Numerical solution of the discontinuous-bottom Shallow-water Equations with hydrostatic pressure distribution at the step

Free-surface flows are usually modelled by means of the Shallow-water Equations: this system of hyperbolic equations exhibits a source term which is proportional to the product of the water depth by the bed slope, and which takes into account the effect of gravity onto fluid mass. Recently, much attention has been paid to the case in which bottom discontinuities are present in the physical domain to be represented: in this case, it is difficult to define the non-conservative product in the distributional sense. Here, the discontinuous-bottom Shallow-water Equations with hydrostatic pressure distribution at the bed step (Bernetti et al., 2006) are discussed in the context of the theory of Dal Maso et al. (1995) [9]; finally, a first-order numerical scheme is presented, which is consistent for regular solutions, and which is able to capture contact discontinuities at bottom steps. Numerous tests are presented to show the feasibility of the scheme and its ability to converge to the exact solution in the cases of smooth as well as discontinuous bed profiles.     

The moment magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> and the energy magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>e</Subscript>: common roots and differences

Starting from the classical empirical magnitude-energy relationships, in this article, the derivation of the modern scales for moment magnitude M _w and energy magnitude M _e is outlined and critically discussed. The formulas for M _w and M _e calculation are presented in a way that reveals, besides the contributions of the physically defined measurement parameters seismic moment M ₀ and radiated seismic energy E _S, the role of the constants in the classical Gutenberg–Richter magnitude–energy relationship. Further, it is shown that M _w and M _e are linked via the parameter Θ = log(E _S/M ₀), and the formula for M _e can be written as M _e = M _w + (Θ + 4.7)/1.5. This relationship directly links M _e with M _w via their common scaling to classical magnitudes and, at the same time, highlights the reason why M _w and M _e can significantly differ. In fact, Θ is assumed to be constant when calculating M _w. However, variations over three to four orders of magnitude in stress drop Δσ (as well as related variations in rupture velocity V _R and seismic wave radiation efficiency η _R) are responsible for the large variability of actual Θ values of earthquakes. As a result, for the same earthquake, M _e may sometimes differ by more than one magnitude unit from M _w. Such a difference is highly relevant when assessing the actual damage potential associated with a given earthquake, because it expresses rather different static and dynamic source properties. While M _w is most appropriate for estimating the earthquake size (i.e., the product of rupture area times average displacement) and thus the potential tsunami hazard posed by strong and great earthquakes in marine environs, M _e is more suitable than M _w for assessing the potential hazard of damage due to strong ground shaking, i.e., the earthquake strength. Therefore, whenever possible, these two magnitudes should be both independently determined and jointly considered. Usually, only M _w is taken as a unified magnitude in many seismological applications (ShakeMap, seismic hazard studies, etc.) since procedures to calculate it are well developed and accepted to be stable with small uncertainty. For many reasons, procedures for E _S and M _e calculation are affected by a larger uncertainty and are currently not yet available for all global earthquakes. Thus, despite the physical importance of E _S in characterizing the seismic source, the use of M _e has been limited so far to the detriment of quicker and more complete rough estimates of both earthquake size and strength and their causal relationships. Further studies are needed to improve E _S estimations in order to allow M _e to be extensively used as an important complement to M _w in common seismological practice and its applications.     

A decision support system for post-earthquake reliability assessment of structures subjected to aftershocks: an application to L��Aquila earthquake, 2009

The post-earthquake assessment of existing structures can be further complicated by the progressive damage induced by the occurrence of a sequence of aftershocks. This work presents a simple methodology for the calculation of the probability of exceeding a certain limit state in a given interval of time. The time-decaying mean daily rate of occurrence of significant aftershock events is modeled by employing a site-specific aftershock model for the L??Aquila 2009 aftershock sequence (central Italy). The number of aftershock events occurring in a given interval of time elapsed after the main event is modeled using a non-homogenous Poisson model. An equivalent single-degree of freedom structure with cyclic stiffness degradation is used in order to evaluate the progressive damage caused by a sequence of aftershock events. Given the time history of the main-shock and the residual damage caused by it, the probability of exceeding a set of discrete limit states in a given interval of time is calculated. Of particular importance is the time-variant probability of exceeding the limit state in a 24-h (a day) interval of time which can be used as a proxy for the life-safety considerations regarding the re-occupancy of the structure and to complement the results of visual inspections for prioritizing the emergency operations. The method presented herein can also be used in an adaptive manner, progressively conditioned on the time-histories of aftershock events following the main-shock and on the corresponding residual damage caused by them.     

