Earthquake Time Series Research Articles

DETERMINATION OF DESIGN EARTHQUAKES IN SEISMIC HAZARD ANALYSIS THROUGH MONTE CARLO SIMULATION

A method is demonstrated using Monte Carlo simulation (stochastic modelling) techniques that allows the extraction of information about design earthquakes that constitute the most likely combinations of earthquake magnitude/epicentral distance that would actually generate the computed hazard ground motion at a site of interest, taking into account the log-normal scatter in the attenuation relationship. A worked example, at three different return periods, is shown for a realistic case in Greece. The results demonstrate the range of events that may contribute to the hazard, from which median or modal values can be derived. This method should be very useful in cases where it is desired to select earthquake time series representing the hazard for engineering analyses. In the example shown, the most probable magnitude/distance pairs are those that would produce predicted deterministic acceleration values of about half the design ground motion.

A physical mechanism for temporal variation in seismicity in Southwest Japan related to the great interplate earthquakes along the Nankai trough

A significant correlation has been reported between the intraplate (inland) and the great interplate earthquakes in Southwest Japan, based on historical earthquake data since 868. The frequency of intraplate earthquakes is high for several decades before and up to a decade after great interplate earthquakes. To explain the correlation, we treated two types of interaction between the inland faults and the plate boundary: (a) in which the stress changes caused by great interplate earthquakes affect the occurrence of intraplate earthquakes; and (b) in which the stress changes caused by intraplate earthquakes trigger other intraplate earthquakes and great interplate earthquakes. To simulate the sequences of these earthquakes, we calculated the static stress changes resulting from large intraplate and great interplate earthquakes and also estimate the rate of increase in tectonic stress on the faults and the plate boundary. The estimated rates of increase here are smaller than those used in previous studies. Thus, in our models, stress changes could more strongly affect the seismicity than previously considered. We simulated the earthquake sequences for our models in four cases: (i) with no interaction among the inland faults in Southwest Japan and the plate boundary along the Nankai trough; (ii) with stress changes on the inland faults caused only by great interplate earthquakes; (iii) with stress changes on the plate boundary caused only by large intraplate earthquakes; and (iv) with stress changes both on the inland faults and on the plate boundary caused by large intraplate earthquakes. The simulated time series in case (i), of course, shows no correlation between intraplate and great interplate earthquakes. Those in cases (iii) and (iv) also show no significant correlation. Only the time series of intraplate earthquakes in case (ii) shows a temporal variation similar to that of the real intraplate earthquakes before and after the great interplate earthquakes. We examined statistically the similarity between the simulated time series and the real earthquake data. About 40% of the time series in case (ii) are significantly similar, although in the other three cases less than 5% of the time series are. Understanding of the effects of stress changes on the inland faults caused by the great interplate earthquakes along the Nankai trough is essential to explain the temporal variation in seismicity in Southwest Japan before and after the great interplate earthquakes.

On the frequency distribution of interoccurrence times of earthquakes

The distributions of discrete frequency, N, versus interoccurrence time, t (in days), of M ≥ 7 earthquakes in the Taiwan region during the 1900–1994 period, M ≥ 6 earthquakes in the north-south seismic belt of China during the 1900–1990 period, and M ≥ 5.5 earthquakes in Southern California, U.S.A., during the 1914–1995 period are studied through two statistical models (gamma function and exponential function). Results show that both the exponential function and gamma function can describe the distributions. However, the former is more appropriate than the latter. This indicates that the three time series of earthquakes have a significant component of Poisson processes, even though the tectonic conditions, the fault distributions and the size of the three seismic regions are different.

Multifractal Measures of Time Series of Earthquakes.

