Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment

Probabilistic seismic risk assessment for spatially distributed lifelines is less straightforward than for individual structures. While procedures such as the ‘PEER framework’ have been developed for risk assessment of individual structures, these are not easily applicable to distributed lifeline systems, due to difficulties in describing ground‐motion intensity (e.g. spectral acceleration) over a region (in contrast to ground‐motion intensity at a single site, which is easily quantified using Probabilistic Seismic Hazard Analysis), and since the link between the ground‐motion intensities and lifeline performance is usually not available in closed form. As a result, Monte Carlo simulation (MCS) and its variants are well suited for characterizing ground motions and computing resulting losses to lifelines. This paper proposes a simulation‐based framework for developing a small but stochastically representative catalog of earthquake ground‐motion intensity maps that can be used for lifeline risk assessment. In this framework, Importance Sampling is used to preferentially sample ‘important’ ground‐motion intensity maps, and K‐Means Clustering is used to identify and combine redundant maps in order to obtain a small catalog. The effects of sampling and clustering are accounted for through a weighting on each remaining map, so that the resulting catalog is still a probabilistically correct representation. The feasibility of the proposed simulation framework is illustrated by using it to assess the seismic risk of a simplified model of the San Francisco Bay Area transportation network. A catalog of just 150 intensity maps is generated to represent hazard at 1038 sites from 10 regional fault segments causing earthquakes with magnitudes between five and eight. The risk estimates obtained using these maps are consistent with those obtained using conventional MCS utilizing many orders of magnitudes more ground‐motion intensity maps. Therefore, the proposed technique can be used to drastically reduce the computational expense of a simulation‐based risk assessment, without compromising the accuracy of the risk estimates. This will facilitate computationally intensive risk analysis of systems such as transportation networks. Finally, the study shows that the uncertainties in the ground‐motion intensities and the spatial correlations between ground‐motion intensities at various sites must be modeled in order to obtain unbiased estimates of lifeline risk. Copyright © 2010 John Wiley & Sons, Ltd.     

Zn上的k次不可约多项式与k阶Carmichael数

设n是合数,如果对一切f（x）∈Zn[x]都满足f（x）nk≡f（x）mod（n,r（x））,那么就称n是模r（x）的k阶Carmichael数,这里r（x）是Zn[x]上的k次首一不可约多项式,用Ck,r（x）表示所有这种数的集合,并且定义Ck=Ur（x）Ck,r（x）.k阶Carmichael数,当k=4时,已证明了n=pq,p,q是不同的奇素数,p2-1,q3-1均整除n4-1,则n∈C4.主要目的是将k=4时得出的结论推广到k≥4的一般情形,利用孙子定理,通过构造Zn上的首一k次不可约多项式f（x）的方法,得出：在k≥4时,设n=pq,如果k=2m,m≥2,pm-1,q2m-1-1均整除nk-1,则n∈Ck;如果k=2m＋1,m≥2,pm-1,pm＋1-1,q2m-1均整除nk-1,则n∈Ck.     

K_0固结饱和粘土三轴压缩与拉伸循环强度之间的关系

针对有应力反向与无应力反向两种循环应力条件,进行了k0固结饱和粘土不排水循环三轴压缩与拉伸强度试验。为了分析三轴压缩与三轴拉伸循环强度之间关系,依据3个围压下三轴压缩循环强度试验结果,确定了与不同循环破坏次数对应的Mohr-Coulomb循环强度指标。据此预测k0固结土样三轴拉伸循环强度,预测结果小于实测结果,当循环破坏次数为2 000时,两者之间相对偏差为13%左右。因此,可以依据Mohr-Coulomb强度理论建立k0固结饱和粘土不排水三轴压缩与拉伸循环强度之间的关系。     

Localization of temperature anomalies in the Upper Rhine Graben: insights from geophysics and neotectonic activity

The European Cenozoic Rift System hosts major temperature anomalies in Central Europe. In its central segment, the Upper Rhine Graben (URG), temperatures range from 75°C to nearly 150°C at a depth of 2000 m. Different hypotheses have been suggested to explain the localization of these anomalies. Our review and comprehensive interpretation of gravimetric and magnetic data, as well as neotectonic activity patterns, suggests that low-density, mostly magnetic and fractured granitic basement is systematically associated with major temperature anomalies. Further analyses provide insight into different heat transport processes contributing to the localization of these anomalies. Magnetic and gravity anomalies are known to represent lithological variations associated with the pre-Permian. We show their spatial relationship with positive temperature anomalies in the URG. Correlation between magnetics and temperature reveal a mean contribution of heat production to the temperature anomaly of about 10–15°C. A slightly higher mean value is obtained from correlation between gravity and temperature, which may be attributed to effects resulting from fracture porosity. The spatial relationship between temperature anomalies and neotectonic patterns indicates compressional shear and uplift regime for the major anomalies of the central segment of the URG. This is in agreement with different numerical models indicating free convection on fracture zones linked to faults. Our findings show that about 15–25% of the temperature anomaly can be attributed to variation in heat production. Hydrothermal circulation convection along faults, activated by the tectonic context, may explain the remaining 75–85% of the temperature anomalies.     

