Bayesian analysis of the local intensity attenuation

We present a method that allows us to incorporate additional information from the historical earthquake felt reports in the probability estimation of local intensity attenuation. The approach is based on two ideas: a) standard intensity versus epicentral distance relationships constitute an unnecessary lter between observations and estimates; and b) the intensity decay process is a ected by many, scarcely known elements; hence intensity decay should be treated as a random variable as is the macroseismic intensity. The observations related to earthquakes with their epicenter outside the area concerned, but belonging to homogeneous zones, are used as prior knowledge of the phenomenon, while the data points of events inside the area are used to update the estimates through the posterior means of the quantities involved

Bayesian analysisof a probability distribution for local intensity attenuation

Intensity attenuation and its variation as a function of the distance and earthquake size is still a critical issue in evaluating seismic hazard. We present a method that allows us to incorporate additional information from the historical earthquake felt reports in the probability estimation of local intensity attenuation. The approach is based on two ideas: a) standard intensity versus epicentral distance relationships constitute an unnecessary filter between observations and estimates; and b) the intensity decay process is affected by many, scarcely known elements (the physical parameters of the source, propagation path effects, building vulnerability, the semi-qualitative character of macroseismic scales, etc.). Hence intensity decay should be treated as a random variable as is the macroseismic intensity. We assume here that decay, defined on the set {0,1, ..., I0}, follows a binomial distribution with parameters (I0, p); p depends on the distance from the epicenter and is related to the probability of null decay at that distance. According to the Bayesian approach this p parameter is, in turn, a Beta random variable. The observations related to earthquakes with their epicenter outside the area concerned, but belonging to homogeneous zones, are used as prior knowledge of the phenomenon, while the data points of events inside the area are used to update the estimates through the posterior means of the quantities involved. Our methodology is described in detail in an application to the Umbria-Marche area in Central Italy. The data sets examined are the macroseismic intensity database DOM4.1 and the zonation ZS.4, both compiled by the Italian Group for Defence against Earthquakes (GNDT). The method is validated by comparing the observed and the estimated intensity data points of the Camerino (28/07/1799) and of the Colfiorito (26/09/1997) earthquakes

Mining Macroseismic Fields to Estimate the Probability Distribution of the Intensity at Site

The analysis of the seismic attenuation is a prominent and problematic component of hazard assessment. Over the last decade it has become increasingly clear that the intrinsic uncertainty of the decay process must be expressed in probabilistic terms. This implies estimating the probability distribution of the intensity at a site Is as the combination of the distribution of the decay DI and of the distribution of the intensity I0 found for the area surrounding that site. We focus here on the estimation of the distribution of DI. Previous studies presented in the literature show that the intensity decay in Italian territory varies greatly from one region to another, and depends on many factors, some of them not easily measurable. Assuming that the decay shows a similar behavior in function of the epicenter-site distance when the same geophysical conditions and building vulnerability characterize different macroseismic fields, we have classified some macroseismic fields drawn from the Italian felt report database by applying a clustering algorithm. Earthquakes in the same class constitute the input of a two-step procedure for the Bayesian estimation of the probability distribution of I at any distance from the epicenter, conditioned on I0, where DI is considered an integer, random variable, following a binomial distribution. The scenario generated by a future earthquake is forecast either by the predictive distribution in each distance bin, or by a binomial distribution whose parameter is a continuous function of the distance. The estimated distributions have been applied to forecast the scenario actually produced by the Colfiorito earthquake on 1997/09/26; for both options the expected and observed intensities have been compared on the basis of some validation criteria. The same procedure has been repeated using the probability distribution of DI estimated on the basis of each class of macroseismic fields identified by the clustering algorithm

The intensity attenuation of Colfiorito and other strong earthquakes: the viewpoint of forecasters and data gatherers

This article has been originated by thoughts on previous analyses related to the proba- bilistic treatment of the macroseismic attenuation, from which it turns out that in Italian territory the intensity decay I varies greatly from one region to another, depending on many factors, some of them not easily measurable. By applying a clustering algorithm we classified some macroseismic fields drawn from the Italian felt report database in three classes. Earthquakes into the same class constituted the input of a two-step procedure for the Bayesian estimation of the probability distribution of I at any distance from the epicenter, conditioned on I0, where I is considered an integer, random variable, following a binomial distribution. The estimated distributions were validated by forecasting the macroseismic field of the Colfiorito earthquake. In this article we deal with the issues left open by those statistical analyses by following two ways: on one hand we test the procedure by forecasting the macroseismic field of other strong earthquakes recorded in Italy during the last century and, on the other hand, we ask the reasons of peculiarities in the results to experts in other fields. The article is hence an introductory work, an example of the possibility and of the need of exchange of knowledge

A Smart Voting Subsystem for Distributed Fault Tolerance

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Probability distribution of the macroseismic intensity attenuation in the Italian volcanic districts

