H2 regularity for the p(x)-Laplacian in two-dimensional convex domains

In this paper we study the H2 global regularity for solutions of the p(x)-Laplacian in two-dimensional convex domains with Dirichlet boundary conditions. Here p:Ω→[p1, ∞) with p∈Lip(Ω-) and p1>1. © 2013 Elsevier Inc.Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Interior penalty discontinuous Galerkin FEM for the p(x)p(x)-Laplacian

In this paper we construct an "Interior Penalty" Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)-$Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log H\"{o}lder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the Conforming Galerkin Method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.Comment: 26 pages, 2 figure

Wood Anderson Magnitude Scale for Mt. Vesuvius

A Mathcad-8 program to calculate a revised magnitude scale is presented. An application to Mt. Vesuvius is included as a program test. Wood-Anderson seismograms for 131 local earthquakes recorded at station BKE (Osservatorio Vesuviano seismic network) were synthesized to estimate local magnitude from the original definition: Ml=log Amax(D) - logAo(D) The distance correction logAo(D) was empirically determined simulating a wave packet which propagates in a structure with assigned Q. Moment magnitude (calculated both with Kanamori and Tatcher-Hanks formulas) was also determined from the displacement spectra. Finally a relation between Wood-Anderson magnitude and duration magnitude was derived, allowing the estimate of local magnitude from the duration of the earthquake

Re-calibration of the magnitude scales at Campi Flegrei, Italy, on the basis of measured path and site and transfer functions

The quantification of the seismic energy of earthquakes occurring in volcanic regions is of great importance in order to better understand the dynamics of the volcano. The amount of the released energy and its variation during seismic crises can be considered as an indicator of the source processes acting inside the volcano. In this context, the effect of the propagation in attenuative media should be considered to correct for path effects and to properly estimate the seismic energy released at the source. Moreover, in order to allow a comparison with the dynamic processes occurring in different volcanic areas, the use of magnitude scales as homogeneous as possible is strongly recommended, In this framework, new duration-based Local (Ml) and Moment (Mw) magnitude scales are obtained for the Campi Flegrei area (southern Italy), by analysing a data-set of local volcano-tectonic earthquakes. First the S-wave quality factor for the investigated area was experimentally calculated and then the distance-correction curve, logA0(r), to be used in the Richter formula Ml = logAmax − logA0(r), was numerically estimated by measuring the attenuation properties and hence propagating a synthetic S-wave-packet in the earth medium. The Local magnitude scale was normalized in order to fit the Richter formula valid for Southern California at a distance of 10 km. Ml magnitude was estimated by synthesizing Wood-Anderson seismograms and measuring the maximum amplitude. For the same data-set, Moment magnitude from S-wave distance and site corrected displacement spectra was obtained. Comparisons between Local and Moment magnitudes determined in the present paper, and the old Duration magnitude (Md) routinely used at the Istituto Nazionale di Geofisica e Vulcanologia - Osservatorio Vesuviano are presented. Moreover, relationships between Ml and Mw calculated for two reference sites are also derived

Seismic Q estimates in Umbria-Marche (central Italy): hints for the retrieval of a new attenuation law for seismic risk

In the Umbria Marche (Central Italy) region an important earthquake sequence occurred in 1997, characterized by nine earthquakes with magnitudes in the range between 5 and 6, that caused important damages and causalities. In the present paper we separately estimate intrinsic- and scattering- Q −1 parameters, using the classical MLTWA approach in the assumption of a half space model. The results clearly show that the attenuation parameters Qi −1 and Qs −1 are frequency dependent. This estimate is compared with other attenuation studies carried out in the same area, and with all the other MLTWA estimates obtained till now in other tectonic environments in the Earth. The bias introduced by the half space assumption is investigated through numerical solutions of the Energy Transport equation in the more realistic assumption of a heterogeneous crust overlying a transparent mantle, with a Moho located at a depth ranging between 35 and 45 km below the surface. The bias introduced by the half space assumption is significant only at high frequency. We finally show how the attenuation estimates, calculated with different techniques, lead to different PGA decay with distance relationships, using the well known and well proven Boore’s method. This last result indicates that care must be used in selecting the correct estimate of the attenuation parameters for seismic risk purposes. We also discuss the reason why MLTWA may be chosen among all the other available techniques, due to its intrinsic stability, to obtain the right attenuation parameters

Recalibration of the Magnitude Scales at Campi Flegrei, Italy, on the Basis of Measured Path and Site and Transfer Functions

New duration-based local (ML) and moment (Mw) magnitude scales are obtained for the Campi Flegrei area through analysis of a dataset of local volcanotectonic earthquakes. First, the S-wave quality factor for the investigated area was experimentally calculated, and then the distance-correction curve, log A0(r), to be used in the Richter formula ML = log Amax − log A0(r), was numerically estimated by measuring the attenuation properties and, hence, propagating a synthetic S-wave packet in the earth medium. The local magnitude scale was normalized to fit the Richter formula that was valid for Southern California at a distance of 10 km. ML was estimated by synthesizing Wood–Anderson seismograms and measuring the maximum amplitude. For the same dataset, the moment magnitude was obtained from S-wave distance-corrected and site-corrected displacement spectra. Comparisons between local and moment magnitudes determined, along with the old duration magnitude (MD) routinely used at the Istituto Nazionale di Geofisica e Vulcanologia– Osservatorio Vesuviano, are presented and discussed. Moreover, the relationships between ML and Mw calculated for two reference sites are also derived

