On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

Estimates of heat flow and heat production and a thermal model of the São Francisco craton

An updated analysis of geothermal data from the highland area of eastern Brazil has been carried out and the characteristics of regional variations in geothermal gradients and heat flow examined. The database employed includes results of geothermal measurements at 45 localities. The results indicate that the Salvador craton and the adjacent metamorphic fold belts northeastern parts of the study area are characterized by geothermal gradients in the range of 6–17°C/km. The estimated heat flow values fall in the range of 28–53 mW/m², with low values in the cratonic area relative to the fold belts. On the other hand, the São Francisco craton and the intracratonic São Francisco sedimentary basin in the southwestern parts are characterized by relatively higher gradient values, in the range of 14–42°C/km, with the corresponding heat flow values falling in the range of 36–89 mW/m². Maps of regional variations indicate that high heat flow anomaly in the São Francisco craton is limited to areas of sedimentary cover, to the west of the Espinhaço mountain belt. Crustal thermal models have been developed to examine the implications of the observed intracratonic variations in heat flow. The thermal models take into consideration variation of thermal conductivity with temperature as well as change of radiogenic heat generation with depth. Vertical distributions of seismic velocities were used in obtaining estimates of radiogenic heat production in crustal layers. Crustal temperatures are calculated based on a procedure that makes simultaneous use of the Kirchoff and Generalized Integral Transforms, providing thereby analytical solutions in 2D and 3D geometry. The results point to temperature variations of up to 300°C at the Moho depth, between the northern Salvador and southern São Francisco cratons. There are indications that differences in rheological properties, related to thermal field, are responsible for the contrasting styles of deformation patterns in the adjacent metamorphic fold belts.     

Comparison of numerical models of two debris flows in the Cortina d’ Ampezzo area,Dolomites, Italy

The accurate prediction of runout distances, velocities and the knowledge of flow rheology can reduce the casualties and property damage produced by debris flows, providing a means to delineate hazard areas, to estimate hazard intensities for input into risk studies and to provide parameters for the design of protective measures. The application of most of models that describe the propagation and deposition of debris flow requires detailed topography, rheological and hydrological data that are not always available for the debris-flow hazard delineation and estimation. In the Cortina d’Ampezzo area, Eastern Dolomites, Italy, most of the slope instabilities are represented by debris flows; 325 debris-flow prone watersheds have been mapped in the geomorphological hazard map of this area. We compared the results of simulations of two well-documented debris flows in the Cortina d’Ampezzo area, carried on with two different single-phase, non-Newtonian models, the one-dimensional DAN-W and the two-dimensional FLO-2D, to test the possibility to simulate the dynamic behaviour of a debris flow with a model using a limited range of input parameters. FLO-2D model creates a more accurate representation of the hazard area in terms of flooded area, but the results in terms of runout distances and deposits thickness are similar to DAN-W results. Using DAN-W, the most appropriate rheology to describe the debris-flow behaviour is the Voellmy model. When detailed topographical, rheological and hydrological data are not available, DAN-W, which requires less detailed data, is a valuable tool to predict debris-flow hazard. Parameters obtained through back-analysis with both models can be applied to predict hazard in other areas characterized by similar geology, morphology and climate.     

Hydrogeology of thermal waters in Viterbo area, central Italy

A conceptual hydrogeological model of the Viterbo thermal area (central Italy) has been developed. Though numerous studies have been conducted on its geological, geochemical and geothermal features, there is no generalized picture defining the origin and yield of the hydrothermal system. These latter aspects have therefore become the objectives of this research, which is based on new hydrogeological and geochemical investigations. The geological setting results in the coexistence of overlapped interacting aquifers. The shallow volcanic aquifer, characterized by fresh waters, is fed from the area around the Cimini Mountains and is limited at its base by the semiconfining marly-calcareous-arenaceous complex and low-permeability clays. To the west of Viterbo, vertical upflows of thermal waters of the sulphate-chloride-alkaline-earth type with higher gas contents, are due to the locally uplifted carbonate reservoir, the reduced thickness of the semiconfining layer and the high local geothermal gradient. The hot waters (30–60°C) are the result of deep circulation within the carbonate rocks (0.5–1.8 km) and have the same recharge area as the volcanic aquifer. The upward flow in the Viterbo thermal area is at least 0.1 m³/s. This flow feeds springs and deep wells, also recharging the volcanic aquifer from below.     

