Bayesian networks for enterprise risk assessment

According to different typologies of activity and priority, risks can assume diverse meanings and it can be assessed in different ways. In general risk is measured in terms of a probability combination of an event (frequency) and its consequence (impact). To estimate the frequency and the impact (severity) historical data or expert opinions (either qualitative or quantitative data) are used. Moreover qualitative data must be converted in numerical values to be used in the model. In the case of enterprise risk assessment the considered risks are, for instance, strategic, operational, legal and of image, which many times are difficult to be quantified. So in most cases only expert data, gathered by scorecard approaches, are available for risk analysis. The Bayesian Network is a useful tool to integrate different information and in particular to study the risk's joint distribution by using data collected from experts. In this paper we want to show a possible approach for building a Bayesian networks in the particular case in which only prior probabilities of node states and marginal correlations between nodes are available, and when the variables have only two states

A Chandra Snapshot Survey for 3C Radio Galaxies with redshifts between 0.3 and 0.5

This paper contains an analysis of short Chandra observations of 19 3C sources with redshifts between 0.3 and 0.5 not previously observed in the X-rays. This sample is part of a project to obtain Chandra data for all of the extragalactic sources in the 3C catalogue. Nuclear X-ray intensities as well as any X-ray emission associated with radio jet knots, hotspots or lobes have been measured in 3 energy bands: soft, medium and hard. Standard X-ray spectral analysis for the 4 brightest nuclei has been also performed. X-ray emission was detected for all the nuclei of the radio sources in the current sample with the exception of 3C 435A. There is one compact steep spectrum (CSS) source while all the others are FRII radio galaxies. X-ray emission from two galaxy clusters (3C 19 and 3C 320); from 6 hotspots in 4 radio galaxies (3C 16, 3C 19, 3C 268.2, 3C 313); and extended X-ray emission on kpc scales in 3C 187 and 3C 313, has been detected.Comment: 33 pages, 22 figures, 7 tables, accepted for publication on the ApJ Supplement Series. arXiv admin note: text overlap with arXiv:1210.602

Gravity changes due to overpressure sources in 3D heterogeneous media: application to Campi Flegrei caldera, Italy

Employing 3D finite element method, we develop an algorithm to calculate gravity changes due to pressurized sources of any shape in elastic and inelastic heterogeneous media. We consider different source models, such as sphere, spheroid and sill, dilating in elastic media (homogeneous and heterogeneous) and in elasto-plastic media. The models are oriented to reproduce the gravity changes and the surface deformation observed at Campi Flegrei caldera (Italy), during the 1982-84 unrest episode. The source shape and the characteristics of the medium have great influence in the calculated gravity changes, leading to very different values for the source densities. Indeed, the gravity residual strongly depends upon the shape of the source. Non negligible contributions also come from density and rigidity heterogeneities within the medium. Furthermore, if the caldera is elasto-plastic, the resulting gravity changes exhibit a pattern similar to that provided by a low effective rigidity. Even if the variation of the source volumes is quite similar for most of the models considered, the density inferred for the source ranges from ∼ 400 kg/m3 (supercritical water) to ∼ 3300 kg/m3 (higher than trachytic basalts), with drastically different implications for risk assessment

Gravity changes due to overpressure sources in 3D heterogeneous media: application to Campi Flegrei caldera, Italy

Employing a 3D finite element method, we develop an algorithm to calculate gravity changes due to pressurized sources of any shape in elastic and inelastic heterogeneous media. We consider different source models, such as sphere, spheroid and sill, dilating in elastic media (homogeneous and heterogeneous) and in elasto-plastic media. The models are oriented to reproduce the gravity changes and the surface deformation observed at Campi Flegrei caldera (Italy), during the 1982-1984 unrest episode. The source shape and the characteristics of the medium have great influence on the calculated gravity changes, leading to very different values for the source densities. Indeed, the gravity residual strongly depends upon the shape of the source. Non negligible contributions also come from density and rigidity heterogeneities within the medium. Furthermore, if the caldera is elasto- plastic, the resulting gravity changes exhibit a pattern similar to that provided by a low effective rigidity. Even if the variation of the source volumes is quite similar for most of the models considered, the density inferred for the source ranges from ∼400 kg/m3 (super critical water) to ∼3300 kg/m3 (higher than trachytic basalts), with drastically different implications for risk assessment

