Power law olivine crystal size distributions in lithospheric mantle xenoliths

Olivine crystal size distributions (CSDs) have been measured in three suites of spinel- and garnet-bearing harzburgites and lherzolites found as xenoliths in alkaline basalts from Canary Islands, Africa; Victoria Land, Antarctica; and Pali Aike, South America. The xenoliths derive from lithospheric mantle, from depths ranging from 80 to 20 km. Their textures vary from coarse to porphyroclastic and mosaic–porphyroclastic up to cataclastic. Data have been collected by processing digital images acquired optically from standard petrographic thin sections. The acquisition method is based on a high-resolution colour scanner that allows image capturing of a whole thin section. Image processing was performed using the VISILOG 5.2 package, resolving crystals larger than about 150 μm and applying stereological corrections based on the Schwartz–Saltykov algorithm. Taking account of truncation effects due to resolution limits and thin section size, all samples show scale invariance of crystal size distributions over almost three orders of magnitude (0.2–25 mm). Power law relations show fractal dimensions varying between 2.4 and 3.8, a range of values observed for distributions of fragment sizes in a variety of other geological contexts.

A fragmentation model can reproduce the fractal dimensions around 2.6, which correspond to well-equilibrated granoblastic textures. Fractal dimensions >3 are typical of porphyroclastic and cataclastic samples. Slight bends in some linear arrays suggest selective tectonic crushing of crystals with size larger than 1 mm. The scale invariance shown by lithospheric mantle xenoliths in a variety of tectonic settings forms distant geographic regions, which indicate that this is a common characteristic of the upper mantle and should be taken into account in rheological models and evaluation of metasomatic models.     

Control of emission rates

The advection-diffusion equation is used for describing the dispersion of pollutants in a limited area. Methods for preventing dangerous levels of pollutants in ecologically important zones are suggested. The methods are based on the control of emission rates of sources and use the direct and adjoint estimates of the average pollution concentration in the zones. While the direct estimates use solutions of the pollution transport problem and permit to study the ecological situation in the whole domain, the adjoint estimates allow getting information only in the selected zones of the domain. The adjoint estimates are obtained with solutions to the adjoint problem and depend explicitly on the positions of the sources and their emission rates, and on the initial distribution of pollutants in the region. In each such estimate, the adjoint problem solution serves as the influence function that shows the quantitative contribution of every source into the pollution of the corresponding zone. This makes the adjoint estimates very efficient tools in the study of the model response to changes in emission rates and initial conditions, as well as in the development of control strategies. Both non-optimal (sufficient) and optimal control strategies are suggested. Each strategy consists in reducing the emission rates of sources, and defines maximum allowable intensity (in case of optimal control), or sufficient intensity (in case of sufficient control) of each source to avoid violations of hygiene standards. Such criteria are designed taking into account dynamic conditions in the atmosphere or ocean (sea), that is, the processes of propagation, dispersion and transformation of pollutants, as well as the number of sources to control, their locations and the sanitary norms. The control methods developed are illustrated with simple examples using two-dimensional dispersion models. However, these methods can also be applied to three-dimensional models. As an example, in the last part of the article, a three-dimensional model of dispersion is considered. In addition, to expand the scope of application of the methods of control of the intensity of sources, the optimal control strategies are applied to a source that emits a chemical substance to clean aquatic systems contaminated with biofilms (remediation) or oil (bioremediation).     

Seismicity, seismotectonics and seismic hazard of Italy

A first generation of probabilistic seismic hazard maps of the Italian country are presented. They are based on seismogenic zoning deriving from a kinematic model of the structural tectonic units and on an earthquake catalogue with the foreshock and aftershock events filtered out. The following ground motion parameters have been investigated and mapped using attenuation equations based on strong-motion recordings of Italian earthquakes: peak ground acceleration and velocity; Arias intensity; strong motion duration; and the pseudovelocity and pseudoacceleration spectral values at 14 fixed frequencies both for the vertical and the largest horizontal component. A Poissonian model of earthquake occurrence is assumed as a default and the hazard maps are presented in terms of ground motion values expected to be exceeded at a 10% probability level in 50 years (return period 475 years) according to the requirement of Eurocode 8 for the seismic classification of national territories, as well as in terms of exceedance probabilities of selected ground motion values. Finally, as a tentative study, the use of hybrid methods (implementing both seismogenic zones and structures), renewal processes (including earthquake forecasting) and the influence of site effects (as the basis for the planning of earthquake scenarios) were explored.     

