ByMuR UR1 Research Unit #2: Hazard Analysis with Bayesian approach
DESCRIPTION OF THE RESEARCH ACTIVITY OF RU2

The main goal of RU2 is the definition and quantification of the hazard coming from natural events in the target area of the city of Naples, by following the procedures and guidelines of RU1 for a homogeneous definition of Bayesian multi-risk. In particular, RU2 will be focused on the assessment of hazard from earthquakes, volcanic eruptions and tsunamis, paying special attention to the correct evaluation of uncertainties.

Since we will be using a Bayesian approach, for each hazardous phenomenon under study we will set up a prior probability distribution, based on models and/or expert opinions. The observations relative to the past occurrence of the hazardous phenomenon in the target area will form the likelihood function. It is likely to suppose that these past data are relative to all the possible factors that can affect the process causing the occurrence of hazardous phenomenon (for example, a tsunami run-up catalog most likely includes tsunami data due submarine earthquakes, submarine landslides, or due to possible volcanic phenomena able to move a great mass of water, and generate a tsunami wave). This implies that particular attention has to be paid in order to analyze and include all such factors, in the construction of the prior probability distribution. Only in this circumstance, the prior estimate can be homogenous with respect to the likelihood function, allowing their combination, via the Bayes' theorem, to obtain a meaningful posterior distribution.

In the following, a detailed structure of the RU2 and the tasks of the personnel are provided.

Task 1: Seismic Hazard

Approaching seismic hazard assessment through Bayesian strategies is innovative. In literature, the techniques commonly applied are not Bayesian, and can be distinguished into two broad classes, on the basis of the models applied to describe earthquake distributions in term of time, space and magnitude. One class is characterized by a probabilistic modelling (this, in turn, is divided into two subclasses, based, one on the so called "source approach", and the other one on the so called "site approach"). The second class is based on a deterministic modeling. In this project, only the probabilistic procedures will be applied. Through a Bayesian approach, we will assess the probabilistic seismic hazard by integrating the assessments from source and site approaches, in order to include in the calculation the different types of information that these two methods bring.

Probabilistic seismic hazard, i.e. the quantification of the probability of exceeding a given ground motion value in the exposure time window in a given area, evaluated through the source approach, is usually made on the basis of statistical modeling of earthquake occurrence and of deterministic modeling of ground motion through the so-called attenuation laws, predicting the propagation of seismic waves in the Earth.

Three factors concur to the probabilistic description of earthquake occurrence: their distributions in time, space and size. In this project, we will apply different models, already proposed by the scientific community, to define these earthquake distributions. These models are based on different hypothesis on the seismogenetic process; this gives to our analysis a much wider perspective of the problem, covering the possibility that a single model is not able to entirely explain the physics of a stochastic natural process.

In the standard probabilistic seismic hazard assessment, the temporal earthquake occurrence is random (i.e., Poissonian), as it has been done in the Italian seismic hazard map MPS04. In the project, we will apply as well more realistic temporal distributions of the seismicity, to include patterns that are widely accepted by the scientific community, like the tendency of earthquakes to occur in clusters. The earthquake spatial distribution will be represented by a spatial smoothing of past seismicity. The last point to define is the earthquake size distribution. It is widely accepted that the earthquake size frequency relationship follows a power law, the so-called Gutenberg-Richter (G-R) law. This power law has universal applicability, to all spatial scales and on a wide range of earthquake magnitude, and it has been used also in MPS04. During this project, a new calibration of the G-R for the test area using the data from the seismic catalog will be done. Moreover, a new Bayesian method to infer the earthquake size distribution will be applied. Starting from the prior hypothesis of the power law earthquake size distribution, the method re-calibrates the probabilities of the different sizes through a likelihood function, designed on the basis of the local size data of past earthquakes.

Once the earthquake probabilistic distribution is set up, the prior distribution of hazard assessment will be evaluated by using MonteCarlo catalog simulation; each catalog will be intended as a representation of the real seismicity. To define the expected ground shaking, the ground motion attenuation laws, calibrated for the target area and already available in literature, will be applied. Finally, a new quantification of site effects is contemplated in the project.

This result will constitute the prior model for the Bayesian approach.

The likelihood function will be defined through the data relative to macroseismic information and, for the most recent earthquakes, through shaking data, due to past events that have caused felt effects in Neapolitan area.

The first step is a seismological study of the area capable to generate damaging earthquakes and felt effects in Naples, in order to have a complete view of tectonic and morphologic setting of the area. By merging the information from all the available databases, through the ShakeMap software, implemented for Italy in general, and specifically for Naples, we will produce an atlas of shaking maps for the past earthquakes in the test area. The databases used will be CPTI - Parametric Catalog of Italian Earthquakes - one of most complete historical catalog worldwide; DBMI - Italian Macroseismic DataBase - a rich source of macroseismic damage effects caused by historical and instrumental earthquakes. The macroseismic damage is represented using the intensity scale, i.e., a discrete scale that defines the level of damage in buildings due to seismic waves. Concerning instrumental seismicity, we will use the ITACA database, that has become available only recently; ITACA is a collection of all the waveforms and peak values of the Italian earthquakes since 1976, with minimum magnitude 3.5. For the definition of the geological setting, DISS - Database of Italy's Seismogenic Sources - and CSI - Catalog of Instrumental Seismicity - will be analyzed.

Once the likelihood function will be built, it will be combined with the prior distribution using a MonteCarlo simulation method; this will provide a numerical evaluation of the posterior seismic hazard for the city of Naples.

Since the seismic hazard assessment we propose is innovative in each single part, the expertise from different research field is needed. Indeed, it is the first time in scientific literature that a Bayesian assessment for seismic hazard, able to integrate the source and site approaches, is proposed. Concerning the source approach, it is the first time that the MonteCarlo approach is implemented in Italy, while it has been applied in other regions, in some cases by the personnel of this project (Faenza et al, 2007, J Geophys Int 171:797-806); lastly, the characterization of the seismic history of a site using ShakeMap code is another novelty of this project.


Task 2: Volcanic Hazard

As mentioned so far, while Bayesian seismic hazard assessment is innovatory, some members of this project are already involved in Bayesian volcanic hazard assessment, having already produced a freeware code named BET_VH (Bayesian Event Tree for Volcanic Hazard), based on a Bayesian event tree. BET_VH makes use of Bayesian inference to study the probability of all concurrent events responsible for the occurrence of volcanic hazardous phenomena, like tephra fall and invasion of pyroclastic density currents. The quantification of the probability that a given volcanic hazardous phenomenon will occur can be subdivided in a logical sequence of events (the tree), that have to occur because of the hazardous phenomenon happens in a certain point around the volcano. Therefore, it is necessary to assign a probability distribution to each of this connected event. This probability has to be conditioned to the occurrence of all the events that form the previous part of the chain. BET_VH evaluates these conditioned probabilities through Bayesian inference, taking into account models (geological, volcanological and theoretical) and past data. BET_VH has been designed for the application at a single volcano, and our team has already applied it to evaluate the hazard due to tephra fall from Campi Flegrei. During this project, BET_VH will be applied again to Campi Flegrei, for evaluating the hazard due to invasion of pyroclastic density currents, and ex-novo to the other two Neapolitan volcanoes, Vesuvius and Ischia, for evaluating both the hazards from tephra fall and pyroclastic density currents. Moreover, another interesting application, usually disregarded in volcanic hazard assessment, is the evaluation of the overall volcanic hazard in the target area, due to the three volcanoes. This probability will be calculated by combining, with appropriate probabilistic weights, the hazard from each single volcano.