By using standard calculus, we discuss some definitions and properties of finite-part integrals, point out the essence of this concept and show how these integrals naturally arise in some integral ...equation applications. A couple of new examples are also described.
We consider wave propagation problems in 2D unbounded isotropic homogeneous elastic media, with rigid boundary conditions. For their solution, we propose and compare two alternative numerical ...approaches, both obtained by coupling the differential equation with the associated space-time boundary integral equation. The latter is defined on an artificial boundary, chosen to surround the (bounded) exterior computational domain of interest. The integral equation defines a boundary condition which is non-reflecting for incoming and also for outgoing waves.
In both approaches, the differential equations are discretized by applying a finite element method combined with the Crank Nicolson time marching scheme, while the discretization of the integral equation is obtained by coupling a time convolution quadrature with a space collocation boundary element method. The construction of the two approaches is described and discussed. Some numerical tests are also presented.
We consider (transient) 3D elastic wave propagation problems in unbounded isotropic homogeneous media, which can be reduced to corresponding 2D ones. For their solution, we propose and compare two ...boundary integral equation approaches, both based on the coupling of a discrete time convolution quadrature with a classical space collocation discretization. In the first approach, the PDE problem is preliminarily replaced by the equivalent well known (vector) space–time boundary integral equation formulation, while in the second, the same PDE is replaced by a system of two (coupled) wave equations, each one of which is then represented by the associated boundary integral equation. The construction of these two approaches is described and discussed. Some numerical testing are also presented.
The geological map of Piemonte Region (Italy) is a graphic representation of the geology of the region, grounded on a large geodatabase, that can be also browsed as an interactive scalable map ...(GeoPiemonte Map) using a WebGIS application. The Map, produced at 1:250,000 scale, is the first original release of the 'GeoPiemonte Map' project. The geological data represented on the map derive from a thorough revision of available geological maps and literature, integrated with unpublished original data. The revision and harmonisation of existing and new data have been based on explicit criteria used for the classification of geologic units and their representation on the Map. These criteria firstly aimed at providing a lithostratigraphic, hierarchic subdivision of Piemonte geologic units and describing them using shared concepts and vocabularies, consistent with IUGS Descriptive Standards for the Geosciences.
•New chemical and isotopic characterization of Lessian's thermal districts is provided.•The hydrogeochemistry approach used identify main active physico-chemical processes.•New geothermometric ...estimations for the studied thermal waters are carried out.•The depths reached by thermal waters are estimated by geochemical data elaboration.•The geochemical model agree with evidences from geological and structural data.
The Po Plain, located in northern Italy between the Alps and the Apennines, hosts several thermal water spots. Some of these thermal waters belong to the thermal districts of Brescia and Verona provinces. This thermalism has been used for therapeutical purposes since the “Roman Age”. During Sept. 2014 - Aug. 2015, a detailed sampling program was carried out to collect water samples of thermal and cold waters in the Lessini Mountain's thermal area, including those in the Sirmione thermal district (project area). Assessment of water chemistry and isotope data, identified distinctive characteristics of thermal waters belonging to the thermal districts investigated in this project (i.e. Caldiero, S.Ambrogio Valpolicella, Colà di Lazise, Lazise and Sirmione). In particular, data show that the Sirmione thermal waters are characterized by a higher temperature and a total salinity and by chemical and isotopic fingerprints that are distinct and unrelated to those of other thermal waters. On the other hand, the data indicate potential correlations between samples from S.Ambrogio Valpolicella and Colà di Lazise and local cold water. Geochemical modeling conducted using PHREEQC, showed that a mixing accompanied by calcite precipitation can explain the chemical characteristics observed in the thermal waters and some cold springs assessed in this project. New geothermometric estimations were performed for main thermal components, obtaining temperature ranges (in°C) of about 92–99, 67–74 and 51–58, respectively for Sirmione, S.Ambrogio Valpolicella-Colà di Lazise and Caldiero thermal districts. Temperature ranges obtained in this work were used to gain an insight into the possible depth reached by thermal waters in the project area, which is characterized by the normal geothermal gradient (30°C/Km). Finally, geochemical findings were elaborated and integrated with geological and structural data in a proposed conceptual model of water circulation. The agreement within data sets is satisfactory in particular in relation to the depth of carbonate-evaporite formations, which represent the thermal reservoirs. Infiltrating waters can seep into the deep through fractured rocks, reaching the Carnian to Upper Cretaceous carbonates and evaporites. In the Caldiero thermal districts the depth reached by thermal waters coincides with the level of the Carnian evaporites (≈ 1.3–1.6 Km) and it agrees with the important role played by dissolved sulphates evidenced by geochemical data. Thermal fluids in Sirmione and S. Ambrogio Valpolicella – Colà di Lazise thermal districts likely interact with Permian-Middle Triassic formations, which are located at greater depths (≈ 2.7–3 Km and ≈ 1.9–2.1 Km, respectively). Once heated at depth, thermal fluids rise through main faults and/or thrust faults, where they may be diluted by circulating surface cold waters.