Cumulative Benioff strain-release, modified Omori's law and transient behaviour of rocks

Irreversible thermodynamic theories with internal state variables can be used to derive a general constitutive law for both transient and steady-state behaviours of rocks. This constitutive law can represent the concepts of damage and damage evolution in either the fibre-bundle model or continuum damage mechanics. We have previously proposed an empirically based constitutive law for both the transient and steady-state behaviours of rocks ultimately derived from laboratory experimental data. We show here that this law is concordant with the general constitutive law derived from irreversible thermodynamic theories, and that the relaxation modulus has a temporal power–law that depends on a structural fractal property of rocks. Our constitutive law predicts forms for the cumulative Benioff strain-release for precursory seismic activations and the modified Omori's laws of aftershocks, both aspects of the temporal fractal properties of seismicity. These seismic properties can also be derived by the fibre-bundle model or continuum damage mechanics. Our model suggests that these time-scale invariant processes of seismicity may be regulated by the fractal structures of crustal rocks.     

A seismic source zone model for the seismic hazard assessment of the Italian territory

We designed a new seismic source model for Italy to be used as an input for country-wide probabilistic seismic hazard assessment (PSHA) in the frame of the compilation of a new national reference map.

We started off by reviewing existing models available for Italy and for other European countries, then discussed the main open issues in the current practice of seismogenic zoning.

The new model, termed ZS9, is largely based on data collected in the past 10 years, including historical earthquakes and instrumental seismicity, active faults and their seismogenic potential, and seismotectonic evidence from recent earthquakes. This information allowed us to propose new interpretations for poorly understood areas where the new data are in conflict with assumptions made in designing the previous and widely used model ZS4.

ZS9 is made out of 36 zones where earthquakes with M_w > = 5 are expected. It also assumes that earthquakes with M_w up to 5 may occur anywhere outside the seismogenic zones, although the associated probability is rather low. Special care was taken to ensure that each zone sampled a large enough number of earthquakes so that we could compute reliable earthquake production rates.

Although it was drawn following criteria that are standard practice in PSHA, ZS9 is also innovative in that every zone is characterised also by its mean seismogenic depth (the depth of the crustal volume that will presumably release future earthquakes) and predominant focal mechanism (their most likely rupture mechanism). These properties were determined using instrumental data, and only in a limited number of cases we resorted to geologic constraints and expert judgment to cope with lack of data or conflicting indications. These attributes allow ZS9 to be used with more accurate regionalized depth-dependent attenuation relations, and are ultimately expected to increase significantly the reliability of seismic hazard estimates.     

Local seismic hazard assessment in areas of weak to moderate seismicity—case study from Eastern Germany

Generally the seismic hazard of an area of interest is considered independent of time. However, its seismic risk or vulnerability, respectively, increases with the population and developing state of economy of the area. Therefore, many areas of moderate seismic hazard gain increasing importance with respect to seismic hazard and risk analysis. However, these areas mostly have a weak earthquake database, i.e., they are characterised by relative low seismicity and uncertain information concerning historical earthquakes. In a case study for Eastern Thuringia (Germany), acting as example for similar places in the world, seismic hazard is estimated using the probabilistic approach. Because of the lack of earthquakes occurring in the recent past, mainly historical earthquakes have to be used. But for these the actual earthquake sources or active faults, needed for the analysis, are imprecisely known. Therefore, the earthquake locations are represented by areal sources, a common practice. The definition of these sources is performed carefully, because their geometrical shape and size (apart from the earthquake occurrence model) influence the results significantly. Using analysis tools such as density maps of earthquake epicentres, seismic strain and energy release support this. Oversizing of areal sources leads to underestimation of seismic hazard and should therefore be avoided. Large location errors of historical earthquakes on the other hand are represented by several alternative areal sources with final superimposition of the different results. In a very similar way information known from macroseismic observations interpreted as source rather than as site effects are taken into account in order to achieve a seismic hazard assessment as realistic as possible. In very local cases the meaning of source effects exceeds those of site effects very likely. The influence of attenuation parameter variations on the result of estimated local seismic hazard is relatively low. Generally, the results obtained by the seismic hazard assessment coincide well with macroseismic observations from the thoroughly investigated largest earthquake in the region.     

