Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Use of microtremor measurement for assessing site effects in Northern Belgium – interpretation of the observed intensity during the MS = 5.0 June 11 1938 earthquake

To provide quantitative information on site effects in the northern part of Belgium, forty-seven H/V microtremor measurements were performed with 5 second seismometers over an area of about 15.000 km². Most of the results show a northward regular increase of the fundamental period in agreement with the augmentation of the Mesozoic and Cainozoic soft sedimentsthickness from a few meters 40 km south of Brussels to 900 m at the Netherlands-Belgium border. The measured resonance frequency values wereconsistent with theoretical computations performed at different sites onthe basis of existing information and shallow seismic experiments. At oneparticular site (Uccle) where borehole data were available, microtremor measurements using an array of four seismological stations with differentapertures allowed to obtain the low frequency part of the Rayleigh wave dispersion curve, extending the range covered by the analysis of surfacewaves artificially generated. The Vs profile derived from the surface waveinversion corroborates the 1 Hz natural frequency of the site. Comparison of these results with the macroseismic information concerning the M_S = 5.0 1938 earthquake which occurred 50 km west of Brussels,confirmed the hypothesis that the geological structure of the Brabant massifis likely to control damage distribution during such an earthquake. Comparisonbetween the intensity map of the 1938 earthquake and the resonance period ofsediments obtained by our microtremor study shows a clear relation betweenthe two parameters. During the 1938 earthquake, site effects played a prominent role due to the dimension of the source whose corner frequency wasabout 1 Hz.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

2002年秋季山东省干旱遥感监测分析

利用极轨气象卫星遥感资料对2002年山东省秋季干旱进行监测和服务,其监测方法主要采用热惯量法。为了提高土壤水分模式的计算精度,将全省分为4个区域,对利用卫星资料反演的地表温度日较差进行植被指数等环境因素订正。在地理信息系统支持下,比较准确地计算出农田受旱面积,效果良好。     

Dynamic theory of rigid-plasticity

This paper deals with an analysis method for the response and motion of soil-like rigid-plastic bodies under seismic loading conditions. A continuity condition to determine the acceleration distribution within the rigid-plastic body when the failure occurs during seismic motions is proposed. Combining this continuity condition of acceleration and the ‘Generalized Limit Equilibrium Method (GLEM)’, the responses of the earth structure during seismic motions as well as the permanent displacements can be obtained, where GLEM is one of the limit equilibrium methods proposed by the authors for static problems and providing the approximate solution for Kötter's equation. The theoretical formulation of the method, the illustrative examples, and some comparisons between the analytical and experimental results are demonstrated.     

Image processing of 2D resistivity data for imaging faults

A methodology to locate automatically limits or boundaries between different geological bodies in 2D electrical tomography is proposed, using a crest line extraction process in gradient images. This method is applied on several synthetic models and on field data set acquired on three experimental sites during the European project PALEOSIS where trenches were dug. The results presented in this work are valid for electrical tomographies data collected with a Wenner-alpha array and computed with an l₁ norm (blocky inversion) as optimization method. For the synthetic cases, three geometric contexts are modelled: a vertical and a dipping fault juxtaposing two different geological formations and a step-like structure. A superficial layer can cover each geological structure. In these three situations, the method locates the synthetic faults and layer boundaries, and determines fault displacement but with several limitations. The estimated fault positions correlate exactly with the synthetic ones if a conductive (or no superficial) layer overlies the studied structure. When a resistive layer with a thickness of 6 m covers the model, faults are positioned with a maximum error of 1 m. Moreover, when a resistive and/or a thick top layer is present, the resolution significantly decreases for the fault displacement estimation (error up to 150%). The tests with the synthetic models for surveys using the Wenner-alpha array indicate that the proposed methodology is best suited to vertical and horizontal contacts. Application of the methodology to real data sets shows that a lateral resistivity contrast of 1:5–1:10 leads to exact faults location. A fault contact with a resistivity contrast of 1:0.75 and overlaid by a resistive layer with a thickness of 1 m gives an error location ranging from 1 to 3 m. Moreover, no result is obtained for a contact with very low contrasts (1:0.85) overlaid by a resistive soil. The method shows poor results when vertical gradients are greater than horizontal ones. This kind of image processing technique should be systematically used for improving the objectiveness of tomography interpretation when looking for limits between geological objects.     

广西百色水电站边坡治理工程

文章通过广西右江百色水利枢纽地下发电厂房进水口与尾水洞高边坡的治理，介绍在此工程中具有特殊性的一些施工方法。该工程地质体为弱风化硅质泥岩夹泥化夹层、强风化含洞穴硅质泥岩石、强风化硅质岩及全强风化辉绿岩，地质条件非常复杂，对坡体的稳定极其不利。根据三维有限元的分析计算和国内有关权威专家的调查研究需施工1500kN、1000kN的锚索方能保证坡体的永久稳定。大吨位的锚索需锚固在强风化岩土体上，锚索设计采用能提高锚固力的防腐型压力分散锚索。通过现场锚索基本试验，其锚固力完全能满足工程需要。为保证进水口总体施工的进度，在施工进水口约30m高的垂直壁上的锚索时，笔者采用了通常施工中较少采用的垂直壁悬吊式施工法，满足了水电站的整体施工进度和要求。     

Probabilistic landslide susceptibility mapping in the Lai Chau province of Vietnam: focus on the relationship between tectonic fractures and landslides

This study evaluates the susceptibility of landslides in the Lai Chau province of Vietnam using Geographic Information System (GIS) and remote sensing data to focus on the relationship between tectonic fractures and landslides. Landslide locations were identified from aerial photographs and field surveys. Topographic, geological data and satellite images were collected, processed, and constructed into a spatial database using GIS data and image-processing techniques. A scheme of the tectonic fracturing of crust in the Lai Chau region was established. Lai Chau was identified as a region with many crustal fractures, where the grade of tectonic fracture is closely related to landslide occurrence. The influencing factors of landslide occurrence were: distance from a tectonic fracture, slope, aspect, curvature, soil, and vegetative land cover. Landslide prone areas were analyzed and mapped using the landslide occurrence factors employing the probability–frequency ratio model. The results of the analysis were verified using landslide location data and showed 83.47% prediction accuracy. That emphasized a strong relationship between the susceptibility map and the existing landslide location data. The results of this study can form a basis stable development and land use planning for the region.     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.