The first Long Period earthquake detected in the background seismicity at Mt. Vesuvius

The typical earthquakes occurring at Mt. Vesuvius are Volcano-Tectonic. On July 20, 2003, an unusual earthquake with low and narrow frequency content was detected. The seismograms presented an emergent onset and a nearly monochromatic spectrum at all stations of the Osservatorio Vesuviano(Istituto Nazionale di Geofisica e Vulcanologia) seismic network. The event was located at about 4 km b.s.l. close to the crater axis and an equivalent duration magnitude of 0.6 was estimated. The nature of this event was investigated by comparing its features with those of two typical Volcano-Tectonic earthquakes occurred inside the same source volume. We compared the spectral content calculating the spectrograms and the coda patterns using the Hilbert Transform. A Seismic Moment Tensor inversion was performed on the low frequency earthquake. The focal mechanisms for the two Volcano-Tectonic earthquakes were estimated with a classical technique and resulted compatible with the stress field acting on the volcano. Taking into account the clear differences with the typical Volcano-Tectonic events as well as the peculiarities retrieved from our analyses (monochromatic, low frequency spectral content, and sustained coda) and also some geochemical observations, we classify the unusual low frequency seismic event detected at Mt. Vesuvius as Long Period earthquake and propose that its origin could be linked to a pressure drop in the deep hydrothermal system

New insights into Mt. Vesuvius hydrothermal system and its dynamic based on a critical review of seismic tomography and geochemical features

The seismic velocity and attenuation tomography images, calculated inverting respectively P-wave travel times and amplitude spectra of local VT quakes at Mt. Vesuvius have been reviewed and graphically represented using a new software recently developed using Mathematica8TM. The 3-D plots of the interpolated velocity and attenuation fields obtained through this software evidence low-velocity volumes associated with high attenuation anomalies in the depth range from about 1 km to 3 km below the sea level. The heterogeneity in the distribution of the velocity and attenuation values increases in the volume centred around the crater axis and laterally extended about 4 km, where the geochemical interpretation of the data from fumarole emissions reveals the presence of a hydrothermal system with temperatures as high as 400-450°C roughly in the same depth range (1.5 km to 4 km). The zone where the hydrothermal system is space-confined possibly hosted the residual magma erupted by Mt. Vesuvius during the recent eruptions, and is the site where most of the seismic energy release has occurred since the last 1944 eruption

Automatic Classification of Seismic Signals at Mt. Vesuvius Volcano, Italy, Using Neural Networks

We present a new strategy for reliable automatic classification of local seismic signals and volcano-tectonic earthquakes (VT). The method is based on a supervised neural network in which a new approach for feature extraction from short period seismic signals is applied. To reduce the number of records required for the analysis we set up a specialized neural classifier, able to distinguish two classes of signals, for each of the selected stations. The neural network architecture is a multilayer perceptron (MLP) with a single hidden layer. Spectral features of the signals and the parameterized attributes of their waveform have been used as input for this network. Feature extraction is done by using both the linear predictor coding technique for computing the spectrograms, and a function of the amplitude for characterizing waveforms. Compared to strategies that use only spectral signatures, the inclusion of properly normalized amplitude features improves the performance of the classifiers, and allows the network to better generalize. To train the MLP network we compared the performance of the quasi-Newton algorithm with the scaled conjugate gradient method. We found that the scaled conjugate gradient approach is the faster of the two, with quite equally good performance. Our method was tested on a dataset recorded by four selected stations of the Mt. Vesuvius monitoring network, for the discrimination of low magnitude VT events and transient signals caused by either artificial (quarry blasts, underwater explosions) and natural (thunder) sources. In this test application we obtained 100% correct classification for one of the possible pairs of signal types (VT versus quarry blasts). Because this method was developed independently of this particular discrimination task, it can be applied to a broad range of other applications

Wiggle-Match dating of wooden samples from iron age sites in Northern Italy

Archaeological excavations carried out at the sites of Laion/Lajen (Bolzano/Bozen) and Stufles-Oberegger (Bressanone/Brixen) in northern Italy uncovered well-preserved wooden samples in cultural layers archaeologically dated to the Iron Age. From the 2 sites, different wooden samples were recovered that were well preserved enough to allow clear identification of the tree species and of the ring structure. Among the different wooden samples, 2 were selected for radiocarbon analyses: from Laion/Lajen, a beam with an unbroken sequence of 158 rings; from Stufles-Oberegger, a combusted trunk with a sequence of 217 rings. Both samples were identified as Larix decidua species. From each sequence, single rings were selected and submitted for accelerator mass spectrometry (AMS) 14C dating analysis at CEDAD. Conventional 14C ages were then calibrated to calendar ages using the IntCal04 atmospheric data set, while the statistical constraints resulting from the defined ring sequence were used to develop a wiggle-matching approach by making use of the Bayesian analysis functions available in OxCal. The obtained results are an important contribution in refining the chronology of the studied sites