We present a paleoenvironmental reconstruction for the mountain fringe between the South-Eastern Alps and the Northern Dinarides (NE-Italy/W-Slovenia) during the Last Glacial Maximum. We focused on a ...new sedimentary and paleoecological archive spanning the LGM acme, located in an aggrading, permanently flooded and ponded plain, dammed by an active fluvioglacial megafan. The ecosystem reconstruction, based on two high resolution pollen records, is supported by a rich plant macrofossil flora and constrained by a robust radiocarbon chronology between 26 and 22calka BP. We show evidence for persistence of boreal trees and of different open boreal forest types throughout the LGM at the south-eastern mountain fringe of the Alps and the Northern Dinarides. Fire frequency is responsible for high, oscillating forest openness. The paleobotanical record is discussed in the light of the ecogeographic diversity of the region. A belt formed by Swiss stone pine, larch and dwarf mountain pine on limestone bedrock, and accompanied by Spruce in the floodplain, extended uphill, while proximal outwash plain supported Scots pine and dwarf mountain pine. These differences arise from groundwater regimes rather than from local climate variability. A steep moisture gradient from the semiarid pedoclimatic regime prevailing in the Adriatic alluvial plain to the forested mountain fringe is related to the orographic rainout triggered by southern air circulation. Mesophytic broad-leaved forest trees did not withstand the LGM temperature extremes in zonal ecosystems at the Alpine–Dinaric fringe; however, the fossil evidence suggests a number of microrefugia in karstic and thermal spring habitats of the northern Adriatic.
•Paleoenvironmental reconstruction at Alps–Dinarides fringe during the Last Glacial Maximum•Relationships between regional geological frame, sedimentary environments, and forest history•Persistence of trees and of different types of open boreal forest throughout the LGM
Moulin and Benedetti (2018), https://doi.org/10.1029/2018TC004958 present a new interpretation of the Neogene‐Quaternary tectonic evolution of the Eastern Southern Alps (ESA) in Veneto‐Friuli. After ...the reinterpretation of literature field data by means of remote sensing analysis (Digital Elevation Model interpretation), they calculated deformation rates of the tectonic structures through age interpretation of geomorphological surfaces of the Veneto‐Friuli piedmont plain. The authors linked the result of surface analysis to the thrust and fold architecture of the ESA basing on the Castellarin et al. (2006), https://doi.org/10.1016/j.tecto.2005.10.013 interpretation of TRANSALP project and the Friuli geological map at the scale 1:150,000 (Carulli, 2006). Discussing their new architecture of the ESA, the authors finally yielded rates of Europe‐Adria plates convergence and suggested fragmentation of Adria over the last 1–2 Ma. The present comment is aimed at discussing several critical points concerning: the use of the geomorphological and chronological data; the misinterpretation of the Digital Terrain Model; the reconstruction of the balanced geological cross section. Moreover, the application of a structural model defined in a certain area to another without considering peculiar structural complexities available in the literature results is geologically and methodologically questionable.
