On estimating frequency-magnitude relations from heterogeneous catalogs

The paper studies the effect of magnitude errors on heterogeneous catalogs, by applying the apparent magnitude theory (seeTinti andMulargia, 1985a), which proves to be the most natural and rigorous approach to the problem. Heterogeneities in seismic catalogs are due to a number of various sources and affect both instrumental as well as noninstrumental earthquake compilations.The most frequent basis of heterogeneity is certainly that the recent instrumental records are to be combined with the historic and prehistoric event listings to secure a time coverage, considerably longer than the recurrence time of the major earthquakes. Therefore the case which attracts the greatest attention in the present analysis is that of a catalog consisting of a subset of higher quality data, generallyS ₁, spanning the interval T ₁ (the instrumental catalog), and of a second subset of more uncertain magnitude determination, generallyS ₂, covering a vastly longer interval T ₂ (the historic and/or the geologic catalog). The magnitude threshold of the subcatalogS ₁ is supposedly smaller than that ofS ₂, which, as we will see, is one of the major causes of discrepancy between the apparent magnitude and the true magnitude distributions. We will further suppose that true magnitude occurrences conform to theGutenberg-Richter (GR) law, because the assumption simplified the analysis without reducing the relevancy of our findings.The main results are: 1) the apparent occurrence rate exceeds the true occurrence rate from a certain magnitude onward, saym _GR; 2) the apparent occurrence rate shows two distinct GR regimes separated by an intermediate transition region. The offset between the two regimes is the essential outcome ofS ₁ being heterogeneous with respect toS ₂. The most important consequences of this study are that: 1) it provides a basis to infer the parameters of the true magnitude distribution, by correcting the bias deriving from heterogeneous magnitude errors; 2) it demonstrates that the double GR decay, that several authors have taken as the incontestable proof of the failure of the GR law and of the experimental evidence of the characteristic earthquake theory, is instead perfectly consistent with a GR-type seismicity.     

Magnetic properties and cation ordering of nanopowders of the synthetic analogue of kuramite, Cu3SnS4

An extensive characterisation of the magnetic properties of synthetic powders of kuramite, with formal composition Cu₃SnS₄, was performed. Powders were investigated through superconducting quantum interference device (SQUID) magnetometry, electron paramagnetic resonance (EPR) spectroscopy, X-ray powder diffraction (XRPD), scanning and transmission electron microscopies (SEM and TEM) and microanalysis. SEM and TEM reveal the presence of nanodimensioned particles. XRPD clearly shows that Cu₃SnS₄ crystallised in a cubic sphalerite-type structural model, in spite of the stannite-type tetragonal structure described for the natural phase. This difference arises from a full random distribution of cations. Synthetic kuramite nanopowders exhibit a marked paramagnetism, originated by the presence of Cu(II), definitely assessed by EPR measurements. Moreover, the overall magnetic behaviour of the sample cannot be simply ascribed to diluted paramagnetism, and this suggests the presence of strong superexchange interactions among Cu(II) ions even at room temperature. The main consequences of these results are the definitive assessment of the chemical formula Cu(I)₂Cu(II)SnS₄ and of a random distribution of Cu(II), Cu(I) and Sn(IV) ions within the available tetrahedral sites.     

Wavefield Migration plus Monte Carlo Imaging of 3D Prestack Seismic Data

Prestack wave‐equation migration has proved to be a very accurate shot‐by‐shot imaging tool. However, 3D imaging with this technique of a large field acquisition, especially one with hundreds of thousands of shots, is prohibitively costly. Simply adapting the technique to migrate many superposed shot‐gathers simultaneously would render 3D wavefield prestack migration cost‐effective but it introduces uncontrolled non‐physical interference among the shot‐gathers, making the final image useless. However, it has been observed that multishot signal interference can be kept under some control by averaging over many such images, if each multishot migration is modified by a random phase encoding of the frequency spectra of the seismic traces. In this article, we analyse this technique, giving a theoretical basis for its observed behaviour: that the error of the image produced by averaging over M phase encoded migrations decreases as M^?1 . Furthermore, we expand the technique and define a general class of Monte‐Carlo encoding methods for which the noise variance of the average imaging condition decreases as M^?1 ; these methods thus all converge asymptotically to the correct reflectivity map, without generating prohibitive costs. The theoretical asymptotic behaviour is illustrated for three such methods on a 2D test case. Numerical verification in 3D is then presented for one such method implemented with a 3D PSPI extrapolation kernel for two test cases: the SEG–EAGE salt model and a real test constructed from field data.     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

A numerical Round Robin on tunnels under seismic actions

Although the seismic behaviour of shallow circular tunnels in soft ground is generally safer than aboveground structures, some tunnels were recently damaged during earthquakes. In some cases, damage was associated with strong ground shaking and site amplification, which increased the stress level in the tunnel lining. Pseudo-static and simplified dynamic analyses enable to assess transient changes in internal forces during shaking. Nevertheless, experimental evidences of permanent changes in internal loads in the tunnel lining would suggest that a full dynamic analysis including plastic soil behaviour should be performed when modelling the dynamic interaction between the tunnel and the ground. While sophisticated numerical methods can be used to predict seismic internal forces on tunnel structures during earthquakes, the accuracy of their predictions should be validated against field measurements, but the latter are seldom available. A series of centrifuge tests were therefore carried out at the University of Cambridge (UK) on tunnel models in sand, in the framework of a research project funded by the Italian Civil Protection Department. A numerical Round Robin on Tunnel Tests was later promoted among some research groups to predict the observed behaviour by means of numerical modelling. In this paper, the main results of five selected numerical predictions are summarized and compared with the experimental results.     