The generalized fractal dimensions are measured for the time series based on two complete earthquake catalogues: one with M≥6 earthquakes occurring in the north-south seismic belt of mainland China during the 1900-1990 period published by Ma et al. (1992) and the other with M≥5.5 earthquakes occurring in southern California, USA during the 1915-1994 period compiled by Press and Allen (1995). The log-log plot of Cq versus t, where Cq(t) is the generalized correlation integral and t is the interoccurrence time in years between two events, at positive q shows a linear istribution when t<tc. Dq is the slope of this linear portion. The value of tc decreases from 50.1 to 39.8 years for Chinese earthquakes and from 50.1 to 31.6 years for southern California events as q is increased from 0 to 15. For M≥6 Chinese earthquakes, the well-distributed, monotonically decreasing function of Dq, with increasing q would imply that such earthquakes have formed a multifractal time series. In contrast, the M≥5.5 southern California earthquakes might have not yet formed a complete multifractal time series or the number of these events is too small to accurately estimate the multifractal dimensions, especially for large qs. Different degrees of complexity of fault distributions in the two seismic regions might also be a factor in causing the difference in the Dq-q relations. In addition, the results also suggest that a Dq-q relation is better than the first three commonly-used values of Dq to completely represent a multifractal time series.

Basic principles for evaluating an earthquake prediction method

A three year continuous sample of earthquake predictions based on the observation of Seismic Electric Signals in Greece was published by Varotsos and Lazaridou [1991]. Four independent studies analyzed this sample and concluded that the success rate of the predictions is far beyond chance. On the other hand, Mulargia and Gasperini [1992] (hereafter cited as MG) claim that these predictions can be ascribed to chance. In the present paper we examine the origin of this disagreement. Several serious problems in the study of MG are pointed out, such as: 1. The probability of a prediction's being successful by chance should be approximately considered as the product of three probabilities, PT, PE and PM, i.e., the probabilities with respect to time, epicenter and magnitude. In spite of their major importance, PE and PM were ignored by MG. The incorporation of PE decreases the probability for chancy success by more than a factor of 10 (when PE is taken into account it can be shown that the VAN predictions cannot be ascribed to chance). 2. MG grossly overestimated the number of earthquakes that should have been predicted, by taking different thresholds for earthquakes and predictions. With such an overestimation, MG's procedure can “reject” even an ideally perfect earthquake prediction method. 3. MG's procedure did not take into account that the predictions were based on three different types of electrical precursors with different lead‐times. 4. MG applied a Poisson distribution to the time series of earthquakes but included a large number of aftershocks. 5. The backward time correlation between predictions and earthquakes claimed by MG is due to misinterpretation of the text of some predictions and an incorrect use of aftershocks. Although even the discussion of the first problem alone is enough to invalidate the claims of MG, we also discuss the other four problems because MG violated some basic principles even in the time domain alone. The results derived in this paper are of general use when examining whether a correlation between earthquakes and various geophysical phenomena is beyond chance or not.

Liquefaction under Random Loading: Unit Energy Approach

Liquefaction triggered by earthquakes is a source of major damage to structures resting on loose to medium sandy soils. The use of energy levels to define the onset of liquefaction has been validated in a previous study involving sinusoidal excitations. The present investigation extends the use of the energy concept to the kind of random excitations present in an earthquake time series. Tests conducted on sand specimens under several confining pressures and at different relative densities support this approach, which provides a solid and suitable link between laboratory and field behavior.

Self-affine fractal features of earthquake time series before and after moderate earthquakes

In this paper we calculate the local fractal dimension valuesD of the self-affine feature of earthquake time series by RMS (root-mean-square) error method, and express the fractal dimensionality by the normalized correlation coefficientR. The fractal dimension values are given for earthquakes occurred in Tangshan, Haicheng, Songpan, Longling, Changshu, Liyang in China and its vicinity by the moving scanning method with different magnitude thresholds and the fixed-window length (100 events). The results show theD values are characterized by decreasing, continued low level in values or by decreasing first and then increasing before moderate earthquakes.