Provisional Elemental Values for IAEA‐Sewage Sludge by Instrumental Neutron Activation Analysis

The International Atomic Energy Agency (IAEA) organised a proficiency test (PT), IAEA‐CU‐2010‐02, for the determination of elements in sewage sludge. The PT sample was analysed by semi‐absolute standardless k₀‐instrumental neutron activation analysis (k₀‐INAA). Results for seven elements (As, Co, Cr, Fe, Hg, Se, Zn) were submitted to the IAEA by our laboratory. All of our results were scored ‘acceptable’ by the ‘result evaluation criteria’ adopted by the IAEA. The same analytical methodology produced quantitative results for twenty‐six additional elements. In total, thirty‐six elements were determined with uncertainty varying from 4 to 11%. This paper presents the provisional mass fractions of twenty‐six additional elements (Ag, Al, Br, Ca, Ce, Cl, Dy, Eu, Ga, Hf, I, K, La, Mg, Mn, Na, Rb, Sb, Sc, Sm, Ta, Tb, Th, V, U, W) not reported by the IAEA. The analytical methodology was discussed with important sources of spectral, nuclear and fission‐product interferences. It was shown that the important components of uncertainties were the k₀ factor, Q₀ factor, detector efficiency, mass and counting statistics. The methodology was validated by analysing the IAEA‐S7 reference material.     

Oligo-Miocene extension in the Lycian orogen: evidence from the Lycian molasse basin,SW Turkey

The Lycian molasse basin of SW Turkey is a NE-SW-oriented basin that developed on an imbricated basement, comprising the allochthonous Mesozoic rocks of the Lycian nappes and Palaeocene-Eocene supra-allochthonous sediments. The imbricated basement has resulted from a complex history related to the emplacement of different tectonic units from Late Cretaceous to Late Eocene. Following imbrication, extensional collapse of the Lycian orogen resulted in extensive emergent areas, some of which coincide with present-day mountains. These were surrounded by interconnected depressions, namely, the Kale-Tavas, Çardak-Dazk?r? and Denizli subbasins.

The Lycian molasse sequence contains a relatively complete record of the tectonic history of the Lycian orogenic collapse from which it was derived. The sequence is characterised by interdependence between tectonism and sedimentation, the latter of which includes fining-and coarsening-upward sedimentary cycles with syn-depositional intrabasinal unconformities.

The Denizli subbasin consists of thick, coarse-grained wedges of alluvial fans and fine-grained fan-delta deposits formed in a shallowmarine environment. Some areas of the fan deltas were colonised by corals, red algae and foraminifera, forming patch reefs.

The first phase of extensional collapse in the region is marked by the Lycian orogenic collapse, which may have been initiated by the beginning of the Oligocene (Rupelian), following the main Menderes metamorphism. Starting in the latest Early Miocene or in the Middle Miocene, the area of the molasse basin was subject to deformation with the Lycian nappes, and to erosion as well. At that time, the Lycian nappes, with some ophiolitic assemblages, were thrust over the molasse deposits and thus, NE-SW-trending folds were formed. The molasse deposits and thrust-related deformational structures were then unconformably covered by Upper Miocene continental deposits which belong to the neotectonic period of SW Turkey. The second phase of extensional collapse is marked by granitic intrusions and the formation of Miocene detachment-related extensional basins. This phase may have been related to the exhumation of the gneissic core of the Menderes Massif, from which fragments were derived and incorporated into the upper parts of the Denizli subbasin during the Aquitanian.     

