Reply to “Comment on ‘Influence of Focal Mechanism in Probabilistic Seismic Hazard Analysis’ by Vincenzo Convertito and André Herrero,” by F. O. Strasser, V. Montaldo, J. Douglas, and J. J. Bommer

We thank F. O. Strasser, V. Montaldo, J. Douglas, and J. J. Bommer for the interest they have shown in our article (Convertito and Herrero, 2004). Strasser et al. (2006) present a critical comment of our work arguing that the solution proposed by Bommer et al. (2003) is a better solution. Note that the authors are nearly the same in both article and comment, except for V. Montaldo. Because this brief article is a reply, we will focus on the arguments directly concerning our article. The main objection supported by Strasser et al. (2006) is that the method we proposed is not appropriate to "styleof-faulting" correction. We completely agree with this assertion because it is simply not the scope of our article. We speak about "focal mechanism" intended as radiation pattern and nothing else. This point is clearly stated in the introduction of Convertito and Herrero (2004): "in this article we consider that the focal mechanism influence is only expressed by radiation pattern changes. In particular we do not consider any tectonic influence, stress drop variation or dynamic effects." The style-of-faulting parameter, even if its identity is blurred (e.g., Bommer et al., 2003), is an empirical definition of a complex set of physical conditions including the tectonic regime, the medium behavior, rock mechanics, rupture dynamics, and so on. In our opinion, the style of faulting is simply too complex to be used directly in our approach. Because the scope of our article is to show how it is possible to insert inside the main equation of probabilistic seismic-hazard analysis (PSHA; e.g., Cornell, 1968), simple physical parameters of the seismic source, that is, how it is possible to integrate deterministic parameters inside a probabilistic approach, we have chosen a small target, limiting ourselves only to the radiation pattern. We believe that the same approach can be used to insert many other parameters of the seismic source inside PSHA by using only a theoretical approach such as the fault strike (which has already been shown by Convertito, 2004), the directivity and stress drop. The second important argumentation is that a method based on regression (i.e., Bommer et al., 2003) is better than the method we propose. Once again we agree with Strasser et al. (2006) and this is clearly stated in the conclusion of our article: "when an attenuation law, including a faulting style parameter, is available for a given region, the use of this attenuation law gives a more reliable estimate of the hazard than the one obtained using the corrective coefficient we propose in this article.

Development of a site conditions map for the Campania-Lucania region (southern Apennines, Italy)

Having a reliable site conditions estimate is an important step to analyze and predict earthquake ground motions. To provide this information for the Campania-Lucania region (southern Apennines, Italy), in the framework of a collaboration with regional civil protection agency, geologic units shown on 1:250,000 scale geologic map, have been sorted together into four categories based on age and geological similarities. According to the site classification defined in engineering building codes, we have assigned to each site classes, a value or range of values of the average shear-wave velocity to 30 m (Vs30) and of the site dominant period. Thus, we have digitized the category boundaries from the map tracing only the geologic contacts that separate units of different site classes. The accuracy of the site-conditions map is only limited by the number of Vs profiles, used to compute the Vs30, and geologic data available so far. Analyses with new data will allow updates and modifications of this map. Anyhow, the resulting site classification map may be an helpful tool to better characterizing the sites effects for those applications where amplification values at large scale are need, such as ground-shaking maps or seismic hazard maps

Italian Map of Design Earthquakes from Multimodal Disaggregation Distributions: Preliminary Results.

Probabilistic seismic hazard analysis allows to calculate the mean annual rate of exceedance of ground motion intensity measures given the seismic sources the site of interest is subjected to. This piece of information may be used to define the design seismic action on structures. Moreover, through disaggregation of seismic hazard, it is possible to identify the earthquake giving the largest contribution to the hazard related to a specific IM value. Such an information may also be of useful to engineers in better defining the seismic treat for the structure of interest (e.g., in record selection for nonlinear seismic structural analysis). On the other hand, disaggregation results change with the spectral ordinate and return period, and more than a single event may dominate the hazard, especially if multiple sources affect the hazard at the site. In this work disaggregation for structural periods equal to 0 sec and 1.0 sec is presented for Italy, with reference to the hazard with a 475 year return period. It will be discussed how for the most of Italian sites more than a design earthquake exist, because of the modelling of seismic sources

Seismic hazard disaggregation in the Molise region, Italy: the case study of Campobasso

Large scale experimentations play a relevant role in the earthquake engineering research, similarly Structural Health Monitoring is able to give information of real structures. A few geotechnical structures are documented, because only data on seismic permanent deformations are available. The present paper deals with seismic hazard of the site of the Student House at University of Molise, where a geotechnical monitoring system has been designed and is currently under implementation. It is aimed at refining the seismic hazard characterization for identifying a set of relevant earthquakes for the theoretical analysis of the structure. Reference earthquakes expressed in terms of magnitude (M), distance (R) and ε, were therefore investigated. Uniform hazard spectra at different structural periods for a 475-year return period were disaggregated. Shapes of both the joint and marginal probability density functions were studied and the first two modes of M, R and ε were extracted and discussed