Physical and stochastic models of earthquake clustering

The phenomenon of earthquake clustering, i.e., the increase of occurrence probability for seismic events close in space and time to other previous earthquakes, has been modeled both by statistical and physical processes.From a statistical viewpoint the so-called epidemic model (ETAS) introduced by Ogata in 1988 and its variations have become fairly well known in the seismological community. Tests on real seismicity and comparison with a plain time-independent Poissonian model through likelihood-based methods have reliably proved their validity.On the other hand, in the last decade many papers have been published on the so-called Coulomb stress change principle, based on the theory of elasticity, showing qualitatively that an increase of the Coulomb stress in a given area is usually associated with an increase of seismic activity. More specifically, the rate-and-state theory developed by Dieterich in the ′90s has been able to give a physical justification to the phenomenon known as Omori law. According to this law, a mainshock is followed by a series of aftershocks whose frequency decreases in time as an inverse power law.In this study we give an outline of the above-mentioned stochastic and physical models, and build up an approach by which these models can be merged in a single algorithm and statistically tested. The application to the seismicity of Japan from 1970 to 2003 shows that the new model incorporating the physical concept of the rate-and-state theory performs not worse than the purely stochastic model with two free parameters only. The numerical results obtained in these applications are related to physical characters of the model as the stress change produced by an earthquake close to its edges and to the A and σ parameters of the rate-and-state constitutive law.     

The use of uniaxial recordings in moment tensor inversions for induced seismic sources

This study shows that the use of uniaxial recordings maintains the linear dependence of the low frequency displacements, with first polarities included, on the moment tensor components, and thus can be easily incorporated in the evaluation of failure mechanism using a moment tensor approach. Synthetic data analysis demonstrates that the errors in the orientation of the principal strain axes of the mechanism solution can be reliably evaluated using a linear error propagation approximation for up to 30% variance in the amplitude data. Case studies at the Kidd Mine indicate that the general characteristics of the mechanism solution are well retrieved, regardless of the type of data used, as relatively small disorientation angles of 15–20° are found between the solutions derived from rotated triaxial data and those from unrotated triaxial data used as uniaxial data, and of 25–30° between the solutions based on rotated triaxial data and those on independent uniaxial data.     

Probabilistic assessment of seismic hazard of dam sites in Jordan

A Probabilistic method is used to evaluate the seismic hazard of nineteen embankment dam sites in Jordan. A line source model developed by McGuire (1978) is used in this study. An updated earthquake catalogue covering the period from 1 A.D. to 1991 A.D. is used for this purpose. This catalogue includes all earthquakes that occurred in Jordan and adjacent areas, more specifically between latitudes 27.0°–35.5° N and longitudes 32.0°–39.0° E.Nine distinct seismic sources of potential seismic activities are identified. The seismic hazard parameters are determined using the method suggested by Kijko and Sellevoll (1989).The Peak Ground Acceleration (PGA) is selected as a measure of ground motion severity. Esteva (1974) attenuation relationship is used in evaluating PGA values at each dam site. Analysis is carried out for 50%, 90%, and 95% probability that is not being exceeded in a life time of 50, 100, and 200 years.Results of analysis indicate that PGA values are higher for dam sites closer to the Dead Sea Fault. This fault is believed to be responsible for most earthquake activities in Jordan and vicinity. The highest PGA value is found to be for Al-Karama dam site.     

