Bayesian techniques for seismic hazard assessment using imprecise data

Some Bayesian methods of dealing with inaccurate or vague data are introduced in the framework of seismic hazard assessment. Inaccurate data affected by heterogeneous errors are modeled by a probability distribution instead of the usual value plus a random error representation; these data are generically called imprecise. The earthquake size and the number of events in a certain time are modeled as imprecise data. Imprecise data allow us to introduce into the estimation procedures the uncertainty inherent in the inaccuracy and heterogeneity of the measuring systems from which the data were obtained. The problem of estimating the parameter of a Poisson process is shown to be feasible by the use of Bayesian techniques and imprecise data. This background technique can be applied to a general problem of seismic hazard estimation. Initially, data in a regional earthquake catalog are assumed imprecise both in size and location (i.e errors in the epicenter or spreading over a given source). By means of scattered attenuation laws, the regional catalog can be translated into a so-called site catalog of imprecise events. The site catalog is then used to estimate return periods or occurrence probabilities, taking into account all sources of uncertainty. Special attention is paid to priors in the Bayesian estimation. They can be used to introduce additional information as well as scattered frequency-size laws for local events. A simple example is presented to illustrate the capabilities of this methodology.     

Probabilistic seismic hazard zonation of Syria

Earthquake hazard maps for Syria are presented in this paper. The Peak Ground Acceleration (PGA) and the Modified Mercalli Intensity (MMI) on bedrock, both with 90% probability of not being exceeded during a life time of 50, 100 and 200 years, respectively are developed. The probabilistic PGA and MMI values are evaluated assuming linear sources (faults) as potential sources of future earthquakes. A new attenuation relationship for this region is developed. Ten distinctive faults of potential earthquakes are identified in and around Syria. The pertinent parameters of each fault, such as theb-parameter in the Gutenberg-Richter formula, the annual rate ₄ and the upper bound magnitudem ₁ are determined from two sets of seismic data: the historical earthquakes and the instrumentally recorded earthquake data (AD 1900–1992). The seismic hazard maps developed are intended for preliminary analysis of new designs and seismic check of existing civil engineering structures.     

Probabilistic assessment of seismic hazard of dam sites in Jordan

A Probabilistic method is used to evaluate the seismic hazard of nineteen embankment dam sites in Jordan. A line source model developed by McGuire (1978) is used in this study. An updated earthquake catalogue covering the period from 1 A.D. to 1991 A.D. is used for this purpose. This catalogue includes all earthquakes that occurred in Jordan and adjacent areas, more specifically between latitudes 27.0°–35.5° N and longitudes 32.0°–39.0° E.Nine distinct seismic sources of potential seismic activities are identified. The seismic hazard parameters are determined using the method suggested by Kijko and Sellevoll (1989).The Peak Ground Acceleration (PGA) is selected as a measure of ground motion severity. Esteva (1974) attenuation relationship is used in evaluating PGA values at each dam site. Analysis is carried out for 50%, 90%, and 95% probability that is not being exceeded in a life time of 50, 100, and 200 years.Results of analysis indicate that PGA values are higher for dam sites closer to the Dead Sea Fault. This fault is believed to be responsible for most earthquake activities in Jordan and vicinity. The highest PGA value is found to be for Al-Karama dam site.     

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.     

Seismic hazard assessment in TERESA test areas based on a Bayesian technique

A method based on Bayesian techniques has been applied to evaluate the seismic hazard in the two test areas selected by the participants in the ESC/SC8-TERESA project: Sannio-Matese in Italy and the northern Rhine region (BGN). A prior site occurrence model (prior SOM) is obtain from a seismicity distribution modeled in wide seismic sources. The posterior occurrence model (posterior SOM) is calculated after a Bayesian correction which, basically, recovers the spatial information of the epicenter distribution and considers attenuation and location errors, not using source zones. The uncertainties of the occurrence probabilities are evaluated in both models.The results are displayed in terms of probability and variation coefficient contour maps for a chosen intensity level, and with plots of mean return period versus intensity in selected test sites, including the 90% probability intervals.It turns out that the posterior SOM gives a better resolution in the probability estimate, decreasing its uncertainty, especially in low seismic activity regions.     

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.     