An Automated Method for Mapping Independent Spatial b Values

We present an automated method for mapping the b values. The algorithm is very simple and presents three advantages: (a) it does not requires any tuning of the parameters like, for instance, a fixed cell size or a maximum radius of the cell; (b) it implies a more appropriate use of the catalog, by using almost all the events in the catalog used (with a tolerance of 1%) with no overlap; (c) it implies the full independence of the b values, thus allowing the statistical comparison of the results using standard tests. Although the resulting b values are comparable with those obtained by applying the other methods of common use in seismology, these latter (a) leave out many earthquakes from the analysis, with loose of useful information, (b) produce diffuse cells overlapping aiming at reaching many cells of the grid in order to get the correct number of events in each cell, and (c) results in correlated b values, which do not allow the test of significance for the differences in the b values. Finally, due to the independence from any ad hoc a-priori choice, our method is suitable for automatic and operator-free procedures.Plain Language Summary The methods usually used in seismology for mapping the b value require the tuning of some parameters depending on the analyzed catalog. Here we propose a method that only implies the choice of the minimum number of earthquakes needed to obtain reliable b value estimates, which does not depend on the specific cases. Due to the mutual complete independence of the resulting b values, the proposed method allows the use of standard statistical tests to compare the results

Real-time risk analysis for hybrid earthquake early warning systems

Earthquake Early Warning Systems (EEWS), based on real-time prediction of ground motion or structural response measures, may play a role in reducing vulnerability and/or exposition of buildings and lifelines. In fact, recently seismologists developed efficient methods for rapid estimation of event features by means of limited information of the P-waves. Then, when an event is occurring, probabilistic distributions of magnitude and source-to-site distance are available and the prediction of the ground motion at the site, conditioned to the seismic network measures, may be performed in analogy with the Probabilistic Seismic Hazard Analysis (PSHA). Consequently the structural performance may be obtained by the Probabilistic Seismic Demand Analysis (PSDA), and used for real-time risk management purposes. However, such prediction is performed in very uncertain conditions which have to be taken into proper account to limit false and missed alarms. In the present study, real-time risk analysis for early warning purposes is discussed. The magnitude estimation is performed via the Bayesian approach, while the earthquake localization is based on the Voronoi cells. To test the procedure it was applied, by simulation, to the EEWS under development in the Campanian region (southern Italy). The results lead to the conclusion that the PSHA, conditioned to the EEWS, correctly predicts the hazard at the site and that the false/missed alarm probabilities may be controlled by set up of an appropriate decisional rule and alarm threshold

Temporal evolution of a seismic sequence induced by a gas injection in the Eastern coast of Spain

Induced seismicity associated with energy production is becoming an increasingly important issue worldwide for the hazard it poses to the exposed population and structures. We analyze one of the rare cases of induced seismicity associated with the underwater gas storage operations observed in the Castor platform, located in the Valencia gulf, east Spain, near a complex and important geological structure. In September 2013, some gas injection operations started at Castor, producing a series of seismic events around the reservoir area. The larger magnitude events (up to 4.2) took place some days after the end of the injection, with EMS intensities in coastal towns up to degree III. In this work, the seismic sequence is analyzed with the aim of detecting changes in statistical parameters describing the earthquake occurrence before and after the injection and identifying possible proxies to be used for monitoring the sequence evolution. Moreover, we explore the potential predictability of these statistical parameters which can be used to control the field operations in injection/storage fluid reservoirs. We firstly perform a retrospective approach and next a perspective analysis. We use different techniques for estimating the value of the expected maximum magnitude that can occur due to antropogenic activities in Castor.Published29012T. Sorgente SismicaJCR Journa

REAL-TIME HAZARD ANALYSIS FOR EARTHQUAKE EARLY WARNING

Earthquake Early Warning Systems (EEWS), based on real-time prediction of ground motion or structural response measures, may play a role in reducing vulnerability and/or exposition of buildings and lifelines. In fact, recently seismologists developed efficient methods for rapid estimation of event features by means of limited information of the P-waves. Then, when an event is occurring, probabilistic distributions of magnitude and source-to-site distance are available and the prediction of the ground motion at the site, conditioned to the seismic network measures, may be performed in analogy with the Probabilistic Seismic Hazard Analysis (PSHA). Consequently the structural performance may be obtained by the Probabilistic Seismic Demand Analysis (PSDA), and used for real-time risk management purposes. However, such prediction is performed in very uncertain conditions which have to be taken into proper account to limit false and missed alarms. In the present study, real-time risk analysis for early warning purposes is discussed. The magnitude estimation is performed via the Bayesian approach, while the earthquake localization is based on the Voronoi cells. To test the procedure it was applied, by simulation, to the EEWS under development in the Campanian region (southern Italy). The results lead to the conclusion that the PSHA, conditioned to the EEWS, correctly predicts the hazard at the site and that the false/missed alarm probabilities may be controlled by set up of an appropriate decisional rule and alarm threshold

Real-time risk analysis for hybrid earthquake early warning systems

Earthquake Early Warning Systems (EEWS), based on real-time prediction of ground motion or structural response measures, may play a role in reducing vulnerability and/or exposition of buildings and lifelines. In fact, recently seismologists developed efficient methods for rapid estimation of event features by means of limited information of the P-waves. Then, when an event is occurring, probabilistic distributions of magnitude and source-to-site distance are available and the prediction of the ground motion at the site, conditioned to the seismic network measures, may be performed in analogy with the Probabilistic Seismic Hazard Analysis (PSHA). Consequently the structural performance may be obtained by the Probabilistic Seismic Demand Analysis (PSDA), and used for real-time risk management purposes. However, such prediction is performed in very uncertain conditions which have to be taken into proper account to limit false and missed alarms. In the present study, real-time risk analysis for early warning purposes is discussed. The magnitude estimation is performed via the Bayesian approach, while the earthquake localization is based on the Voronoi cells. To test the procedure it was applied, by simulation, to the EEWS under development in the Campanian region (southern Italy). The results lead to the conclusion that the PSHA, conditioned to the EEWS, correctly predicts the hazard at the site and that the false/missed alarm probabilities may be controlled by set up of an appropriate decisional rule and alarm threshold

Mechanical Systems: Symmetry and Reduction

Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems