Analysis of macroseismic fields using statistical data depth functions: considerations leading to attenuation probabilistic modelling

Modelling seismic attenuation is one of the most critical points in the hazard assessment process. In this article we consider the spatial distribution of the effects caused by an earthquake as expressed by the values of the macroseismic intensity recorded at various locations surrounding the epicentre. Considering the ordinal nature of the intensity, a way to show its decay with distance is to draw curves—isoseismal lines—on maps, which bound points of intensity not smaller than a fixed value. These lines usually take the form of closed and nested curves around the epicentre, with highly different shapes because of the effects of ground conditions and of complexities in rupture propagation. Forecasting seismic attenuation of future earthquakes requires stochastic modelling of the decay on the basis of a common spatial pattern. The aim of this study is to consider a statistical methodology that identifies a general shape, if it exists, for isoseismal lines of a set of macroseismic fields. Data depth is a general nonparametric method for analysis of probability distributions and datasets. It has arisen as a statistical method to order points of a multivariate space, e.g., Euclidean space \({\mathbb {R}}^{p}\), \(p \ge 1\), according to the centrality with respect to a distribution or a given data cloud. Recently, this method has been extended to the ordering of functions and trajectories. In our case, for a fixed intensity decay \(\varDelta I\), we build a set of convex hulls that enclose the sites of felt intensity \(I_s \ge I_0 -\varDelta I\), one for each macroseismic field of a set of earthquakes that are considered as similar from the attenuation point of view. By applying data depth functions to this functional dataset, it is possible to identify the most central curve, i.e., the attenuation pattern, and to consider other properties like variability, outlyingness, and possible clustering of such curves. Results are shown for earthquakes that occurred on the Central Po Plain in May 2012, and on the eastern flank of Mt. Etna since 1865.     

On unstable ship motions resulting from strong non-linear coupling

In this paper, the modelling of strong parametric resonance in head seas is investigated. Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are contemplated. A third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are analytically derived in terms of hull form characteristics.The main theoretical aspects of the new model are discussed. Numerical simulations obtained from the derived third-order non-linear mathematical model are compared to experimental results, corresponding to excessive motions of the model of a transom stern fishing vessel in head seas. It is shown that this enhanced model gives very realistic results and a much better comparison with the experiments than a second-order model.     

In situ Re–Os isotopic analysis of platinum-group minerals from the Mayarí-Cristal ophiolitic massif (Mayarí-Baracoa Ophiolitic Belt,eastern Cuba): implications for the origin of Os-isotope heterogeneities in podiform chromitites

Chromitite pods in the Mayarí-Cristal ophiolitic massif (eastern Cuba) were formed in the Late Cretaceous when island arc tholeiites and MORB-like back-arc basin basalts reacted with residual mantle peridotites and generated chromite-rich bodies enclosed in dunite envelopes. Platinum-group minerals (PGM) in the podiform chromitites exhibit important Os-isotope heterogeneities at the kilometric, hand sample and thin section scales. ¹⁸⁷Os/¹⁸⁸Os calculated at the time of chromitite crystallization (~90 Ma) ranges between 0.1185 and 0.1295 (γOs = −7.1 to +1.6, relative to enstatite chondrite), and all but one PGM have subchondritic ¹⁸⁷Os/¹⁸⁸Os. Grains in a single hand sample have initial ¹⁸⁷Os/¹⁸⁸Os that spans from 0.1185 to 0.1274, and in one thin section it varies between 0.1185 and 0.1232 in two PGM included in chromite which are only several millimeters apart. As the Os budget of a single micrometric grain derives from a mantle region that was at least several m³ in size, the variable Os isotopic composition of PGM in the Mayarí-Cristal chromitites probably reflects the heterogeneity of their mantle sources on the 10–100 m scale. Our results show that this heterogeneity was not erased by pooling and mingling of individual melt batches during chromitite crystallization but was transferred to the ore deposits on mineral scale. The distribution of the Os model ages calculated for PGM shows four main peaks, at ~100, 500, 750 and 1,000 Ma. These variable Os model ages reflect the presence of different depleted domains in the oceanic (Pacific-related) upper mantle of the Greater Antilles paleo-subduction zone. The concordance between the age of crystallization of the Mayarí-Cristal chromitites and the most recent peak of the Os model age distribution in PGM supports that Os in several grains was derived from fertile domains of the upper mantle, whose bulk Os isotopic composition is best approximated by that of enstatite chondrites; on the other hand, most PGM are crystallized by melts that tapped highly refractory mantle sources.     

Precipitable water evaluations from infrared sun‐photometric measurements analyzed using the atmospheric hygrometry technique

Measurements of direct solar irradiance were taken employing 4 different sun‐photometers at near infrared wavelengths, suitable for use in atmospheric hygrometry. This technique utilising a set of spectral ratios, in and out of selected water vapour absorption bands, was applied to the measurements to obtain accurate evaluations of precipitable water. For all the hygrometric ratios given by the 4 sun‐photometers used at the 3 stations of Sagres, Monchique and Mt. Foia, during the CLEARCOLUMN experiment, we determined the calibration curves by correcting them for the Rayleigh scattering effects and, then, plotting the natural logarithms of such corrected ratios versus the square root of the water vapour mass present along the atmospheric slant path. The regression lines drawn for the various scatter diagrams were estimated to give evaluations of precipitable water with an uncertainty of less than 5%, 3% and 10% at the 3 stations, respectively. The calibration curves of the sun‐photometer located at the Sagres station were determined using the precipitable water evaluations obtained from the local radiosounding measurements taken on 5 clear‐sky days. Those of the sun‐photometers used at the Monchique and Mt. Foia stations were instead determined through intercomparison between subsets of measurements simultaneously taken with various instruments at Sagres and Mt. Foia. Using these calibration curves, we examined all the field measurements determining the time‐patterns of precipitable water at the 3 stations. During the period from 16 June to 25 July 1997, precipitable water was found to vary between 1.1 and 3.7 g cm⁻² at the Sagres station (with an accuracy within ±13%), between 1.0 and 2.8 g cm⁻² at Monchique (±11%) and between 0.8 and 3.0 g cm⁻² at the top of Mt. Foia (±26%).     