Sensitivity analysis of seismic hazard for Western Liguria (North Western Italy): A first attempt towards the understanding and quantification of hazard uncertainty

The use of logic trees in probabilistic seismic hazard analyses often involves a large number of branches that reflect the uncertainty in the selection of different models and in the selection of the parameter values of each model. The sensitivity analysis, as proposed by Rabinowitz and Steinberg [Rabinowitz, N., Steinberg, D.M., 1991. Seismic hazard sensitivity analysis: a multi-parameter approach. Bull. Seismol. Soc. Am. 81, 796–817], is an efficient tool that allows the construction of logic trees focusing attention on the parameters that have greater impact on the hazard.In this paper the sensitivity analysis is performed in order to identify the parameters that have the largest influence on the Western Liguria (North Western Italy) seismic hazard. The analysis is conducted for six strategic sites following the multi-parameter approach developed by Rabinowitz and Steinberg [Rabinowitz, N., Steinberg, D.M., 1991. Seismic hazard sensitivity analysis: a multi-parameter approach. Bull. Seismol. Soc. Am. 81, 796–817] and accounts for both mean hazard values and hazard values corresponding to different percentiles (e.g., 16%-ile and 84%-ile). The results are assessed in terms of the expected PGA with a 10% probability of exceedance in 50 years for rock conditions and account for both the contribution from specific source zones using the Cornell approach [Cornell, C.A., 1968. Engineering seismic risk analysis. Bull. Seismol. Soc. Am. 58, 1583–1606] and the spatially smoothed seismicity [Frankel, A., 1995. Mapping seismic hazard in the Central and Eastern United States. Seismol. Res. Lett. 66, 8–21]. The influence of different procedures for calculating seismic hazard, seismic catalogues (epicentral parameters), source zone models, frequency–magnitude parameters, maximum earthquake magnitude values and attenuation relationships is considered. As a result, the sensitivity analysis allows us to identify the parameters with higher influence on the hazard. Only these parameters should be subjected to careful discussion or further research in order to reduce the uncertainty in the hazard while those with little or no effect can be excluded from subsequent logic-tree-based seismic hazard analyses.     

Time independent seismic hazard analysis in Alborz and surrounding area

The Bayesian probability estimation seems to have efficiencies that make it suitable for calculating different parameters of seismicity. Generally this method is able to combine prior information on seismicity while at the same time including statistical uncertainty associated with the estimation of the parameters used to quantify seismicity, in addition to the probabilistic uncertainties associated with the inherent randomness of earthquake occurrence. In this article a time-independent Bayesian approach, which yields the probability that a certain cut-off magnitude will be exceeded at certain time intervals is examined for the region of Alborz, Iran, in order to consider the following consequences for the city of Tehran. This area is located within the Alpine-Himalayan active mountain belt. Many active faults affect the Alborz, most of which are parallel to the range and accommodate the present day oblique convergence across it. Tehran, the capital of Iran, with millions of inhabitants is located near the foothills of the southern Central Alborz. This region has been affected several times by historical and recent earthquakes that confirm the importance of seismic hazard assessment through it. As the first step in this study an updated earthquake catalog is compiled for the Alborz. Then, by assuming a Poisson distribution for the number of earthquakes which occur at a certain time interval, the probabilistic earthquake occurrence is computed by the Bayesian approach. The highest probabilities are found for zone AA and the lowest probabilities for zones KD and CA, meanwhile the overall probability is high.     

Preliminary seismic hazard maps of Slovenia

The preparation of the preliminary seismic hazard maps of the territory of Slovenia has been based on an expansion of the basic approach laid out by Cornell in 1968. Three seismic source models were prepared. Two of them are based mainly on the earthquake catalogue using the Poissonian probability model. A map of seismic energy release and a map of earthquake epicenter density are used to delineate seismic sources in these models. The geometry of the third model which is based on a rough estimate of seismotectonic setting is taken from the probabilistic seismic hazard analysis of a nuclear power plant in Slovenia. Published ground motion attenuation models based on strong motion records of recent strong earthquakes in Italy are used. Test maps for variable and uniform b-values are presented. The computer program, Seisrisk III, developed by the U.S. Geological Survey is used.     

Probabilistic seismic hazard assessment for the Horn of Africa based on seismotectonic regionalisation

A probabilistic seismic hazard analysis (PSHA) for the Horn of Africa is presented. Our seismicity database consists of a revised and up-to-date regional catalogue compiled from different agencies, checked for completeness with respect to time and homogenized with respect to magnitude (M_s). The seismic source zones are based on our present day knowledge of the regional seismotectonics. Among the results we present regional hazard maps for 0.01 annual probability for intensity and Peak Ground Acceleration (PGA) and hazard curves and response spectra for six economical significant sites within the region. The model uncertainties with respect to seismicity are analysed in a novel approach and form part of a sensitivity analysis that quantifies our PSHA modelling uncertainties.