The intracluster magnetic field power spectrum in Abell 665

The goal of this work is to investigate the power spectrum of the magnetic field associated with the giant radio halo in the galaxy cluster A665. For this, we present new deep Very Large Array total intensity and polarization observations at 1.4 GHz. We simulated Gaussian random three-dimensional turbulent magnetic field models to reproduce the observed radio halo emission. By comparing observed and synthetic radio halo images we constrained the strength and structure of the intracluster magnetic field. We assumed that the magnetic field power spectrum is a power law with a Kolmogorov index and we imposed a local equipartition of energy density between relativistic particles and field. Under these assumptions, we find that the radio halo emission in A665 is consistent with a central magnetic field strength of about 1.3 micro-G. To explain the azimuthally averaged radio brightness profile, the magnetic field energy density should decrease following the thermal gas density, leading to an averaged magnetic field strength over the central 1 Mpc^3 of about 0.75 micro-G. From the observed brightness fluctuations of the radio halo, we infer that the outer scale of the magnetic field power spectrum is ~450 kpc, and the corresponding magnetic field auto-correlation length is ~100 kpc.Comment: 12 pages, 6 figures, accepted for publication on A&A, language editing. For a high quality version see http://erg.ca.astro.it/preprints/a665_halo

Numerical inversion of deformation caused by pressure sources: application to Mount Etna (Italy)

The interpretation of geodetic data in volcanic areas is usually based on analytical deformation models. Although numerical Finite Element modeling allows realistic features such as topography and crustal heterogeneities to be included, the technique is not computationally convenient for solving inverse problems using classical methods. In this paper we develop a general tool to perform inversions of geodetic data by means of 3D FE models. The forward model is a library of numerical displacement solutions, where each entry of the library is the surface displacement due to a single stress component applied to an element of the grid. The final solution is a weighted combination of the six stress components applied to a single element-source. The precomputed forward models are implemented in a global search algorithm, followed by an appraisal of the sampled solutions. After providing extended testing, we apply the method to model the 1993-97 inflation phase at Mt. Etna, documented by GPS and EDM measurements. We consider four different forward libraries, computed in models characterized by homogeneous/ heterogeneous medium and flat/topographic free surface. Our results suggest that the elastic heterogeneities of the medium can significantly alter the position of the inferred source, while the topography has minor effect

Geometrical and physical properties of the 1982-84 deformation source at Campi Flegrei - Italy

Deformation of the ground surface in volcanic areas is generally recognized as a reliable indicator of unrest, possibly resulting from the intrusion of fresh magma within the shallow rock layers. The intrusion process is usually represented by a deformation source such as an ellipsoidal pressurized cavity, embedded within a homogeneous and elastic half-space. Similar source models allow inferring the depth, the location and the (incremental) volume of the intrusion, which are very important parameters for volcanic risk implications. However, assuming a homogeneous and elastic rheology and, assigning a priori the shape and the mechanism of the source (within a very restricted “library” of available solutions) may bias considerably the inference of source parameters. In complete generality, any point source deformation, including overpressure sources, may be described in terms of a suitable moment tensor, while the assumption of an overpressure source strongly restricts the variety of allowable moment tensors. In particular, by assuming a pressurized cavity, we rule out the possibility that either shear failure may precede magma emplacement (seismically induced intrusion) or may accompany it (mixed tensile and shear mode fracture). Another possibility is that a pre-existent weakness plane may be chosen by the ascending magma (fracture toughness heterogeneity). We perform joint inversion of levelling and EDM data (part of latter are unpublished), collected during the 1982-84 unrest at Campi Flegrei caldera: a 43% misfit reduction is obtained for a general moment source if the elastic heterogeneities computed from seismic tomography are accouted for. The inferred source is at 5.2 km depth but cannot be interpreted as a simple pressurized cavity. Moreover, if mass conservation is accounted for, magma emplaced within a shallow source must come from a (generally deeper) reservoir, which is usually assumed to be deep enough to be simply neglected. At Campi Flegrei, seismic tomography indicates that the “deep” magma source is rather shallow (at 7-8 km depth), so that its presence should be included in any thorough attempt to source modeling. Taking into account a deflating source at 7.5 km depth (represented either as a horizontal sill or as an isotropic cavity) and an inflating moment source, the fit of both levelling and EDM data improves further (misfit reduction 80%), but still the best fitting moment source (at 5.5 km depth) falls outside the range of pressurized ellipsoidal cavities. The shallow moment source may be decomposed in a tensile and a shear dislocation. No clue is obtained that the shear and the tensile mechanisms should be located in different positions. Our favourite interpretation is in terms of a crack opening in mixed tensile and shear mode, as would be provided by fluid magma unwelding pre-stressed solid rock. Although this decomposition of the source is not unique, the proposed solution is physically motivated by the minimum overpressure requirement. An important implication of this new interpretation is that the magma emplaced in the shallow moment source during the 1982-84 unrest was not added to already resident magma at the same position

A new interpretation of the 1982-84 unrest episode at Campi Flegrei caldera (Italy) by numerical inversion

The 1982-84 unrest episode at Campi Flegrei was characterized by huge deformation (about 1.8 m uplift) located inside the caldera and significant gravity variations correlated with the elevation changes (about -213 $\mu$Gal/m). Due to the bell shape of the uplift, the source is usually interpreted to have a fixed spherical shape. In the present study, we combine simple point source mechanisms (dipoles and double couples) to represent arbitrary sources such as sphere, ellipsoid or sill. The models are realized by Finite Element and the medium may be characterized by elastic heterogeneities. We study the deformation detected by leveling and EDM techniques by coupling the FE forward models with an inversion procedure. The potential point sources are contained in a volume of 8$\times$8$\times$8 km$^3$ located beneath Pozzuoli, the site of maximum displacement. We calculate the displacement field at each data point for each basic mechanism and we compare the result with the observed value. From the inversion of geodetic data we retrieve the best-fitting source parameters, without fixing the shape a priori. The best-fitting source is located beneath Pozzuoli at about 4.8 km b.s.l. and undergoes to horizontal compression and vertical dilatation

On deformation sources in volcanic areas: Modeling the Campi Flegrei (Italy) 1982–84 unrest

Deformation sources in volcanic areas are generally modeled in terms of pressurized tri-axial ellipsoids or pressurized cracks with simple geometrical shapes, embedded in a homogeneous half-space. However, the assumption of a particular source mechanism and the neglect of medium heterogeneities bias significantly the estimate of source parameters. A more general approach describes the deformation source in terms of a suitable moment tensor. Ratios between moment tensor eigenvalues are shown to provide a strong diagnostic tool for the physical interpretation of the deformation source and medium heterogeneities may be accounted for through 3D finite element computations. Leveling and EDM data, collected during the 1982–84 unrest episode at Campi Flegrei (Italy), are employed to retrieve the complete moment tensor according to a Bayesian inversion procedure, considering the heterogeneous elastic structure of the volcanic area. Best fitting moment tensors are found to be incompatible with any pressurized ellipsoid or crack. Taking into account the deflation of a deeper magma reservoir, which accompanies the inflation of a shallower source, data fit improves considerably but the retrieved moment tensor of the shallow source is found to be incompatible with pressurized ellipsoids, still. Looking for alternative physical models of the dislocation source, we find that the best fit moment tensor can be best interpreted in terms of a mixed mode (shear and tensile) dislocation at 5.5 km depth, striking EW and dipping by ~25°–30° to the North. Gravity changes are found to be compatible with the intrusion of ~60–70·10^6 m^3 of volatile rich magma with density ~2400 kg/m^3

Analytical and 3-D numerical modelling of Mt. Etna (Italy) volcano inflation

n/