Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Appraisal of Seismic Hazard Parameters for the Seismic Regions of the East Circum-Pacific Belt Inferred from a Bayesian Approach

The assessment of seismic hazard parameters is important in the seismically active regions. A straightforward approach is considered for the statistical estimation of the maximum values of earthquake hazard parameters. The Bayesian estimator is suggested and emphasis is given to the evaluation of the maximum possible M_max (regional) magnitude in a future time interval T. This approach allows the uncertainty of earthquake magnitude to be accounted for. Seismic hazard parameters like the -value which is the slope of the magnitude-frequency law (where, b = log_e) and the intensity (rate) of seismic activity and their uncertainties are also estimated. The quantiles of functions of distributions of true and apparent magnitude on a given time interval [0, T] are evaluated, as well. Two main assumptions are adopted for the method:(1) earthquake occurrence is Poissonian and(2) the magnitude-frequency law is of Gutenberg-Richter type with a cutoff maximum value of magnitude. It is needless to say the seismic catalog used must have a large number of events. This requirement leads to the estimation of the parameters referred to some of the most seismically active regions of the world, e.g., Chile, Peru-Equador-South Colombia,Central America and Mexico, which belong to the east part of the circum-Pacific belt.     

Statistics for Modeling Heavy Tailed Distributions in Geology: Part I. Methodology

Many natural phenomena exhibit size distributions that are power laws or power law type distributions. Power laws are specific in the sense that they can exhibit extremely long or heavy tails. The largest event in a sample from such distribution usually dominates the underlying physical or generating process (floods, earthquakes, diamond sizes and values, incomes, insurance). Often, the practitioner is faced with the difficult problem of predicting values far beyond the highest sample value and designing his system either to profit from them, or to protect against extreme quantiles. In this paper, we present a novel approach to estimating such heavy tails. The estimation of tail characteristics such as the extreme value index, extreme quantiles, and percentiles (rare events) is shown to depend primarily on the number of extreme data that are used to model the tail. Because only the most extreme data are useful for studying tails, thresholds must be selected above which the data are modeled as power laws. The mean square error (MSE) is used to select such thresholds. A semiparametric bootstrap method is developed to study estimation bias and variance and to derive confidence limits. A simulation study is performed to assess the accuracy of these confidence limits. The overall methodology is applied to the Harvard Central Moment Tensor catalog of global earthquakes.     

Estimation of earthquake hazard parameters for incomplete and uncertain data files

The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitudem _max, activity rate , and theb parameter in the Gutenberg-Richter distribution) is extended to the cases of incomplete and uncertain data. The method accepts mixed data containing only large (extreme) events and a variable quality of complete data with different threshold magnitude values. Uncertainty of earthquake magnitude is specified by two values, the lower and upper magnitude limits. It is assumed that such an interval contains the real unknown magnitude. The proposed approach allows the combination of different quality catalog parts, e.g. those where the assignment of magnitude is questionable and those with magnitudes precisely determined.As an illustration of the method, the seismic hazard analysis for western Norway and adjacent sea area (4–8°E, 58–64°N) is presented on the basis of the strongest earthquakes felt during the period 1831–1889 and three complete catalog parts, covering the period 1890–1987.Paper presented at the 21st General Assembly of the European Seismological Commission held in Sofia, 1988.On leave from Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland.     

Pathways to seismic hazard evaluation: Extreme and characteristic earthquakes in areas of low and high seismicity

The general philosophy of seismic hazard evaluation described here is appropriate for selection of seismic input to regional earthquake engineering codes prior to detailed on-site inspections and geotechnical assessments. Some probabilistic seismic hazard methodologies which can be applied in areas of low and high seismicity, are briefly described to emphasise the main equations with specimen results. Three aspects of hazard assessment are explored by different pathways. These include the analysis of regional earthquake catalogues to obtain magnitude recurrence, particularly using Gumbel extreme value statistics. This is extended to assess ground shaking hazard which is usually sought by earthquake engineers. Thirdly, the concept of earthquake perceptibility is developed, leading to the identification of an earthquake magnitude or type which is characteristic of a region. This most perceptible earthquake is most likely to be felt at any site in a region and provides an earthquake selection criterion which can be used in aseismic design of noncritical structures. Because there are several methods of seismic hazard evaluation, the view is expressed that it is sensible for practical purposes to seek results from different methods or different pathways to the hazard evaluation.Paper presented at the Commission of the European Communities' School on Earthquake Hazard Evaluation, Athens, and at the 21st General Assembly of the European Seismological Commission, held in Sofia, 1988.Now at School of Environmental Sciences, University of East Anglia, University Plain, Norwich NR4 7TJ, U.K.     