For 0.01 annual probability we find randomly oriented horizontal PGA that exceed just 0.2 g and MM-scale intensity VIII in the Afar depression and southern Sudan. Uncertainties amount to 20% g PGA in some cases, mainly due to attenuation uncertainties. Intensity uncertainties seldom exceed 0.5 intensity units. Relatively large seismic hazard is found for Djibouti (VIII for 0.01 annual probability), slightly lower for the port of Massawa (between VII and VIII for 0.01 annual probability) and low for the port of Assab (between VI and VII for 0.01 annual probability).     

Seismic hazard assessment under complex source size distribution of mining-induced seismicity

It is well-documented that a variety of factors controlling the rockmass fracturing process in mines often results in a complexity of mining event size distribution. In such cases, the estimation of the probability functions of source size parameterizations, with the use of presently known distribution models, brings about an unacceptable and systematic over- or underestimation of the seismic hazard parameters. It is, therefore, recommended that the non-parametric, kernel estimators of the event size distribution functions, be applied to stationary hazard studies in mining seismicity.These data-driven estimators, adapted to seismic source size characterization, accurately fit all kinds of data underlying distributions, regardless of their complexity. Recently, the non-parametric approach to size characterization was supported by a special method of uncertainty analysis based on resampling techniques. At present, it is a fully developed method, which provides point and interval estimates of size distribution functions and related hazard parameters. Two examples of its use in studying mining seismic data are presented and discussed in this paper. The analyzed data sets were recorded in two different copper mines in Poland. The smoothed bootstrap test for multimodality, which is a specialized tool for investigating the shapes of probability densities, provided highly significant proof that in both cases the probability densities of source size parameterization were complex thus implied the superiority of the non-parametric estimation to the classic, model-based approach in the studied cases. The data were then used to construct non-parametric, kernel estimates of the source size cumulative distribution function (CDF), the exceedance probability and the mean return period. Furthermore, confidence intervals for these quantities were also estimated. The intervals for CDF were narrow, showing that the procedures of non-parametric estimation and resampling based uncertainty analysis were precise. Due to the fact that the mean return period is very sensitive to values of the CDF, in particular for larger events sizes, the uncertainty of the return period estimates was not insignificant but remained manageable. The point and interval estimates of source size CDF and hazard parameters so obtained were compared with the respective point estimates achieved from the inappropriate in the case of complex magnitude distributions, model-based approach.     

Estimation of seismic hazard parameters in TERESA test areas

A general overview of some of the problems involved in earthquake catalogue handling is given as part of the works carried out into the ESC/SC8-TERESA project related with the seismic hazard assessment in two selected test areas: Sannio-Matese in Italy and the northern Rhine region (BGN). Furthermore, the necessary input data to be used in the calculation of seismic hazard has been obtained, including earthquake source zones and their seismic hazard parameters.The importance is pointed out of detailed analysis of seismic catalogues, mainly in relation to the use of aftershock information, the historical records of the region, and the possible temporal and spatial variation of seismicity, which could have an important influence on short-term hazard assessment.     

Tectonic stress,seismicity, and seismic hazard in the southeastern Carpathians

Intermediate-depth earthquakes in the Vrancea region occur in response to stress generation due to descending lithosphere beneath the southeastern Carpathians. In this article, tectonic stress and seismicity are analyzed in the region on the basis of a vast body of observations. We show a correlation between the location of intermediate-depth earthquakes and the predicted localization of maximum shear stress in the lithosphere. A probabilistic seismic hazard assessment (PSHA) for the region is presented in terms of various ground motion parameters on the utilization of Fourier amplitude spectra used in engineering practice and risk assessment (peak ground acceleration, response spectra amplitude, and seismic intensity). We review the PSHA carried out in the region, and present new PSHA results for the eastern and southern parts of Romania. Our seismic hazard assessment is based on the information about the features of earthquake ground motion excitation, seismic wave propagation (attenuation), and site effect in the region. Spectral models and characteristics of site-response on earthquake ground motions are obtained from the regional ground motion data including several hundred records of small and large earthquakes. Results of the probabilistic seismic hazard assessment are consistent with the features of observed earthquake effects in the southeastern Carpathians and show that geological factors play an important part in the distribution of the earthquake ground motion parameters.     