New Generation of Probabilistic Seismic Hazard Assessment for the Area Cologne/Aachen Considering the Uncertainties of the Input Data

A new earthquake catalogue for central, northern and northwestern Europe with unified M_w magnitudes, in part derived from chi-square maximum likelihood regressions, forms the basis for seismic hazard calculations for the Lower Rhine Embayment. Uncertainties in the various input parameters are introduced, a detailed seismic zonation is performed and a recently developed technique for maximum expected magnitude estimation is adopted and quantified. Applying the logic tree algorithm, resulting hazard values with error estimates are obtained as fractile curves (median, 16% and 84% fractiles and mean) plotted for pga (peak ground acceleration; median values for Cologne 0.7 and 1.2 m/s² for probabilities of exceedence of 10% and 2%, respectively, in 50 years), 0.4 s (0.8 and 1.5 m/s²) and 1.0 s (0.3 and 0.5 m/s²) pseudoacclerations, and intensity (I₀ = 6.5 and 7.2). For the ground motion parameters, rock foundation is assumed. For the area near Cologne and Aachen, maps show the median and 84% fractile hazard for 2% probability of exceedence in 50 years based on pga (maximum median value about 1.5 m/s²), and 0.4 s (>2 m/s²) and 1.0 s (about 0.8 m/s²) pseudoaccelerations, all for rock. The pga 84% fractile map also has a maximum value above 2 m/s² and shows similarities with the median map for 0.4 s. In all maps, the maximum values fall within the area 6.2–6.3° E and 50.8–50.9° N, i.e., east of Aachen.     

Natural and man-induced stress evolution of slopes: the Monte Mario hill in Rome

The paper deals with stress-release effects induced by man-made cuts or excavations into natural stiff clay slopes that experienced erosion in response to valley deepening. The study was focused on the Monte Mario hill in Rome (Italy), which formed part of an area of recent urban expansion. The methodology of the study relied on a reference engineering-geology model, which was developed on the basis of site and laboratory data and stress–strain analyses. The latter analyses were carried out with the finite-difference code FLAC 4.0. Numerical modelling was based on a sequential approach, taking into account the main evolutionary stages of the Tiber river valley in Romeȁ9s urban area and then making cuts at the bottom of the slope located south of the Monte Mario Astronomical Observatory. The simulation revealed the stress-release effects that fluvial erosion and excavation fronts have caused on the investigated slopes and their consequent gravitational instabilities. These processes appear with metre-scale displacements, followed by stress-release cracks (actually observed on the slopes under review). In quantifying stress-release deformations, the simulation took into account the possible role of creep in the observed retardation of stress-release effects.Research activities were carried on with the co-operation of Dȁ9Arcangelo A. (Consorzio TREESSE, andrea.darcangelo@libero.it) and Moretti S. (IMG S.r.l. Servizi Tecnici per lȁ9Ingegneria e lȁ9Ambiente, moretti@img-srl.it)     

Initiation and development of pull-apart basins with Riedel shear mechanism: insights from scaled clay experiments

Typical pull-apart structures were created in scaled clay experiments with a pure strike-slip geometry (Riedel type experiments). A clay slab represents the sedimentary cover above a strike-slip fault in the rigid basement. At an early stage of the development of the deformation zone, synthetic shear fractures (Riedel shears) within the clay slab display dilatational behaviour. With increasing basal displacement the Riedel shears rotate and open further, developing into long, narrow and deep troughs. The shear displacement and the low angle with the prescribed principal basal fault set them apart from tension gashes. At a more evolved stage, synthetic segments (Y-shears) parallel to the basal principal fault develop and accommodate progressive strike-slip deformation. The Y-shears connect the tips of adjacent troughs developed from the earlier Riedel shears, resulting in the typical rhomb-shaped structures characteristic for pull-apart basins. The Strait of Sicily rift zone, with major strike-slip systems being active from the Miocene to the Present, comprises pull-apart basins at different length scales, for which the structural record suggests development by a mechanism similar to that observed in our experiments.     

基于点重要度的地形LOD简化算法及精度

在分析、讨论目前关于3维地形模型简化与误差控制方法的基础上,提出了一种基于点重要度进行连续LOD模型简化的算法.并以5种典型地貌的实验数据作为运行实例,给出了点重要度与地貌类型之间的精度关系.这为今后连续LOD模型的合理建立提供了一种新思路和方法,也为模型的简化提供了科学依据.     

Spatial process and data models: Toward integration of agent-based models and GIS

The use of object-orientation for both spatial data and spatial process models facilitates their integration, which can allow exploration and explanation of spatial-temporal phenomena. In order to better understand how tight coupling might proceed and to evaluate the possible functional and efficiency gains from such a tight coupling, we identify four key relationships affecting how geographic data (fields and objects) and agent-based process models can interact: identity, causal, temporal and topological. We discuss approaches to implementing tight integration, focusing on a middleware approach that links existing GIS and ABM development platforms, and illustrate the need and approaches with example agent-based models.     

Fuzzy neural network models for liquefaction prediction

Integrated fuzzy neural network models are developed for the assessment of liquefaction potential of a site. The models are trained with large databases of liquefaction case histories. A two-stage training algorithm is used to develop a fuzzy neural network model. In the preliminary training stage, the training case histories are used to determine initial network parameters. In the final training stage, the training case histories are processed one by one to develop membership functions for the network parameters. During the testing phase, input variables are described in linguistic terms such as ‘high’ and ‘low’. The prediction is made in terms of a liquefaction index representing the degree of liquefaction described in fuzzy terms such as ‘highly likely’, ‘likely’, or ‘unlikely’. The results from the model are compared with actual field observations and misclassified cases are identified. The models are found to have good predictive ability and are expected to be very useful for a preliminary evaluation of liquefaction potential of a site for which the input parameters are not well defined.