Complexity of seismic process; measuring and applications — A review

Recent methods of analysis of so called disordered systems show that many objects and processes that earlier were considered as completely random reveal clear evidence of having some ordered structure in both time and space. These new methods (fractals, percolation, nonlinear dynamics and complexity theories) allow visualization and quantitative assessment of the level of complexity (orderliness) of these structures, using both theoretical models and experimental data. We consider sequentially some aspects of structural and evolutionary complexity of dynamics of seismic process and the technique of measuring this property.It is shown that the physical properties of geophysical medium are not always self-consistent and manifest fractal behavior on selected spatial and temporal scales. Mechanical percolation theory can be used for modeling geometry of fracture process. Namely, we consider fractal and connectivity aspects of delayed failure, including energy emission during fracturing. Special attention is paid to relating the intensity of geophysical anomalies to the strain in the framework of the pressure-induced anomalous strain-sensitivity (percolation) model, which explains naturally the observed heterogeneity of response of a geophysical media to the strain variation.Different methods of measuring the dynamic complexity of seismological time series are applied to magnitude and waiting time sequences of Caucasian earthquakes. The fractal (correlation) dimension d₂ of the latter is high (larger than 8), but the former one has as low dimension as 1.6–2.5, which makes waiting time sequences a promising tool for revealing precursory changes.The same nonlinear technique allow detecting significant changes in the seismic regime during external electromagnetic forcing by MHD pulses; similar tests on the laboratory scale show the possibility of triggering/controlling stick-slip process by relatively weak electromagnetic or mechanical forcing.Lastly, the predictive potential of complexity analysis of seismological time series is considered. For example, percolation model predicts the increase of the number of large events and the scatter of magnitudes of events, decrease of the magnitude-frequency relation slope and appearance of multifractality at approaching the final rupture.It seems that seismology can benefit from using the new techniques to cope with the complexity of earthquake machine; for example, the measures of complexity can be characteristic for a given region and change before strong earthquake.     

四川盆地北部长兴组生物礁地震响应特征与分布规律

井下钻探结果和地震资料表明四川盆地北部上二叠统长兴组生物礁发育,通过对典型井长兴组岩性与电性资料的分析,明确了生物礁的岩性与储层发育特征。根据井下生物礁及围岩岩性与电性资料并结合过井地震剖面反射波的几何特征,建立台地边缘生物礁的地震正演数值模型,通过对比生物礁模型地震正演记录与实际生物礁地震剖面,建立针对研究区台地边缘生物礁的地震响应特征模式。依据生物礁的地震响应特征对该地区连片二、三维地震测线开展地震相分析,通过已有钻井地震相与沉积相对应关系分析,指出了长兴组生物礁在该地区的分布规律。四川北部地区地震相与沉积相带具有良好的对应关系,存在环台棚-海盆相的台地前缘斜坡-台地边缘生物礁相-开阔台地相沉积体系,地震剖面上生物礁的外部形态呈丘状或透镜状,内部为杂乱反射特征;礁盖白云岩具有亮点反射特征,生物礁底界面出现上凸或者下凹反射现象,生物礁的上部地层具有披覆反射结构,四川盆地北部地区长兴组台地边缘生物礁相在台棚-海盆相东、西两侧沿北西向呈条带状展布,分布面积大于2000km~2,生物礁气藏勘探潜力巨大。     

Physics of the Omori law: Inferences from interevent time distributions and pore pressure diffusion modeling

Empirical laws and statistics of earthquakes are valuable as a basis for a better understanding of the earthquake cycle. In this paper we focus on the postseismic phase and the physics of aftershock sequences. Using interevent time distributions for a catalogue of Icelandic seismicity, we infer that the parameter C₂ in the Omori law, often considered to represent incomplete detection of aftershocks, is at least in part related to the physics of the earthquake process. We investigate the role of postseismic pore pressure diffusion after two Icelandic earthquakes on the rate of aftershocks and what we can infer about the physical meaning of C₂ from the diffusion process. Using the Mohr–Coulomb failure criterion we obtain a rate of triggered points in our diffusion model that agrees with the modified Omori law, with a value of C₂ that is consistent with data. Our pore pressure diffusion model suggests that C₂ is related to the process of reducing high pore pressure gradients existing across a fault zone at short times after a main shock.     