Preparing a seismic hazard model for Switzerland: the view from PEGASOS Expert Group 3 (EG1c)

The seismic hazard model used in the PEGASOS project for assessing earth-quake hazard at four NPP sites was a composite of four sub-models, each produced by a team of three experts. In this paper, one of these models is described in detail by the authors. A criticism sometimes levelled at probabilistic seismic hazard studies is that the process by which seismic source zones are arrived at is obscure, subjective and inconsistent. Here, we attempt to recount the stages by which the model evolved, and the decisions made along the way. In particular, a macro-to-micro approach was used, in which three main stages can be described. The first was the characterisation of the overall kinematic model, the “big picture” of regional seismogenesis. Secondly, this was refined to a more detailed seismotectonic model. Lastly, this was used as the basis of individual sources, for which parameters can be assessed. Some basic questions had also to be answered about aspects of the approach to modelling to be used: for instance, is spatial smoothing an appropriate tool to apply? Should individual fault sources be modelled in an intraplate environment? Also, the extent to which alternative modelling decisions should be expressed in a logic tree structure has to be considered.     

Influence of attenuation models in seismic hazard evaluation for the North-Eastern Sicily area

From the influence already revealed by attenuation models on the values of expected intensity for North-Eastern Sicily, the necessity arises to quantify the weight of these models and of their respective coefficients on the projection of intensity.A first evaluation is presented in this paper using the Sponheuer, Blake, and Grandori models.A comparison of the expected intensity maps allows a first critical estimate, showing the greater adaptability of the Grandori model to describe the attenuation of intensity for the investigated area.     

Probabilistic macroseismic hazard assessment for Nicaragua (preliminary results)

A probabilistic macroseismic hazard assessment has been done for Nicaragua. For this, the most complete catalogue for Central America, compiled by NORSAR in Norway has been used. In this catalogue, empirical intensity attenuation relations were found. Using these empirical relations, magnitudes were changed to epicentral intensities expected in sites where no intensities had been reported. The calculated intensities from a polygon surrounding Nicaragua were used to assess the macroseismic hazard in the region. For the whole polygon, the cumulative intensity frequency was calculated resulting in a b-value of 0.60 for an intensity interval of V–IX. The time completeness was also studied indicating that, for strong events causing higher intensities (I ₀ VII), the catalogue is complete for events that have been recorded since 1840. The whole polygon was cut into independent seismotectonic regions where the statistical procedure (intensity frequency and time completeness) was done.     

The importance of paleoseismology in seismic hazard studies for critical facilities

This paper is intended to provide a perspective on the use of paleoseismological studies in the seismic hazard assessment of critical facilities, such as dams, chemical/petrochemical facilities and nuclear power plants. In particular, the use of data obtained from paleoseismological studies for probabilistic seismic hazard analyses, when the required probabilities of exceedance are very low (e.g. 10^{− 6}–10^{− 7}) is considered. Recent revisions to the IAEA Safety Standards that provide guidance to Member States in their work related to the seismic safety of nuclear power plants are presented to illustrate the importance of this emerging discipline.     

Estimation of seismic hazard with allowance for noncircular isoseismals of arbitrary orientation

A new mathematical model describing the field of macroseismic intensity has been elaborated. It is based on elliptic isoseismals. The orientation of the main axes of elliptic isoseismals depends on the direction of stretching of the main geological structures on the investigated territory.The new model of a macroseismic field was applied to the territory of Eastern Uzbekistan. Some results of macroseismic investigations of the effect of large regional earthquakes were used as initial data.A noncircular model of a macroseismic field was introduced into the integral of the seismic shakability of Riznichenko and, according to the model, a macroseismic shakability map for the territory of Eastern Uzbekistan was computed in isolines of the long-term mean return period of vibrations for the intensity I 8.Paper presented at the 21st General Assembly of the European Seismological Commission, Sofia, 1988.     

Atlas of macroseismic maps for French earthquakes with their principal characteristics

The SIRENE macroseismic database has been utilized to draw isoseismal maps for the 140 best-documented French earthquakes, characterized by epicentral intensities of at least V (MSK) and located in all parts of the country. A study of focal depths derived from available local intensity data using an intensity versus distance decay law (Sponheuer) shows that the focal depths of most of the events considered do not exceed about 10 km. Their distribution correlates fairly well with regional dynamic geology features. A relationship is then computed between magnitude, intensity and focal distance, based on 73 instrumenta]ly recorded earthquakes (M _L between 3.3 and 6.3) and on 217 mean radius values (from 2 to 380 km) for isoseismals of intensity VIII to III (MSK). This relationship is applied to historical earthquakes contained in the database SIRENE which are characterised by their intensity only. These results are used in the evaluation as well deterministic as probabilistic of the seismic hazard on the national territory.