How natural are Alpine mountain rivers? Evidence from the Italian Alps

Historical, human‐induced channel adjustments in lowland gravel‐bed rivers have been documented in several geographical contexts worldwide. In particular, it is now widely accepted that the vast majority of European rivers are far from any natural, reference state prior to anthropic disturbances, and a ‘complete’ restoration is hardly achievable. However, few investigations have addressed changes that have occurred in mountain rivers of the Alps, and these channels are commonly reckoned quite ‘natural’ by society. This paper intends to describe how human pressure on Italian Alpine basins has been quite relevant for several centuries – in terms of land‐use variations, in‐channel structures, timber transport (splash damming) and riparian vegetation management – such that nowadays ‘reference conditions’ cannot be found even in small mountain creeks. In addition, recent natural climatic variations (e.g. the Little Ice Age) are superimposed on human disturbances, thus defying the definition of any ‘equilibrium’ morphological conditions even under ‘human‐free’ states. A summary of published as well as unpublished works on historical channel adjustments in rivers of the Italian Alps is presented in order to document the impacts deriving from human pressure at different basin scales and for different river morphologies, from steep confined streams to large unconfined rivers. General options for river management and restoration actions aiming to combine geomorphological functionality and flood hazard mitigation are discussed, in the light of the current European legislative context. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparing efficacy of different taxonomic resolutions and surrogates in detecting changes in soft bottom assemblages due to coastal defence structures

Sandy shores on the West coast of the North Adriatic Sea are extensively protected by different types of defence structures to prevent coastal erosion. Coastal defence schemes modify the hydrodynamic regime, the sediment structure and composition thus affecting the benthic assemblages. This study examines the effectiveness in detecting changes in soft bottom assemblages caused by coastal defence structures by using different levels of taxonomic resolution, polychaetes and/or bivalves as surrogates and different data transformations. A synoptic analyses of three datasets of subtidal benthic macrofauna used in studies aimed at assessing the impact of breakwaters along the North Adriatic coast has been done. Analyses of similarities and correlations between distance matrices were done using matrices with different levels of taxonomic resolution, and with polychaetes or bivalves data alone. Lentidium mediterraneum was the most abundant species in all datasets. Its abundance was not consistently related to the presence of defence structures. Moreover, distribution patterns of L. mediterraneum were masking the structure of the whole macrofaunal assemblages. Removal of L. mediterraneum from the datasets allowed the detection of changes in benthic assemblages due to coastal defences. Analyses on different levels of taxonomic resolution showed that the level of family maintained sufficient information to detect the impacts of coastal defence structures on benthic assemblages. Moreover, the outcomes depended on the transformation used. Patterns of distribution of bivalves, used as surrogates, showed low correlations with the patterns of the total macrofaunal species assemblages. Patterns of polychaetes, if identified to the species or genus level showed higher correlations with the whole dataset. However, the identification of polychaetes to species and genus level is as costly as the identification of all macrobenthic taxa at family level.This study provided additional evidences that taxonomic sufficiency is a useful tool in environmental monitoring, also in investigations on the impacts of coastal defence structures on subtidal macrofauna. The use of coarser taxonomic level, being time-efficient, would allow improving sampling designs of monitoring programs by increasing replication in space and time and by allowing long term monitoring studies.     

Under the surface: Pressure-induced planetary-scale waves,volcanic lightning,and gaseous clouds caused by the submarine eruption of Hunga Tonga-Hunga Ha'apai volcano

We present a narrative of the eruptive events culminating in the cataclysmic January 15, 2022 eruption of Hunga Tonga-Hunga Ha'apai Volcano by synthesizing diverse preliminary seismic, volcanological, sound wave, and lightning data available within the first few weeks after the eruption occurred. The first hour of eruptive activity produced fast-propagating tsunami waves, long-period seismic waves, loud audible sound waves, infrasonic waves, exceptionally intense volcanic lightning and an unsteady volcanic plume that transiently reached—at 58 ?km—the Earth's mesosphere. Energetic seismic signals were recorded worldwide and the globally stacked seismogram showed episodic seismic events within the most intense periods of phreatoplinian activity, and they correlated well with the infrasound pressure waveform recorded in Fiji. Gravity wave signals were strong enough to be observed over the entire planet in just the first few hours, with some circling the Earth multiple times subsequently. These large-amplitude, long-wavelength atmospheric disturbances come from the Earth's atmosphere being forced by the magmatic mixture of tephra, melt and gasses emitted by the unsteady but quasi-continuous eruption from 0402±1–1800 UTC on January 15, 2022. Atmospheric forcing lasted much longer than rupturing from large earthquakes recorded on modern instruments, producing a type of shock wave that originated from the interaction between compressed air and ambient (wavy) sea surface. This scenario differs from conventional ideas of earthquake slip, landslides, or caldera collapse-generated tsunami waves because of the enormous (～1000x) volumetric change due to the supercritical nature of volatiles associated with the hot, volatile-rich phreatoplinian plume. The time series of plume altitude can be translated to volumetric discharge and mass flow rate. For an eruption duration of ～12 ?h, the eruptive volume and mass are estimated at 1.9 ?km³ and ～2 900 ?Tg, respectively, corresponding to a VEI of 5–6 for this event. The high frequency and intensity of lightning was enhanced by the production of fine ash due to magma—seawater interaction with concomitant high charge per unit mass and the high pre-eruptive concentration of dissolved volatiles. Analysis of lightning flash frequencies provides a rapid metric for plume activity and eruption magnitude. Many aspects of this eruption await further investigation by multidisciplinary teams. It represents a unique opportunity for fundamental research regarding the complex, non-linear behavior of high energetic volcanic eruptions and attendant phenomena, with critical implications for hazard mitigation, volcano forecasting, and first-response efforts in future disasters.