Seismic hazard assessments for two test areas — ‘Southern Italy’ and ‘Belgium—The Netherlands—Germany’

Within the activity of the ESC Subcommission 8 Engineering Seismology, Project TERESA, seismic hazard calculations have been performed for two areas of a different earthquake activity. Fundamental seismological data (earthquake catalogues, macroseismic observations and maps) and some additional geological information were analyzed and processed to prepare inputs for hazard computations. Great attention has been paid to verifying the reliability of the input data. Seismic hazards obtained for five sites of the region of high seismic activity (Sannio-Matese, southern Italy) and six sites of the region of low seismic activity (Brabant Massif and northern Rhine, Belgium—The Netherlands—Germany) are presented and discussed.     

Seismic hazard assessment in Jordan and its vicinity

The earthquake hazard in Jordan and its vicinity is assessed on the basis of probabilistic methods. For this purpose, an updated earthquake catalog is compiled which covers the period between AD 1–1989. The earthquakes lie between latitudes 27.0°-35.5° N and longitudes 32.0°-39.0° E. Thirteen seismic zones are defined on a regional seismic and tectonic map presented for the area. Point-source and line-source models are used. The seismic hazard parameters, namely, theb-parameter (of the Gutenberg-Richter relation),m ₁ (the upper bound magnitude), and ₄ (the annual rate of occurrence of earthquakes with local magnitudeM _L 4.0) are calculated for each zone. The results of the seismic hazard assessment are displayed as iso-acceleration contours expected to be exceeded during typical economic life times of structures, i.e. 50 and 100 years. For each model, two seismic hazard maps are derived. In order to determine the importance of the South-eastern Mediterranean zone and the north part of the Red Sea zone from a seismic hazard point of view for Jordan, one seismic hazard map which corresponds to 50 years' economic life for every model, excluding the seismicity of these zones, is derived.     

Short Term and Short Range Seismicity Patterns in Different Seismic Areas of the World

The aim of this work is to quantitatively set up a simple hypothesis for occurrence of earthquakes conditioned by prior events, on the basis of a previously existing model and the use of recent instrumental observations. A simple procedure is presented in order to determine the conditional probability of pairs of events (foreshock-mainshock, mainshock-aftershock) with short time and space separation. The first event of a pair should not be an aftershock, i.e., it must not be related to a stronger previous event. The Italian earthquake catalog of the Istituto Nazionale di Geofisica (ING) (1975–1995, M 3.4), the earthquake catalog of the Japan Meteorological Agency (JMA) (1983–1994, M 3.0) and that of the National Observatory of Athens (NOA) (1982–1994, M 3.8) were analyzed. The number of observed pairs depends on several parameters: the size of the space-time quiescence volume defining nonaftershocks, the inter event time, the minimum magnitude of the two events, and the spatial dimension of the alarm volume after the first event. The Akaike information criterion has been adopted to assess the optimum set of space-time parameters used in the definition of the pairs, assuming that the occurrence rate of subsequent events may be modeled by two Poisson processes with different rates: the higher rate refers to the space-time volume defined by the alarms and the lower one simulates earthquakes that occur in the nonalarm space-time volume. On the basis of the tests carried out on the seismic catalog of Italy, the occurrence rate of M 3.8 earthquakes followed by a M 3.8 mainshock within 10 km and 10 days (validity) is 0.459. We have observed, for all three catalogs, that the occurrence rate density for the second event of a couple (mainshock or aftershock) of magnitude M₂ subsequent to a nonaftershock of magnitude M₁ in the time range T can be modeled by the following relationship: (T, M₂) = 10^{a + b(M1 - M2)} with b varying from 0.74 (Japan) to 1.09 (Greece). The decrease of the occurrence rate in time for a mainshock after a foreshock or for large aftershocks after a mainshock, for all three databases, obeys the Omori's law with p changing from 0.94 (Italy) to 2.0 (Greece).     