CHAOTIC ANALYSIS OF A TIME SERIES COMPOSED OF SEISMIC EVENTS RECORDED IN JAPAN

A chaotic analysis approach was applied to an earthquake time series recorded in the Japanese area in order to test the assumption that the earthquake process could be the manifestation of a chaotic low dimensional process. For the study of the seismicity we have used a time series consisting of time differences between two consecutive seismic events with magnitudes greater than 2.6. The results of our study show that the underlying mechanism, as expressed by the time series, can be described by low dimensional chaotic dynamics. The power spectrum of the time series shows a power law profile with two slopes, α=1.4 in the low frequency and α=0.05 in the high frequency regions, while the slopes of the correlation integrals show an apparent plateau at the scaling region, which saturates at the value D≈3.2. The largest Lyapunov exponent was found to be ≈0.9. The positive value of the largest Lyapunov exponent reveals strong sensitivity to initial conditions of the supposed earthquake dynamics.

A non-stationary Poisson model of long term seismicity in Northern China

In the fifties and sixties, after investigating the worldwide and local catalogues respectively, Aki and Knopoff found that the time series of earthquakes were non-Poissonian even if with aftershocks excluded. At that time it was of importance in earthquake prediction because the nonrandomness in earthquake series gave rise to the hope that some useful message for predicting earthquake risk in the future. In the end of the sixties the probabilistic method was introduced into the assessment of seismic hazard at a site, it became possible to estimate the seismic risk even if the earthquakes happen randomly. Thereafter it is reportedly found that the time series of mainshocks with aftershocks removed are Poissonian. It is worth mentioned that some criterions for a stationary Poisson distribution in the reports are only necessary, not sufficient.

On the analysis of self-similarity of earthquake sequence and its application in earthquake prediction

This paper has introduced the method of self-similarity analysis of time series into the analysis and study of earthquake sequence, and then researched its application in earthquake prediction. As parameter of earthquake time series, we can take the cumulated sum of the numbers of equivalent earthquakesQ=ΣN*, the numbers of equivalent earthquakeN*, maximum magnitudeM max, average magnitudeQ=ΣN*, and the difference ΔN* between the numbersN* in two adjacent time intervals. The given method may be applied to analysis of long-period seismic sequences in different regions as well as to anlysis of seismic sequence in the aftershock region of strong earthquake. For making quantitative analysis the coefficient of self-similarity of earthquake sequence in order of timeμs was introduced. The results of self-similarity analysis were obtained for the earthquake sequences in North China, West South China, the Capital region of China, and for the East Yamashi region of Japan. They show that in period or half year to several years beforeM⩾7.0 andM⩾6.0 earthquakes occurred in these regions separately, the self-similarity coefficientμs calculated by using the above-mentioned parameters had remarkably anamalous decrease variations. The duration time ofμs anomaly depends on the earthquake magnitude and may be different from different regions. Therefore, the self-similarity coefficient in order of timeμs can be considered as a long-medium term precursory index.

On some problems about testing stochastic models of the earthquake time series

Decision on whether or not a specific stochastic model is an adequate description of the earthquake time series depends on (a) the characteristics of the earthquake sample (total time interval, magnitude range, inclusion or not of dependent events) and (b) the selection of counting interval,τ, which seems to be of crucial importance. Certain improvements are proposed for handling earthquake samples when tested against stochastic models. Particularly, it is proposed thatτ should be nonarbitrarily selected as equal to the mean return period of events of magnitude equal to or larger than the lower magnitude,Mmin, for which the data are complete. A methodological experiment has been performed using three data sets of South Aegean intermediate depth main shocks of variableMmin. It is clear that the distribution gradually approaches the simple Poisson model as the counting interval decreasingly approaches a nonarbitrarily selected value, which indicates the important misleading effect of using arbitrarily selected counting intervals. The efficiency of the proposed improvements in stochastic modelling of volcanic eruption and tsunami time series is discussed.