The distribution of C2S and NH3 in two Bok globules at different evolutionary stages: CB246 and CB34

Two Bok globules, L1253 (CB246) and CB34, have been mapped in the C₂S (2₁–1₀) transition and in the NH₃ (1, 1) and NH₃ (2, 2) inversion transitions, respectively. By comparing the C₂S map of L1253 (CB246) with the NH₃ map of the same globule from Lemme et al., a clumped onion structure results as a consequence of the chemical and dynamical evolution of the object. From the derived parameters it appears that both L1253 (CB246) and CB34 are close to virial equilibrium.     

On the water vapour absorption in the 8–13 μm spectral region for different atmospheric conditions

Experimental measurements of the absorption coefficient of atmospheric water vapour, at wavelengths between 8 and 13 m, are examined on the basis of atmospheric models describing the meteorological conditions of the observed atmospheres to obtain estimates of the foreign-broadening absorption coefficient for homogeneous paths. The results show that the variable contribution given by unresolved lines predominates on the continuum term due to wing effects of remote lines, even for rather high spectral resolutions.Associated with estimates of the self-broadening absorption coefficient, as proposed byRoberts et al. (1976), these data are applied to a wide set of atmospheric models, corresponding to various latitudes and seasons, indicating that the two components of the atmospheric absorption coefficient are closely related to the surface temperature. Because of the variable weights given by foreign- and self-broadening terms, the atmospheric absorption coefficient turns out to increase with the surface temperature with different rates at various wavelengths.     

Fault‐controlled dolomite bodies as palaeotectonic indicators and geofluid reservoirs: New insights from Gargano Promontory outcrops

The Upper Jurassic to Lower Cretaceous platform‐slope to basinal carbonate strata cropping out in Gargano Promontory (southern Italy) are partly dolomitized. Fieldwork and laboratory analyses (petrographic, petrophysical and geochemical) allowed the characterization of the dolomite bodies with respect to their distribution within the carbonate succession, their dimensions, geometries, textural variability, chemical stability, age, porosity, genetic mechanisms and relation with tectonics. The dolomite bodies range from metres to kilometres in size, are fault‐related and fracture‐related, and probably formed during the Early Cretaceous at <500 m burial depths and temperatures <50°C. The proposed dolomitization model relies on mobilization of Early Cretaceous seawater that flowed, downward and then upward, along faults and fractures and was modified in its isotopic composition moving through Triassic and Jurassic strata that underlie the studied dolomitized succession. Despite the numerous cases reported in literature, this study demonstrates that hydrothermal and/or high‐temperature fluids are not necessarily required for fault‐controlled dolomitization. Distribution and geometries of dolomite bodies can be used for palaeotectonic reconstructions, as they partly record the characteristics (size, attitude and kinematics) of the palaeo‐faults, even if not preserved, that controlled dolomitization. In Gargano Promontory, dolomites record Early Cretaceous palaeo‐faults from metres to kilometres long, striking north‐west/south‐east to east/west and characterized by normal to strike‐slip kinematics. Dolomitization increases the matrix porosity by up to 7% and, therefore, can improve the geofluid storage capacity of tight, platform‐slope to basinal limestones. The results have a great significance for characterization of geofluid (for example, hydrocarbons) reservoirs hosted in similar dolomitized carbonate successions. Distribution, size and shapes of reservoir rocks (i.e. dolomite bodies) could be broadly predictable if the characteristics of the palaeo‐fault system present at the time of dolomitization are known.     

Identification of source of a marine oil-spill using geochemical and chemometric techniques

The current work aimed to identify the source of an oil spill off the coast of Maranhão, Brazil, in September 2005 and effect a preliminary geochemical survey of this environment. A combination of bulk analytical parameters, such as carbon isotope (δ¹³C) and Ni/V ratios, and conventional fingerprinting methods (High Resolution Gas Chromatography and Mass Spectrometry) were used. The use of bulk methods greatly speeded source identification for this relatively unaltered spill: identification of the likely source was possible at this stage. Subsequent fingerprinting of biomarker distributions supported source assignment, pointing to a non-Brazilian oil. Steranes proved the most useful biomarkers for sample correlation in this work. Distribution patterns of environmentally more resilient compound types, such as certain aromatic structures, proved inconclusive for correlation, probably in view of their presence in the background.     

A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil

A constitutive model for granular materials is developed within the framework of strain–hardening elastoplasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution. The effects of these irreversible microscopic processes are described macroscopically as accumulated plastic strain. Plastic strain drives the evolution of internal variables which model phenomenologically the changes of mechanical properties induced by grain crushing by controlling the geometry of the yield locus and the direction of plastic flow. An application of the model to Pozzolana Nera is presented. The stress–dilatancy relationship observed for this material is used as a guidance for the formulation of hardening laws. One of the salient features of the proposed model is its capability of reproducing the stress–dilatancy behaviour observed in Pozzolana Nera, for which the minimum value of dilatancy always follows the maximum stress ratio experienced by the material. Copyright © 2002 John Wiley & Sons, Ltd.