Evidence of two-stage extensional tectonics from the northern edge of the Edremit Graben,NW Turkey

Western Turkey is a place of active continental extension, characterized by the occurrence of several WNW-ESE-trending major grabens. The central part of the northern edge of the Edremit Graben is delineated by various geological units, namely the metamorphic Kazda? Massif, the Mid-Cretaceous Çetmi mélange, the sedimentary Küçükkuyu formation, and loose Plio-Quaternary deposits. Detailed structural and sedimentological study suggests a two-stage extensional evolution of the area, separated by a short break in the tectonic regime. The first stage, possibly related to back-arc extension and/or orogenic collapse, is marked by the activity of a newly described low-angle detachment fault, the ?elale detachment fault, from the latest Oligocene onward. The fault plane, separating the mylonitized rocks of the Kazda? Massif in the footwall from the unmetamorphosed Çetmi mélange and Küçükkuyu formation in the hanging wall, must have played a significant role in the initial exhumation processes of the Kazda? Massif at that time. The Lower Miocene syntectonic Küçükkuyu formation has recorded the initiation and filling up of a small basin, which has developed in a typical supra-detachment basin, above the detachment fault. After a short phase of possible compression and erosion, the second stage—which marks the onset of neotectonic activity—is marked by the development of Plio-Quaternary step-like normal faults, which cut through all the previous units. Coarse, loose sediments were deposited following the fault activity. These local results are extrapolated to apply to the entire Edremit Graben. In that case, its evolution is seen as the succession of two extensional stages, characterized by distinct structural and sedimentological patterns, and possibly separated by a short compressional phase.     

Plio-Quaternary evolution of the Küçük Menderes Graben Southwestern Anatolia,Turkey

The Küçük Menderes Graben (KMG) is part of the horst-graben system of southwestern Anatolia (Turkey), bounded by the Bozda? horst in the north and the Ayd?n horst in the south. The Plio-Quaternary evolution of the KMG has been evaluated using the nature of the Miocene-Quaternary fill sediments and palaeostress analysis of slip data measured in different parts of the graben.

The graben is composed of five subbasins—the Kiraz, Ödemi?, Bay?nd?r, Da?k?z?lca-Torbal? and Selçuk—that are connected to each other through narrow Quaternary troughs. The Da?k?z?lca, Kiraz and Selçuk basins bear Miocene and younger sequences whereas the other subbasins are largely filled by Quaternary sediments. The maximum thickness of the Quaternary fill reaches about 270 m in the Ödemi? and Bay?nd?r subbasins.

The calculated slip results indicate multidirectional extension, three successive deformational periods, and possible counterclockwise rotation in the KMG during the post-Miocene period. The first phase was a strike-slip regime under N-S compression, followed by a second phase of deformation which resulted in ENE-WSW extension with strike-slip components. The final phase of deformation was NE-SW extension which constituted the final evolution of the KMG.

The graben gained its present morphological configuration via the onset of E-W-trending, high-angle normal faulting imposed on the regionwide synformal structure during the Plio-Quaternary. The KMG evolved as a result of rifting during the Plio-Quaternary which followed Late Miocene unroofing of the Menderes Massif and the evolution of the Büyük Menderes and Gediz grabens.     

Neogene basin development around Söke-Kuşadası (western Anatolia) and its bearing on tectonic development of the Aegean region

The AMS study has been performed on various types of the basement – Variscan granitic and surrounding – Mesozoic sedimentary rocks in the Velká Fatra Mountains, Tatric Superunit of the Central Western Carpathians. The Velká Fatra Mts. provides good opportunity for AMS study because of composite S-type and I-type granite character of pluton and clear relations to Mesozoic sedimentary rocks in the cover and nappe positions. The granitic massif consists of the three types of weakly magnetic peraluminous granites (350 – 340 Ma in age), ranging from two-mica granites to biotite granodiorites in composition and carrying accessory monazite and ilmenite; whereby they resemble common S-type and/or Ilmenite Series granite. This pre-existing granitic body was intruded by relatively young (304 Ma old) metaluminous to subaluminous, strongly magnetic (due to magnetite) tonalitic intrusion of the I-type and/or Magnetite Series granite. In all S-types investigated as well as in the I-type tonalite body, the magnetic fabrics are not uniform, but slightly variable within a body and differing from body to body. The magnetic fabrics in all granitic rocks can be classified as mostly magmatic in origin, only subordinately affected by ductile deformation. The Alpine overprint of the magnetic fabric of the Variscan granite frequent in the central areas of the Central Western Carpathians was only weak in the Velká Fatra Mts. and the magnetic fabrics of these granites thus mostly comprise the original Variscan magmatic fabrics. On the other hand, in the marginal parts of the Velká Fatra Mts. the magnetic fabrics in granites are locally conformable to the deformational magnetic fabrics in surrounding sedimentary rocks (Mesozoic in age) thus indicating at least local effects of the Alpine deformation. The magnetic fabrics in Mesozoic sedimentary rocks covering the crystalline basement are partially (Cover Formation) to entirely (Nappe Units) deformational in origin.