Poissonian and negative binomial modelling of earthquake time series in the Aegean area

The time distribution of mainshocks listed in 25 data sets, covering several magnitude classes, time intervals and seismotectonic segments of the Aegean area, has been tested against the Poisson and negative binomial (Pascal) theoretical models. In each χ 2 test we make the null hypothesis of fit by a Poisson or Pascal distribution at the 5% and 1% significance levels. In each test the counting interval is non-arbitrarily selected as equal to the mean return period, T m , of earthquakes of magnitude equal to or larger than the minimum magnitude in the earthquake sample. Values of T m have been calculated from magnitude-frequency relationships determined by linear regression analysis. Twenty-two earthquake data sets are successfully modelled by the Poisson process at both the 5% and 1% levels. In contrast, only six sets are successfully modelled by the Pascal distribution. The results clearly indicate that the occurrence of earthquake mainshocks in the Aegean is stationary and random with respect to time regardless of the segment, time interval and magnitude class considered. A short review of earlier similar studies shows that contradictory results were obtained, which may be the result of several methodological problems. The most important problem seems to be the arbitrary selection of counting intervals when tests are performed. The degree of crustal heterogeneity, which varies from place to place, may provide a physical basis for explanation of earthquake time modelling and for the contradictions in earlier results.

Is a destructive earthquake imminent in southeastern Sicily?

Southeastern Sicily, which has frequently experienced ruinous earthquakes in historic times, has only been site of minor activity in the last two centuries. Two precision levelling surveys that we carried out in 1983 and 1989 detected high rates of crustal deformation. The usual hypothesis of tectonic stationarity applied to both the time series of historical earthquakes and deformation rates would favour the imminence of an I ⩾ IX event. On the other hand, the characteristic patterns of recent seismicity strongly oppose this conclusion, suggesting that the apparent contradiction is caused by a tectonic nonstationarity, an issue that seems also confirmed by palaeogeodetic data.

An analysis of the earthquake time series at Mount St. Helens, Washington, in the framework of recent volcanic activity

The analysis of the earthquake time distribution at Mount St. Helens reveals a good correlation between the physical state of the volcano and statistical parameters of earthquake sequence. There are three main seismic phases in the whole 1980–1986 period. The first one precedes the main eruption of May 18, 1980. It begins with a sudden increase of the seismicity level in late March and continues with an Utsu (1961) type decay of the seismic occurrence rate, characterized by a small value of the decay coefficient, β. The second phase lasts from the cataclysmic eruption on May 18, 1980 until the continuous dome building episode in 1983 and is characterized by a very slow exponential increase of the background level of seismicity. The third phase covers the remaining part of the sample and is characterized by a stationary earthquake clustering process episodically interrupted by peaks of activity related to eruptions. The trends in seismic occurrence rate within each phase, as well as the statistical parameter variations at each transition, are analyzed and discussed in the framework of volcanic activity. This leads to the conclusion that statistical techniques may give a significant contribution in understanding changes in volcanic processes such as those at Mount St. Helens.

Long-term Cyclicities in Earthquake Energy Release and Major River Flow Volumes in Virginia and Missouri Seismic Zones

Abstract We have investigated the time series for earthquake strain energy releases and flow volumes for the major rivers that bisect the regions of seismicity in Virginia (Giles County; central Virginia) and Missouri (New Madrid) seismic zones. Our procedure is to integrate with respect to time over data lengths up to 70 years duration and then to subtract a least squares straight-line fit. The resulting residual earthquake and flow volume time series and their spectral densities both exhibit dominant periods in the 20–30 year range. These common cyclities lend support for an important role of water in intraplate seismogenesis. The fracture permeability of crystalline rocks, caused by a long history of compressional and extensional tectonic episodes, together with the driving potential supplied by long-term cyclical variations in streamflow, can result in the diffusion of fluid pressure transients to focal depths as deep as 20 km. At those depths there is also present a quasi-static, hydrolytic weakening effect of water on asperities present in the fault zones. This combination of mechanical and chemical effects can cause intraplate earthquakes in highly-stressed crustal volumes.