Sb–Hg ore deposit distribution controlled by brittle structures: The case of the Selvena mining district (Monte Amiata, Tuscany, Italy)

This paper deals with the tectonic control on the hydrothermal system that gave rise to Sb–Hg ore deposits in the Monte Amiata area that was one of the most relevant mining district for the exploitation of mercury in Italy. The study area (Selvena mining district) is located in southern Tuscany (inner Northern Apennines) one of the most important mineralized area in the western Mediterranean region. Southern Tuscany was severely affected by Middle–Late Miocene low-angle normal faults, later dissected by Pliocene–Pleistocene faults, coeval magmatism (Late Miocene–Pleistocene) and hydrothermal activity (Pliocene–Present). The Selvena mining district is located south of Middle Pleistocene Monte Amiata volcanic complex. Our structural and kinematic study is based on the integration among fieldwork, borehole and mine data. The results highlight two Pleistocene–Holocene left-lateral transtensional shear zones linked by normal faults, defining a coeval pull-apart structure. Here, the Sb–Hg mineralization, transported by meteoric hydrothermal fluids mainly, is particularly diffuse and concentrated in the cataclasites and in damage zones of the normal faults. Furthermore, a widespread mineralization also occurs in the cataclasites of Miocene low-angle normal faults. Mine evidence suggests that ore-bearing fluids percolated through structural conduits located along the fault planes and resulting parallel to the intermediate stress axis. Geological structures and ore deposit distribution are related to a single hydrothermal circuit, with meteoric water channelled to depth through conduits parallel to the intermediate stress axis of the transcurrent shear zones; then, hydrothermal fluids mainly ascended through the almost vertical deformation zones located at the intersection between normal and strike-slip faults. Thus, hydrothermal fluids permeated also the Middle–Late Miocene cataclasites. This study shed light on the relationships between geological structures and mineralization in southern Tuscany and underlines the importance to investigate mine areas to understand hydrothermal fluids path.     

Earthquakes in Switzerland and surrounding regions during 2010

This report of the Swiss Seismological Service summarizes the seismic activity in Switzerland and surrounding regions during 2010. During this period, 407 earthquakes and 85 quarry blasts were detected and located in the region under consideration. With a total of only 19 events with M_L ≥ 2.5, the seismic activity in the year 2010 was below the average over the previous 35 years. The two most noteworthy earthquakes were the M_L 3.4 Barrhorn event near Sankt Niklaus (VS) and the M_L 3.0 event of Feldkirch, both of which produced shaking of intensity IV.     

Regional-scale seafloor mapping and geohazard assessment. The experience from the Italian project MaGIC (Marine Geohazards along the Italian Coasts)

Recent developments in seafloor imaging and mapping techniques greatly improved our capability of identifying marine geohazards affecting continental margins. Geomorphic features can be detected in great detail by high-resolution multibeam imaging and regarded as geohazard indicators; the most common include slide scars and deposits, canyon headscarps and steep erosional flanks, fault-related seafloor unevenness, mud volcanoes, pockmarks, gravity flow deposits, erosional scours and bedforms indicating sediment mobility at diverse temporal/spatial scale. These processes are widespread on Italian continental margins and are potential indicators of geohazard for human settlements and infrastructures in the offshore and coastal zones. The national Project MaGIC (Marine Geohazards along the Italian Coasts) aims at documenting potential geohazards based on the acquisition of high-resolution multibeam bathymetry and on the production of maps of the geohazard-related geomorphic features for most of the Italian continental margins. With reference to this issue, we discuss some of the most frequent problems dealing with reconnaissance, interpretation and cartographic representation of geohazard-related geomorphic features at a regional scale.     

应用振型叠加方法研究1997年11月8日中国西藏玛尼地震震源机制

利用包括长周期体波、Rayleigh波和Love波在内的三分向波形记录,根据PREM模型应用自由振荡振型叠加方法计算理论地震图,反演1997年11月8日西藏玛尼Ms7.9地震的矩张量.获得的最佳双力偶的节面解为:NP1(走向343°,倾角76°,滑动角-177°),NP2(走向252°,倾角87°,滑动角-13°);地震矩为1.43×1020 Nm,Mw为7.4.其结果与哈佛大学的CMT解较一致.地震的发震断层面为北东东近东西方向,断层性质主要为左旋走滑断层,与地质背景、应力场特征相符合.研究使用的是适用于区域性地震的矩张量快速确定的方法,可以用来对区域性的地震活动给出准确而快速的监测.     

Seismic activity accompanying the outbreak of the 1991–1993 eruption of Mt. Etna (Italy)

The character and location of seismic activity accompanying the onset of the 1991–1993 eruption at Mt. Etna are compatible with the surface evidence of the volcanic pile rupture. Both the epicentral distribution and the focal mechanisms of a swarm that occurred on December 14, 1991, agree with magma ascent occurring along the main NNW-SSE-trending structure of the volcano and the consequent opening of a system of effusive fissures with the same trend. A typical mainshock-aftershock sequence, recorded the day after and indicating transcurrent displacement occurring along the second-principal structure of Etna (NE-SW), depicts the tectonic response of the volcanic pile and the underlying basement to major stresses applied by the magma push.