Probabilistic seismic hazard maps for Panama

Probabilistic seismic hazard maps in term of Modified Mercalli (MM) intensity are derived by applying the Cornell-McGuire method to four earthquake source zones in Panama and adjacent areas. The maps contain estimates of the maximum MM intensity for return periods of 5, 25 and 100 yr. The earthquake phenomenon is based on the point source model. The probabilistic iso-intensity map for a return period of 50 yr indicates that the Panama Suture Zone (PSZ) could experience a maximum (MM) intensity IX, and the Panama Fracture Zone (PFZ) an MM intensity VIII, for the rest of the area this varies from IV up to VIII. The present study intends to serve as a reference for more advanced approaches, to stimulate discussions and suggestions on the data base, assumptions and inputs, and path for the risk based assessment of the seismic hazard in the site selection and in the design of common buildings and engineering.     

Effect of Aftershocks on Earthquake Hazard Estimation: An Example from the North Anatolian Fault Zone

In order to investigate the effect of aftershocks on earthquake hazard estimation, earthquake hazard parameters (_m, b and M_max) have been estimated by the maximum likelihood method from the main shocks catalogue and the raw earthquakes catalogue for the North Anatolian Fault Zone (NAFZ). The main shocks catalogue has been compiled from the raw earthquake catalogue by eliminating the aftershocks using the window method. The raw earthquake catalogue consisted of instrumentally detected earthquakes between 1900 and 1992, and historical earthquakes that occurred between 1000–1900. For the events of the mainshock catalogue the Poisson process is valid and for the raw earthquake catalogue it does not fit. The paper demonstrates differences in the hazard outputs if on one hand the main catalogues and on the other hand the raw catalogue is used. The maximum likelihood method which allows the use of the mixed earthquake catalogue containing incomplete (historical) and complete (instrumental) earthquake data is used to determine the earthquake hazard parameters. The maximum regional magnitude (M_max, the seismic activity rate (_m), the mean return period (R) and the b value of the magnitude-frequency relation have been estimated for the 24°–31° E, 31°–41° E, 41°–45° E sections of the North Anatolian Fault Zone from the raw earthquake catalogue and the main shocks catalogue. Our results indicate that inclusion of aftershocks changes the b value and the seismic activity rate _m depending on the proportion of aftershocks in a region while it does not significantly effect the value of the maximum regional magnitude since it is related to the maximum observed magnitude. These changes in the earthquake hazard parameters caused the return periods to be over- and underestimated for smaller and larger events, respectively.     

Spatial-temporal variability of seismic hazard in peninsular India

This paper examines the variability of seismic activity observed in the case of different geological zones of peninsular India (10°N–26°N; 68°E–90°E) based on earthquake catalog between the period 1842 and 2002 and estimates earthquake hazard for the region. With compilation of earthquake catalog in terms of moment magnitude and establishing broad completeness criteria, we derive the seismicity parameters for each geologic zone of peninsular India using maximum likelihood procedure. The estimated parameters provide the basis for understanding the historical seismicity associated with different geological zones of peninsular India and also provide important inputs for future seismic hazard estimation studies in the region. Based on present investigation, it is clear that earthquake recurrence activity in various geologic zones of peninsular India is distinct and varies considerably between its cratonic and rifting zones. The study identifies the likely hazards due to the possibility of moderate to large earthquakes in peninsular India and also presents the influence of spatial rate variation in the seismic activity of this region. This paper presents the influence of source zone characterization and recurrence rate variation pattern on the maximum earthquake magnitude estimation. The results presented in the paper provide a useful basis for probabilistic seismic hazard studies and microzonation studies in peninsular India.     

Seismic hazard maps for Jordan and vicinity

Probabilistic methods are used to quantify the seismic hazard in Jordan and neighbouring regions. The hazard model incorporates the uncertainties associated with the seismicity parameters and the attenuation equation. Seven seismic sources are identified in the region and the seismicity parameters of these sources are estimated by making use of all the available information. Seismic hazard computations and the selection of peak ground acceleration and modified Mercalli intensity values at the nodes of a 25 × 25 km mesh covering the region under study are carried out by two different computer programs.The results of the study are presented through a set of seismic hazard maps displaying iso-acceleration and iso-intensity contours corresponding to specified return periods. The first set of maps is derived based on the seismicity data assessed in this study and display our best estimate of the seismic hazard for Jordan and the neighbouring areas. The second set of maps which shows the alternative estimate of seismic hazard is based solely on the seismicity parameters reported by other researchers. The third set of maps, called the Bayesian estimate of seismic hazard, reflects the influence of expert opinion involving more conservative assumptions regarding the Red Sea and Araba faults.     

A Systematic Test on Precursory Seismic Quiescence in Armenia

A systematic test on seismic quiescence occurring before largeearthquakes is conducted. For a fixed geographical location, the degree ofclustering in space and time is analysed and the results are testedagainst randomized earthquake catalogs.A gridding technique allows to investigate the entirespatial volume covered by a certain earthquake catalog. The result is a significance K(x,t) for seismic quiescence as a function ofspace and time. A point (x,t) is considered as quiet, if K(x,t) exceeds a threshold value K⁽⁹⁹⁾ such that the nullhypothesis is rejected with a probability of p 99%. Becauseearthquake clusters, like aftershocks and swarm events, generateerroneous quiescence, declustered catalogs are also investigated andthe influence of the clusters is discussed.Applying this method to an earthquake catalog from Armenia,several cases of seismic quiescence before mainshocks are obtained.These quiescence periods occur in the originaldata as well as in the declustered data. Using alarm conditions, itis found that quiescence periods and mainshocks are correlated`better-than-chance'. Thus, the results support the claim thatseismic quiescence makes a contribution to the improvement of seismichazard assessment.     

Estimation of earthquake hazard parameters for incomplete and uncertain data files

The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitudem _max, activity rate λ, and theb parameter in the Gutenberg-Richter distribution) is extended to the cases of incomplete and uncertain data. The method accepts mixed data containing only large (extreme) events and a variable quality of complete data with different threshold magnitude values. Uncertainty of earthquake magnitude is specified by two values, the lower and upper magnitude limits. It is assumed that such an interval contains the real unknown magnitude. The proposed approach allows the combination of different quality catalog parts, e.g. those where the assignment of magnitude is questionable and those with magnitudes precisely determined. As an illustration of the method, the seismic hazard analysis for western Norway and adjacent sea area (4–8°E, 58–64°N) is presented on the basis of the strongest earthquakes felt during the period 1831–1889 and three complete catalog parts, covering the period 1890–1987.     

Seismic Hazard for Selected Sites in Greece: A Bayesian Estimate of Seismic Peak Ground Acceleration

A procedure for estimating maximum values of seismic peak ground accelerationat the examined site and quantiles of its probabilistic distribution in a future timeinterval of a given length is considered. The input information for the method areseismic catalog and regression relation between peak seismic acceleration at a givenpoint and magnitude and distance from the site to epicenter (seismic attenuation law).The method is based on Bayesian approach, which simply accounts for influenceof uncertainties of seismic acceleration values. The main assumptions for the method are Poissonian character of seismic events flow and distribution law of Gutenberg-Richter's type. The method is applied to seismic hazard estimation in six selected sitesin Greece.     

Evaluating of the earthquake hazard parameters with Bayesian method for the different seismic source regions of the North Anatolian Fault Zone

The earthquake hazard parameters and earthquake occurrence probabilities are computed for the different regions of the North Anatolia Fault Zone (NAFZ) using Bayesian method. A homogenous earthquake catalog for M _S magnitude which is equal or larger than 4.0 is used for a time period between 1900 and 2015. Only two historical earthquakes (1766, M _S = 7. 3 and 1897, M _S = 7. 0) are included in Region 2 (Marmara Region) where a large earthquake is expected in the near future since no large earthquake has been observed for the instrumental period. In order to evaluate earthquake hazard parameters for next 5, 10, 20, 50, 100 years, M _max (maximum regional magnitude), β value, λ (seismic activity or density) are computed for the different regions of NAFZ. The computed M _max values are changed between 7.11 and 7.89. While the highest magnitude value is calculated in the Region 9 related to Tokat-Erzincan, the lowest value in the Region 10 including the eastern of Erzincan. The “quantiles” of “apparent” and “true” magnitudes of future time intervals of 5, 10, 20, 50, and 100 years are calculated for confidence limits of probability levels of 50, 70 and 90 % of the 10 different seismic source regions. The region between Tokat and Erzincan has earthquake hazard level according to the determined parameters. In this region the expected maximum earthquake size is 7.8 with 90 % occurrence probability in next 100 years. While the regional M _max value of Marmara Region is computed as 7.61, expected maximum earthquake size is 7.37 with 90 % occurrence probability in next 100 years.     

Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

Assessment of tsunami hazard in the Italian seas

A method for the evaluation of tsunami potential in the seas surrounding Italy is presented. A major difficulty for performing reliable estimates of tsunami occurrence is that the existing tsunami catalog for Italy includes a small number of cases. This is due partly to the catalog incompleteness, strangely more pronounced in our century, and partly to the relative infrequency of tsunamis along the Italian seas. Evaluation of tsunami activity is therefore deduced by complementing the tsunami catalog data with data on seismicity that are by far more abundant and reliable. Analysis of seismicity and assessment of earthquake rate in coastal and submarine regions form the basis of the present method to perform tsunami potential estimates for Italy. One essential limitation of the method is that only tsunamis of seismic origin are taken into account, which leads to an underestimation of the tsunami potential. Since tsunamis generated by earthquakes are much more frequent than events produced by slumps or volcanic eruptions, the underestimation is not dramatic and very likely affects only a limited portion of the Italian coasts. In the present application of the method, eight separate regions have been considered that together cover all the coasts of Italy. In each region, seismicity has been independently examined and the earthquake potential has been calculated in small 20 × 20 cells. Then, on the basis of suitable assumptions, tsunami potential has been evaluated in each cell. According to this study, the Italian coasts that are the most exposed to the attacks of locally generated tsunamis are to be found in the Messina Straits, in Tyrrhenian coasts of Calabria, in the Ionian Sicilian coasts around Catania, and in the Gargano promontory in the Southern Adriatic Sea. Furthermore, this study confirms that the Northern Adriatic Sea has a low level of tsunami potential, in agreement with recent studies emphasizing that the large historical events concerning this region included in the first versions of the Italian tsunami catalog are largely overestimated and must be decreased.     

Probabilistic seismic hazard analysis of Kahramanmaras Province,Turkey

Kahramanmaras and its surroundings are under the influence of East Anatolian and Dead Sea fault zones which have significance in the tectonics of Turkey. The long-term energy accumulation in these zones creates a very high risk level in terms of seismic hazard. In this study, the seismic hazard of Kahramanmaras Province and its vicinity was tried to be determined by using the probabilistic seismic hazard method approach. The earthquake catalog used in the study comprises 424 earthquakes equal or greater than M _w ?=?4.0, covering a time period between 1 January 1900 and 1 January 2015. The earthquake data have been compiled from the catalogs of the International Seismological Center (ISC), Republic of Turkey Prime Ministry Disaster and Emergency Management Precidency (RTPMDEMP), Bogazici University Kandilli Observatory and Earthquake Research Institute. Seismic sources that could affect the study area have been identified according to the Earthquake Model of the Middle East (EMME). Seismic hazard parameters and peak horizontal acceleration values were obtained by using the selected attenuation relationships, and the results were given with iso-acceleration maps corresponding to a recurrence period of 475 years. The calculated peak horizontal acceleration values are generally varying between 0.21 and 0.41 in the study area. The result of this study shows that the southeastern parts of the study area have a greater seismic hazard compared with other parts.     

Spatial variation of seismicity parameters across India and adjoining areas

An attempt has been made to quantify the variability in the seismic activity rate across the whole of India and adjoining areas (0–45°N and 60–105°E) using earthquake database compiled from various sources. Both historical and instrumental data were compiled and the complete catalog of Indian earthquakes till 2010 has been prepared. Region-specific earthquake magnitude scaling relations correlating different magnitude scales were achieved to develop a homogenous earthquake catalog for the region in unified moment magnitude scale. The dependent events (75.3%) in the raw catalog have been removed and the effect of aftershocks on the variation of b value has been quantified. The study area was divided into 2,025 grid points (1°×1°) and the spatial variation of the seismicity across the region have been analyzed considering all the events within 300 km radius from each grid point. A significant decrease in seismic b value was seen when declustered catalog was used which illustrates that a larger proportion of dependent events in the earthquake catalog are related to lower magnitude events. A list of 203,448 earthquakes (including aftershocks and foreshocks) occurred in the region covering the period from 250 B.C. to 2010 A.D. with all available details is uploaded in the website .