Simulation of earthquake ground motions using autoregressive moving average (ARMA) models

AbstractParsimonious representations of recorded earthquake acceleration time series are obtained by fitting stationary autoregressive moving average models after a variance‐stabilizing transformation. Simulated acceleration series are then constructed by generating realizations from the fitted stationary models and applying the reverse transformation. As demonstrated on three components of a typical series, the response spectra for the observed and simulated series show good agreement for periods of less than eight seconds. Further, the model parameters for the three components are very similar, suggesting a consistency which could be useful for identifying site‐specific characteristics.

POSSIBILITY OF A GREAT EARTHQUAKE IN THE TOKAI DISTRICT, CENTRAL JAPAN

The Tokai district has been considered to be one of the probable sites of great interplate earthquakes in the near future. This idea is based on the time series of historical great earthquakes and the fairly high rate of crustal movement observed in this region for more than 80 years. The last great earthquake was the Ansei earthquake of 1854 (M=8.4). The western half of the source region of this earthquake ruptured again in the 1944 Tonankai earthquake, but the eastern half, i.e., the Tokai district, remain unruptured for 122 years. The recurrence time interval of great earthquakes in this region estimated from historical earthquakes, topographical and geological evidences, observed strain rates, the rate of plate convergence, etc. varies from 120 years to more than 600 years. There are several observations which may suggest that this region has already been in the long-term precursory stage. However, it is questionable that these observations represent real precursors to the future Tokai earthquake. It seems possible that the next great earthquake will occur south of the Izu Peninsula and will release the strain in the Tokai district. In any case, the Tokai district should be watched carefully for every conceivable precursors in order to make a successful prediction.

Evidence for earthquake triggering stress

Earthquake time series are constructed by making counts per unit time of earthquakes with magnitudes greater than a chosen threshold. The time series from widely separated regions show strong correlations with one another, and it is suggested that tectonic plates are subjected to a fluctuating stress field that results in these changes in seismic activity.

Spectra of earthquake time series

An earthquake time series consists of the (possibly weighted) number of events of a given class of earthquakes per unit time as a function of time. The spectrum of a single earthquake time series and the cross spectrum between different series determine the usefulness of past events in predicting future ones. The spectra of earthquakes might also shed light on the possible triggering of earthquakes by such things as tidal potential changes and other earthquakes.Much of the past work on earthquake time series has dealt with seeking significant periodicities in the data. In most cases [Davidson, 1938] significance tests have failed to take into account the correlation between events that result from the aftershock phenomena. In the spectral domain, nonrandom bunching of events due to aftershocks results in a nonwhite spectrum.

Statistical prediction of earthquakes

Statistical prediction is an extension of Fourier spectrum analysis of time series. Historical attempts at prediction of earthquakes have centered on the question of periodicity. A survey of work in this field is given, both preceding and following critical investigations by Jeffreys. Present evidence indicates earthquakes to be uncorrelated events; observed deviations from the Poisson distribution, previously attributed to dependence in time, may be an effect of spatial inhomogeneity. It is fallacious to infer properties of the earthquake process on the basis of the shape of the distribution function of number of events in time. Some restrictions are shown to apply to the use of direct extrapolation methods in earthquake time series. Multiple prediction is a possibility; however, the actual measurement of geophysical variables for prediction purposes has progressed very slowly. Direct measurements of stresses and strains at depth are needed; values based on the theoretical release of strains by earthquakes are insufficient. Plotting the square roots of earthquake energies yields no specific strain information of predictive value. The estimation of earthquake risks is different, in principle, from the prediction problem. Mathematical techniques are available for risk estimation. A simplified model of the earthquake process is suggested, which may satisfy elementary requirements for purposes of engineering, city planning, and earthquake insurance.