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.     

Comparison of two methods for seismic hazard assessment in a low-seismicity area

The EGO method, developed by Egozcue et al. and the SRAMSC method, originally developed by Cornell and later programmed by McGuire, to assess the seismic hazard, are compared for the low seismicity area Belgium, The Netherlands, and NW Germany. Using the same input data, the results of the EGO method without the majority criterion and the SRAMSC method with upper bound XII agree very well. The influence of the zoning is investigated for the EGO method. It is not necessary to define the zones for the EGO method so strictly as for the SRAMSC method, but too wide zones can give bad results.     

Understanding Perturbation on the Simplex: A Simple Method to Better Visualize and Interpret Compositional Data in Ternary Diagrams

Perturbation is an operation defined on the simplex and can be used for centering compositional data in a ternary diagram, applying objective criteria. Because a straight line in the original diagram is still astraight line in the perturbed diagram, gridlines or compositional fields defined by straight lines can easily be included in the operation. Simultaneous perturbation of data, gridlines, and/or compositional fields is shown to improve both visualization and graphical interpretation of compositions in ternary diagrams. This is illustrated by some examples using simulated as well as real data.     

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.     

Assessment of seismic hazard for the Sannio-Matese area of Southern Italy — A summary

The working group on Test Regions for Evaluation of Methods for Seismic Hazard Assessment in Europe (TERESA), consisted of 15 members from 10 different European countries. Methods and experience gathered in these countries have been compared and discussed for two test areas in Europe: the Sannio-Matese region, Southern Italy, with high seismic activity, and the border region between Belgium, The Netherlands, and Federal Republic of Germany, with low activity.This paper summarizes the results for one of the test areas, Sannio-Matese. Most of the participants used statistical procedures to assess earthquake hazard, receiving results in terms of probability of occurrence for intensity as the ground-motion parameter. It was found that careful preparation of input data and parameters is the major influencing factor, therefore most of the efforts of the working group was devoted to this task.The scatter of the obtained results of the group is considerable, mainly because of the uncertainties in the data and the subjectiveness involved in the procedures. For better control of both factors, more objective methods have to be developed.     

Seismic hazard computations for regions with low earthquake activity — A case study for the Belgium,The Netherlands and NW Germany area

The algorithms to evaluate seismic hazard, used and/or developed by five teams participating in the TERESA project, applied to the low seismicity area Belgium, The Netherlands and NW Germany are compared. The main differences in the results can be explained by the majority criterion of Egozcue et al. (1989), the differences in the upper bound and zonification and, in some cases, by a higher attenuation.     

A method to estimate intensity occurrence probabilities in low seismic activity regions

The estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively established because several problems arise when macroseismic historical data are incomplete and the active zones are not well determined. The purpose of this paper is to present a method that estimates site occurrence probabilities and at the same time measures the uncertainties inherent in these probabilities in low activity regions. The region to be studied is divided into very broad seismic zones. An exponential intensity probability law is adjusted for each zone and the degree of uncertainty in the assumed incompleteness of the catalogue is evaluated for each intensity. These probabilities are used to establish what may be termed ‘prior site occurrence models’. A Bayesian method is used to improve ‘prior models’ and to obtain the ‘posterior site occurrence models’. Epicentre locations are used to recover spatial information lost in the prior broad zoning. This Bayesian correction permits the use of specific attenuation for different events and may take into account, by means of conservative criteria, epicentre location errors. Following Bayesian methods, probabilities are assumed to be random variables and their distribution may be used to estimate the degree of uncertainty arising from (a) the statistical variance of estimators, (b) catalogue incompleteness and (c) mismatch of data to prior assumptions such as Poisson distribution for events and exponential distribution for intensities. The results are maps of probability and uncertainty for each intensity. These maps exhibit better spatial definition than those obtained by means of simple, broad zones. Some results for Catalonia (NE of Iberian Peninsula) are shown.     

Assessing wavestorm hazard evolution in the NW Mediterranean with hindcast and buoy data

It has been suggested that climate change might modify the occurrence rate of large storms and their magnitude, due to a higher availability of energy in the atmosphere-ocean system. Forecasting physical models are commonly used to assess the effects. No one expects the physical model forecasts for one specific day to be accurate; we consider them to be good if they adequately describe the statistical characteristics of the climate. The Peak-Over-Threshold (POT) method is a common way to statistically treat the occurrence and magnitude of hazardous events: here, occurrence is modelled as a Poisson process and magnitude over a given threshold is assumed to follow a Generalized Pareto Distribution (GPD). We restrict our attention to Weibull-related GPDs, which exhibit an upper bound, to comply with the fact that any physical process has a finite upper limit. This contribution uses this framework to model time series of log-significant wave-height constructed joining quasi-collocated hindcast data and buoy measurements. Two of the POT model parameters (inhomogeneous Poisson rate and logarithm of the GPD shape parameter are considered to be a combination of a linear function of time and a series indicator function. The third parameter, logarithm of the GPD upper bound, is considered to have only a series indicator component. The resulting parameters are estimated using Bayesian methods. Using hincast and buoy series, the time span of the data set is extended, enhancing the precision of statistical results about potential linear changes. Simultaneously the statistical behaviour of hincast and buoy series are compared. At the same time, the step function allows to calibrate the statistical reproduction of storms by hindcasting.     

Compositional Data in Geostatistics: A Log-Ratio Based Framework to Analyze Regionalized Compositions

Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. Here, these problems are illustrated, and a solution, based on the principle of working in coordinates using orthonormal logratio representations, is presented. This approach offers a tool for standard geostatistical studies. One of the advantages the method has is that it allows the usual inconsistencies with indicator kriging to be overcome through simplicial indicator kriging. A general way of modelling crossvariograms of coordinates, based on the matrix valued variation variogram, is discussed. In summary, the main aspects related to the modelling and analysis of regionalized compositions have had satisfactory solutions found for them. The proposed methodology is illustrated with public data from a survey concerning arsenic contamination in underground water in Bangladesh.