown. Sharp changes in the pattern of Rayleigh-Schuster’s hodograph for the diurnal periodicity of earthquakes were revealed. They are located in the time vicinity of the moments of the equinox. The result supports the idea of the natural gen- esis of the diurnal periodicity of earthquakes and the important role of the Sun.

Diurnal periodicity of earthquakes and its seasonal variations

Analysis of earthquake catalogues on 14 world regions has revealed a distinct diurnal periodicity of seismic events in all of them. The amplitude of the diurnal variations usually decreases with an increase in earthquake energy, although in some regions, the time series of strong earthquakes also demonstrate diurnal periodicity. Earthquakes are more frequent at night. The acrophase of the course of diurnal seismicity correlates with geographic longitude. The Rayleigh — Schuster hodographs of diurnal periodicity demonstrate sharp changes (kinks) in the vicinity of the equinox and solstice moments. The annual hodograph of the diurnal periodicity of earthquakes is distinctly divided by the equinox moments into segments with different slopes. The defined segments differ in the amplitude and acrophase of the course of diurnal seismicity. The data imply influence of the mutual positions of the Sun and Earth on seismicity in different world regions. Possible mechanisms responsible for such influence are discussed.

GLOBAL LOW DIMENSIONAL SEISMIC CHAOS IN THE HELLENIC REGION

In this study, we present results concerning seismogenesis in the Hellenic region (land and sea of Greece), applying nonlinear analysis to an earthquake time series. The model of the dripping faucet is used as a physical interpretation of the seismic process and the construction of inter-event seismic time series. Geometrical and dynamical characteristics estimated in the reconstructed state space support the low dimensional, chaotic character of the global seismic process in the Hellenic region. The method of stochastic surrogate data was employed to the exclusion of "pseudo chaos" caused by the nonlinear distortion of a purely stochastic process. These results are in agreement with general theoretical models concerning distributed driven threshold dynamics applied to the case of seismic processes. Moreover, the observed global character of low dimensionality and chaoticity over such a complex system of faults supports the hypothesis that seismogenesis is characterized by spatiotemporal intermittent chaos throughout the Hellenic region.

Features of earthquake occurrence in a complex normal fault network: Results from a synthetic seismicity model of the Taupo Rift, New Zealand

The Taupo Rift in the central North Island of New Zealand is a region of active extension of up to 15 mm/yr in the back‐arc of the Hikurangi subduction system. Mapping and trenching has defined a network of active normal faults. Because the paleoseismic and historical earthquake catalogs are short and inhomogeneous, a deterministic computer model of seismicity has been constructed to better understand the earthquake history. The model consists of 26 primary normal fault segments (corresponding to mapped faults with vertical displacement rates of ∼0.1–1.6 mm/yr) and 4700 randomly distributed small normal faults in a ∼40 × 25 km area. All of the model faults interact elastically. Parameters of the model are adjusted to reproduce the geologically observed displacement rates, a regional b value of ∼1.0, and average slip/event of ∼1 m. The result is a long catalog of 500,000 events, magnitude 3.82 to 6.62, which simulates a time period of ∼2 Myr. Characteristic slip events on each segment are mostly well defined and their recurrence times can usually be described by a three parameter Weibull distribution. The coefficient of variation (CV) for recurrence intervals ranges from 0.12 to 1.22 with an average of 0.66; these reduce by about half if fault interactions are turned off. The time series of characteristic earthquakes shows clear evidence of triggered slip up to about 3 years after large magnitude events, followed by relative seismic quiescence. On all segments the moment release rate is relatively stable over time periods of more than about five recurrence intervals (∼2–20 kyr) but can vary on time scales less than that.

Diurnial periodicity of strong earthquakes of Garm research area

The diurnial periodicity of Garm Polygon earthquakes of various energy classes K [(magnitudes M): weak, K 8.0 (M > 2.2)] has been studied. The time series of weak earthquakes is characterized by maximum activity at night and a clear diurnal periodicity that practically disappears for moderate earthquakes. Such periodicity can be traced again in the time series of the strong earthquakes practically antiphased to weak earthquakes; i.e., the maximum strong earthquakes occurred during the day time.

Correlated earthquakes in a self-organized model

Abstract. Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of scale-invariance. It is an avalanching process that displays power-laws in the event sizes, in the epicenter distances as well as in the waiting-time distributions, and also aftershock rates obeying a generalized Omori law. We thus confirm that there is a relation between temporal and spatial clustering of the activity in this kind of models. The fluctuating boundaries of possible slipping areas show that the size of the largest possible earthquake is not always maximal, and the average correlation length is a fraction of the system size. This suggests that there is a concrete alternative to the extreme interpretation of self-organized criticality as a process in which every small event can cascade to an arbitrary large one: the new picture includes fluctuating domains of coherent stress field as part of the global self-organization. Moreover, this picture can be more easily compared with other scenarios discussing fluctuating correlations lengths in seismicity.