新旧立体交叉隧道系统力学耦合作用全过程与规律

新旧立体交叉隧道系统耦合演化的非线性规律研究尚处于探索阶段。基于穿越过程中与工后的新旧立体交叉隧道系统耦合作用过程与机制分析,定量分析了其耦合作用中应力与位移状态变化的全过程;根据隧道稳定性非线性分析,分别从岩土体的黏弹塑性、动力学与能量耗散等3方面研究了立体交叉隧道非线性演化规律,并建立了其发生耦合作用的黏弹塑性、动力学与能量的标准及其演化函数;在此基础上,系统总结了新旧立体交叉隧道系统耦合演化总体特征,指出其耦合区域在空间上具有拓展性,耦合演化在时间上具有延续性。其研究结果为立体交叉隧道稳定性定量分析与控制研究提供了新思路。     

Crustal and upper mantle seismic structure of the Australian Plate, South Island, New Zealand

Seismic reflection and refraction data were collected west of New Zealand's South Island parallel to the Pacific–Australian Plate boundary. The obliquely convergent plate boundary is marked at the surface by the Alpine Fault, which juxtaposes continental crust of each plate. The data are used to study the crustal and uppermost mantle structure and provide a link between other seismic transects which cross the plate boundary. Arrival times of wide-angle reflected and refracted events from 13 recording stations are used to construct a 380-km long crustal velocity model. The model shows that, beneath a 2–4-km thick sedimentary veneer, the crust consists of two layers. The upper layer velocities increase from 5.4–5.9 km/s at the top of the layer to 6.3 km/s at the base of the layer. The base of the layer is mainly about 20 km deep but deepens to 25 km at its southern end. The lower layer velocities range from 6.3 to 7.1 km/s, and are commonly around 6.5 km/s at the top of the layer and 6.7 km/s at the base. Beneath the lower layer, the model has velocities of 8.2–8.5 km/s, typical of mantle material. The Mohorovicic discontinuity (Moho) therefore lies at the base of the second layer. It is at a depth of around 30 km but shallows over the south–central third of the profile to about 26 km, possibly associated with a southwest dipping detachment fault. The high, variable sub-Moho velocities of 8.2 km/s to 8.5 km/s are inferred to result from strong upper mantle anisotropy. Multichannel seismic reflection data cover about 220 km of the southern part of the modelled section. Beneath the well-layered Oligocene to recent sedimentary section, the crustal section is broadly divided into two zones, which correspond to the two layers of the velocity model. The upper layer (down to about 7–9 s two-way travel time) has few reflections. The lower layer (down to about 11 s two-way time) contains many strong, subparallel reflections. The base of this reflective zone is the Moho. Bi-vergent dipping reflective zones within this lower crustal layer are interpreted as interwedging structures common in areas of crustal shortening. These structures and the strong northeast dipping reflections beneath the Moho towards the north end of the (MCS) line are interpreted to be caused by Paleozoic north-dipping subduction and terrane collision at the margin of Gondwana. Deeper mantle reflections with variable dip are observed on the wide-angle gathers. Travel-time modelling of these events by ray-tracing through the established velocity model indicates depths of 50–110 km for these events. They show little coherence in dip and may be caused side-swipe from the adjacent crustal root under the Southern Alps or from the upper mantle density anomalies inferred from teleseismic data under the crustal root.     

灰岩冻融循环的劣化规律研究

基于岩石损伤理论推导了冻融循环作用下岩石的损伤劣化模型,并采用冻融循环试验方式测试了后崴子隧道灰岩岩样冻融循环后的物理力学特征变化规律,分析了其损伤劣化规律。获得了岩样的质量、纵波波速随冻融循环呈现先增后减的趋势,单轴抗压强度持续减小,弹性模量和峰值应变逐渐增大的结果。分析获得了冻融循环作用下灰岩总损伤变量与应变的关系,冻融和载荷的共同作用会使总损伤加剧,但损伤曲线表明耦合作用也可适当缓解这一影响,且灰岩应变值趋于一致,表明影响灰岩强度极限的主要因素可以不考虑冻融循环。     