We present the probabilistic version of the analysis performed in Azzaro et al. (2006a) on the attenuation of the seismic intensity in Italian volcanic districts. The main results are the estimate of the probability distribution of the intensity at site IS, conditioned on the site-epicenter distance d and on I0, and then, assuming the mode of this distribution as estimator of IS, the forecasting of future macroseismic fields given I0. To this end we have modified the method presented in Rotondi and Zonno (2004) by inserting the following innovative elements: identification of possible different trends and exploitation of knowledge from prior experience or data. Data set. The intensity dataset considered in the present analysis is the same used in the study by Azzaro et al. (2006a), based on a deterministic approach. We consider a total of 38 earthquakes located in the Italian volcanic areas, so distributed: Etna region (24 events), Aeolian Islands (6 events), Vesuvius-Ischia (3 events) and Albani Hills (5 events). The CMTE local earthquake catalogue (Azzaro et al., 2000, 2002, 2006b) has been used for the Etna region while for the other Italian volcanic districts (Aeolian Islands, Ischia, Vesuvius and Albani Hills) the CPTI04 Italian seismic catalogue (Gruppo di lavoro CPTI, 2004) and the DBMI04 associated database (Stucchi et al., 2007) have been considered (Tab. 1). For the analysis, subsets of earthquakes with epicentral intensity I0 ≥ VII MCS and I0 ≥ VI MCS were used for the Etna region and for the other Italian volcanic districts, respectively. Probability model. We cite here the key-elements of the probabilistic method, referring to Rotondi and Zonno (2004) for a detailed description. Instead of adding a gaussian error to deterministic relationships which express the intensity decay as a function of some factors (epicentral intensity, site-epicenter distance, depth, site types, and styles of faulting), we treat the decay as an aleatory variable defined on the domain {0, I0}. Consequently, we assume that the intensity IS is a discrete binomial distributed variable Bin(I0 , p) where pI0 means the probability of null decay, and p belongs to [0,1]. According to the Bayesian approach, p is considered as a random variable following the beta distribution Beta(α, β). Since mean and variance of p are functions of the α, β hyperparameters, we can express our initial knowledge on the decay process through these parameters. To do this, we have divided each macroseismic field in bins of fixed width and the intensity data points in subsets according to this spatial subdivision. For each bin we have repeated the following procedure: a) assessing the prior values to α, β, that is a prior distribution for p; b) updating, through Bayes’ theorem, the hyperparameters on the basis of the current observations; c) estimating the p parameter through the mean of its posterior distribution. By substituting this estimate in the distribution Bin(I0 , p), we obtain an updated binomial distribution indicated as plug-in distribution. Its mode has been assumed as the expected value of the intensity at the sites within the corresponding bin. To predict the intensity at any distance we have smoothed the p’s estimated in the different bins through a monotonically decreasing function; the lowest mean squared error was given by the inverse power function . Hence, the mode of the plug-in distribution obtained by setting p=g(d) provides an expected value for IS at any distance. If, on the contrary, we assume that, from the attenuation viewpoint, the sites inside any bin behave in the same way, we can average over the domain [0,1] of p by integrating the product of the likelihood with respect to the posterior Beta distribution of p. In this way we have obtained the so-called predictive distribution for every bin and its mode is taken as expected value for IS at any site inside that bin. Trends in the intensity decay. We have analysed the macroseismic field of the 38 earthquakes constituting our dataset (Tab. 1) by drawing the decay versus the site-epicenter distance of each data point. A quick look at these graphical representations suggests that these earthquakes do not show an homogeneous decay. To identify different trends in the decay, we have synthetized the information contained in each field by collecting, in a matrix, median, mean, and quartile of each set of distances from the epicenter of the points with the same ΔI. Then we have applied to this matrix a clustering algorithm based on the evaluation of the distance between each pair of rows of the matrix. The dataset has been thus partitioned into two groups of events according to their attenuation trend: the first set mainly formed by the earthquakes of Mt. Etna and Vesuvius-Ischia areas, the second one including the events of the Aeolian Islands and Albani Hills. The set 1 shows an higher decay than the set 2, so two different spatial scales are required: bins of width 1 km for the set 1 and of width 25 km for the set 2. A similar classification analysis was performed in Zonno et al. (2008) on 55 earthquakes representative of the Italian territory; in that case three classes were identified. The probabilistic analysis above described has been separately applied to the two sets, discriminating the events of from those of , and using as a priori distributions for the parameters p’s those indicated in Zonno et al. (2008) for the class of earthquakes with the highest attenuation. The hyperparameters α’s and β’s have been then updated through the observed intensity data points according to the expressions α=α0 + ΣNn=1 IS (n) and β= β0 + ΣNn=1 (I0 - IS (n)). Some results. For each bin the values of the predictive probability function of for the Etna area and Aeolian Islands, are shown in Fig. 1; the squares indicate the values of the intensity decay computed through the logarithmic regressions (Tab. 2) obtained by Azzaro et al. (2006) with the same dataset. These values can be compared with the mode of the predictive function in each bin. The fit between the two methods is good but much more information is provided by the probabilistic approach. In addition to the estimate of the intensity at any site, the probability distribution of IS provides a measure of the uncertainty and its values can be directly used in the software “SASHA” (D’Amico and Albarello, 2007) to calculate the probabilistic seismic hazard at the site. Conclusions. The identification of different decay trends produced by the clustering algorithm matches well with that already presented in the literature (Azzaro et al. 2006), and this suggests that the method could be successfully applied to other cases. Only two earthquakes in Albani Hills - 1876/10/26, I0 VI-VII, 1927/12/26, I0 VII-VIII - are unexpectedly included in the set 1 together with the events of Mt. Etna and Vesuvio-Ischia areas; further, detailed analyses are required to explain such an anomaly. Some problems are still open: a) most of the earthquakes here considered have epicentral intensity I0 VII or VIII, so that we have evaluated the probability functions of IS conditioned on these two values of I0. Also other values of I0 must be used in the analysis; b) the method should be also validated on other earthquakes not included in the dataset of Tab. 1, on the basis of probabilistic measures of the degree to which the model predicts the decay in the data points of a macroseismic field (Rotondi and Zonno, 2004)