Plain Language Summary
The late Quaternary sedimentary successions of Eastern Southern Alps (ESA) recorded important deformations related to the ongoing Europe/Adria collision. Their chronology has been updated in the last years, thanks to detailed surveys and analyses. Our knowledge on the tectonic architecture of the ESA has been recently improved by the new Geological maps of Italy (CARG Project: Zanferrari, Avigliano, Monegato, et al., 2008, Zanferrari, Avigliano, Grandesso, et al., 2008; Zanferrari et al., 2013). However, the bulk of the tectonic and chronological data was discarded or improperly used in Moulin and Benedetti (2018), https://doi.org/10.1029/2018TC004958 in their estimate of the shortening and associated rates and hence in the subsequent discussion on the fragmentation of Adria.
Key Points
The chronological constraints and the shortening rates derive from misreading of the available literature and not from new original data
The description of the tectonic structures do not consider updated geological information available for the study area
The balanced cross‐section is inconsistent with the major crustal models for the Eastern Southern Alps, no alternate discussion is provided
In this paper we examine the computation of the potential generated by space–time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we ...consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the currently used ones. Both are of Gaussian type: the classical Gauss–Jacobi quadrature rule in the case of a Dirichlet problem, and the classical Gauss–Radau quadrature rule in the case of a Neumann problem. Both of them give very accurate results by using a few quadrature nodes, as long as the potential is evaluated at a point not very close to the boundary of the PDE problem domain. To deal with this latter case, we propose an alternative rule, which is defined by a proper combination of a Gauss–Legendre formula with one of product type, the latter having only 5 nodes.
The proposed quadrature formulas are compared with the second order BDF Lubich convolution quadrature formula and with two higher order Lubich formulas of Runge–Kutta type. An extensive numerical testing is presented. This shows that the new proposed approach is very competitive, from both the accuracy and efficiency points of view.
The Messinian–Quaternary history of tectonic and climatic control on sedimentation in the eastern Southern Alps, northern Italy, was reconstructed using an integrated petrographic and ...sedimentological analysis of five sedimentary successions. These units mainly consist of fluvial conglomerates of the Tagliamento sequence, deposited within the eastern Southern Alps since the Upper Miocene (“Messinian Salinity Crisis”). At that time, the closure of marine gateways between the Atlantic Ocean and the Mediterranean Sea caused a drop in sea level, causing exchanged fluvial erosion and widening of the Alpine catchments. Sediment composition in the Upper Miocene to Lower Pliocene units shows an abrupt change in the source areas: from sediments characterized by carbonate rock fragments to detritus rich in low-grade metamorphic grains. In spite of tectonic activity within the eastern Southern Alps, no major modifications in sediment supply took place during the Pliocene–Early Pleistocene time span. In the Middle Pleistocene the first major expansion of the Alpine glaciers triggered a change in drainage patterns and a marked increase in erosion rates. Predominantly climatic control on sedimentation in the Tagliamento basin and the erosion of the Carnic Alps produced sediments rich in quartz, siltstone and metamorphic rock fragments, deposited in the Upper Pleistocene unit and in modern river sediments.
In this paper, initially we consider the (two- and three-dimensional) interior and exterior problems for the scalar wave equation, with a Neumann boundary condition and, in general, with nontrivial ...data. For these problems, we derive a space-time hypersingular boundary integral equation formulation. Then, in the two-dimensional case, we propose a numerical approach for the computation of the extra 'volume' integrals generated by the problem data. To solve the above integral equation in the two-dimensional case, we propose to use second-order Lubich convolution quadrature for the discretization of the time integral, coupled with a (space) epsilon -collocation boundary element method. We also analyse the numerical evaluation of all the integrals required by this method. Finally, to show the efficiency of the proposed numerical approach and to detect its convergence rate, we solve some two-dimensional test problems by applying the new method, as well as the corresponding Galerkin one. Several numerical examples are presented.
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