高能量冲击作用下淤泥孔压特征规律试验研究

以往动力排水固结室内试验,通常冲击能量不够,很难激发软土某些工程响应,对应加固机制难以发现。通过可提供高冲击能的多向高能高速电磁力冲击智能控制试验系统,针对淤泥类超软土进行静动力排水固结模型试验,获得了淤泥孔压等响应特征：夯击瞬间（6 ms）上部孔压增长及下降时间非常短,且其重复性好;初始两遍夯击结束后中部孔压变化呈双峰型,其时间间隔随着夯击遍数增加而逐渐变大,最后不复存在;每遍夯击瞬时中部土压均出现急剧增长与快速减小,增长幅度随夯击遍数增加呈减小趋势,但每遍夯完后数天内土压值均大于夯前值;每遍夯击孔压消散后最终值都小于初始孔压,说明在一定的排水条件下,淤泥这类超软土地基确实可夯击;夯击后残余应力作用机制存在,且其对沉降起主要作用,而一定静力荷载的这种机制不明显;排水板插设扰动效应不可忽视,但该扰动效应随软土埋深增大而减少。     

An integrated multi-scale 3D seismic model of the Archaean Yilgarn Craton, Australia

The collection of a range of different seismic data types has greatly improved our understanding of the crustal architecture of Australia's Archaean Yilgarn Craton over the last few years. These seismic data include broadband seismic studies, seismic receiver functions, wide-angle recordings and mine-scale to deep seismic reflection transects. Each data set provides information on the three-dimensional (3D) tectonic model of the Yilgarn Craton from the craton scale through to the mine scale. This paper demonstrates that the integration and rationalisation of these different seismic data sets into a multi-scale 3D geological/seismic model, that can be visualised at once in a single software package, and incorporating all available data sets, significantly enhances this understanding. This enhanced understanding occurred because the integrated 3D model allowed easy and accurate comparison of one result against another, and facilitated the integrated questioning and interrogation across scales and seismic method. As a result, there are feedback questions regarding understanding of the individual seismic data sets themselves, as well as the Yilgarn Craton as a whole.The methodology used, including all the data sets in the model range, had to allow for the wide range of data sets, frequencies and seismic modes. At the craton scale, P-wave, S-wave and surface wave variations constrained the 3D lithospheric velocity model, revealing noticeable large-scale velocity variations within and across the craton. An interesting feature of the data, easily identified in 3D, is the presence of a fast S-wave velocity anomaly (> 4.8 km s^− 1) within the upper mantle. This velocity anomaly dips east and has a series of step-down offsets that coincide approximately with province and terrane boundaries of the Yilgarn Craton.One-dimensional receiver function profiles show variations in their crustal velocity across the craton. These crustal velocity variations are consistent with the larger-scale geological subdivision of the craton, and provide characteristic profiles for provinces and terranes. The receiver function results and the deep seismic reflection data both agree on the depth to the Moho, and both indicate an increase in Moho depth to the east. The 2D seismic refraction results in the south-west of the craton provide crustal thickness information, an indication of middle and lower crustal compositions, and information regarding the broad-scale architectural framework.At the province- and terrane-scale, the deep seismic reflection data and the mine-scale seismic data provide geometric constraints on crustal architecture, in particular the orientation of the region's fault systems as well as variations in the thickness of the granite–greenstone succession. Integration of the results from wide-angle seismic refraction data coincident with the deep seismic reflection data provided additional constraints on likely upper crustal lithologies.The integrated 3D seismic model implies the dominant geodynamic process involved the development of an orogenic belt that developed with a series of contractional (folding and thrusting) events, separated by equally important extensional events. The seismic reflection data in particular suggests that extensional movement on many shear zones was more common than previously thought.The seismic reflection data suggest that the dominant mineral systems involved deeply sourced fluid flowing up crustal-penetrating shear zones. These deeply sourced fluids were further focussed into sites located above fault-breached domal regions in the upper crust.     

A three-phase model for evaluating the seismic resistance of soils reinforced by a network of symmetrically inclined piles

The stability analysis of a piled embankment under seismic loading is considered, with a special emphasis on the optimization of the reinforcement layout by splitting the initial group of vertical piles into two symmetrically inclined arrays of parallel inclusions. The bidirectionally-reinforced soil thus obtained is appropriately described, at the macroscopic scale, by a three-phase model, conceived as an extension of the two-phase model previously developed for unidirectionally-reinforced soils. The model is implemented in a finite element formulation and related numerical code, which is used for simulating the behavior of the piled embankment up to failure. The results of these simulations, which favourably compare with upper bound yield design calculations, clearly indicate that the seismic resistance of the embankment can be considerably increased from symmetrically inclining the piles, even without taking the potential benefits of their flexural resistance into account.