PROBABILISTIC PROCEDURE TO ESTIMATE THE MACROSEISMIC INTENSITY ATTENUATION IN THE ITALIAN VOLCANIC DISTRICTS

In Italian volcanic areas, we apply a probabilistic procedure for Macroseismic Intensity Attenuation estimates. The procedure, following the Bayesian approach, allows to exploit additional information on historical earthquakes. The method, given the epicentral intensity and the site epicenter distance, begins from selected earthquakes intensity data points and ends at the assessment of the intensity (Is) probability distribution at a site. Our probabilistic method provides a probability function matrix that can be directly applied for the computation of probabilistic seismic hazard at the site

Probabilistic procedure to estimate the macroseismic intensity attenuation in the Italian volcanic districts

In this work we apply a probabilistic procedure to estimate the macroseismic intensity attenuation in the volcanic areas of Italy which allows to exploit additional information on historical earthquakes following the Bayesianapproach. The method starts from the intensity data points of the selected earthquakes and arrives at theassessment of the probability distribution for the intensity at a site given the epicentral intensity and thesite-epicenter distance. The CMTE local earthquake catalogue has been used for the Etna region while for theother Italian volcanic districts (Aeolian Islands, Ischia, Vesuvius and Albani Hills) the CPTI04 Italian seismic catalogue and the DBMI04 associated database have been considered. For the analysis, subsets of earthquakeswith epicentral intensity I0 ≥ VII MCS and I0 ≥ VI MCS were used for the Etna region and for the other Italian volcanic districts, respectively. Only earthquakes with more than 10 felt observations have been considered. The results show a specific attenuation trend for the Etna region compared with the other Italian volcanic areas

Forecasting macroseismic scenarios through anisotropic attenuation: a Bayesian approach

In this work we aim at two objects: quantifying, by a binomial-beta probabilistic model, the uncertainty involved in the assessment of the intensity decay, an ordinal quantity often incorrectly treated as real variable, and, given the finite dimension of the fault, modelling non-symmetric decays but exploiting information collected from previous studies on symmetric cases. To this end we transform the plane so that the ellipse having the fault length as maximum axis is changed into a circle with fixed diameter. We start from an explorative analysis of a set of macroseismic fields representative of the Italian seismicity among which we identify three different decay trends by applying a hierarchical clustering method. Then we focus on the exam of the seismogenic area of Etna volcano where some fault structures are well recognizable as well as the anisotropic trend of the attenuation. As in volcanic zones the seismic attenuation is much quicker than in other zones, we first shrink and then transform the plane so that the decay becomes again symmetric. Following the Bayesian paradigm we update the model parameters and associate the estimated values of the intensity at site with the corresponding locations in the original plane. Backward validation and comparison with the deterministic law are also presented

Design, synthesis and biological activity of selective hCAs inhibitors based on 2-(benzylsulfinyl)benzoic acid scaffold

A large library of derivatives based on the scaffold of 2-(benzylsulfinyl)benzoic acid were synthesised and tested as atypical inhibitors against four different isoforms of human carbonic anhydrase (hCA I, II, IX and XII, EC 4.2.1.1). The exploration of the chemical space around the main functional groups led to the discovery of selective hCA IX inhibitors in the micromolar/nanomolar range, thus establishing robust structure-activity relationships within this versatile scaffold. HPLC separation of some selected chiral compounds and biological evaluation of the corresponding enantiomers was performed along with molecular modelling studies on the most active derivatives