Gravity field recovery from airborne gradiometer data using collaction and taking into account correlated errors

Least squares collocation is a very comprehensive method for gravity field modelling, since it may use known noise characteristics of the data. In many earlier applications the errors affecting the data were considered uncorrelated, mainly due to the difficulty in estimating the systematic character of such kind of errors. In this study, error covariance functions of airborne gravity gradiometer data are estimated by comparing model covariance functions with empirical covariance functions of the gravity gradiometer data. The model covariance functions were estimated from accurate surface gravity data and continuated upward to the height of the airborne measurements using the covariance propagation law. The estimated error covariance functions were modeled as finite ones and used as an additional information for the prediction of gravity anomalies from gravity gradiometer data. The assessment of the prediction results was made by comparing the gravity values predicted from the airborne gradient data and showed up to 25% improvement compared to not using correlated errors.     

Modelling in-situ upgrading of heavy oil using operator splitting method

The in-situ upgrading (ISU) of bitumen and oil shale is a very challenging process to model numerically because of the large number of components that need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Operator splitting methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as the splitting error. The best splitting method for modelling a given process minimises the splitting error whilst improving computational performance compared to a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to the modelling of ISU. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error. While this error has been extensively analysed for linear operators for a wide range of methods, the results cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. In this paper, we investigate the application of various operator splitting techniques to the modelling of the ISU of bitumen and oil shale. The techniques were tested on a simplified model of the physical system in which a solid or heavy liquid component is decomposed by pyrolysis into lighter liquid and gas components. The operator splitting techniques examined include the sequential split operator (SSO), the Strang-Marchuk split operator (SMSO) and the iterative split operator (ISO). They were evaluated on various test cases by considering the evolution of the discretization error as a function of the time-step size compared with the results obtained from a fully implicit simulation. We observed that the error was least for a splitting scheme where the thermal conduction was performed first, followed by the chemical reaction step and finally the heat and mass convection operator (SSO-CKA). This method was then applied to a more realistic model of the ISU of bitumen with multiple components, and we were able to obtain a speed-up of between 3 and 5.     

A robust cylindrical fitting to point cloud data

Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers.     

Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices

The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude–longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.     

Generalized numerical error analysis with applications to geochronology and thermodynamics

A general numerical error propagation procedure is developed to calculate the error in a quantity derived from measurements which are subject to errors. It is an alternative to computer intensive techniques such as Monte Carlo and can be applied to quite complex analytical problems where correlation among the measurement errors and among the final errors in results are present. Previous formulations have usually ignored correlated errors. Some of the assumptions involved in error propagation can also be checked numerically. This is an advantage over analytical formulations which cannot assess the validity of the calculated errors. Formulation as computer subroutines permits the analysis to be added to existing programs. Examples from the fields of geochronology and thermodynamics are used to highlight the advantages and the flexibility of the method.     

苏州粉土地层地连墙施工对地层扰动影响研究

采用三维有限差分软件FLAC3D对地下连续墙施工进行模拟,分析苏州地区粉土地层中地连墙施工对土体扰动及周边建筑物影响。利用UBCSAND硬化规律对外部扰动作用下土体强度逐步发挥的力学特性进行表征,模拟开挖过程中浅层土体变形,并对地连墙施工中成槽开挖、钢筋混凝土施工及混凝土硬化进行全过程模拟。计算结果表明,硬化模型较好地反映地连墙施工扰动下浅层土体力学特性;地连墙成槽阶段地层变形随深度的增加而减小,地表以下20 m范围内地层变形显著,而深部土体变形较小;钢筋混凝土浇筑施工对地层变形起到抑制作用;混凝土硬化阶段地层变形趋于稳定。在该基础上采用硬化模型对苏州某基坑地连墙施工进行数值仿真,模拟结果和现场实测吻合较好。     

Adaptive hierarchical upscaling of flow in heterogeneous reservoirs based on an a posteriori error estimate

This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool.     

Statistical modelling of thermal annealing of fission tracks in apatite

We develop an improved methodology for modelling the relationship between mean track length, temperature, and time in fission track annealing experiments. We consider “fanning Arrhenius” models, in which contours of constant mean length on an Arrhenius plot are straight lines meeting at a common point. Features of our approach are explicit use of subject matter knowledge, treating mean length as the response variable, modelling of the mean-variance relationship with two components of variance, improved modelling of the control sample, and using information from experiments in which no tracks are seen.

This approach overcomes several weaknesses in previous models and provides a robust six parameter model that is widely applicable. Estimation is via direct maximum likelihood which can be implemented using a standard numerical optimisation package. Because the model is highly nonlinear, some reparameterisations are needed to achieve stable estimation and calculation of precisions. Experience suggests that precisions are more convincingly estimated from profile log-likelihood functions than from the information matrix.

We apply our method to the B-5 and Sr fluorapatite data of Crowley et al. (1991) and obtain well-fitting models in both cases. For the B-5 fluorapatite, our model exhibits less fanning than that of Crowley et al. (1991), although fitted mean values above 12 μm are fairly similar. However, predictions can be different, particularly for heavy annealing at geological time scales, where our model is less retentive. In addition, the refined error structure of our model results in tighter prediction errors, and has components of error that are easier to verify or modify. For the Sr fluorapatite, our fitted model for mean lengths does not differ greatly from that of Crowley et al. (1991), but our error structure is quite different.     

Characteristics of Oil Contamination and Numerical Modelling of Its Transport in Fracture-Karst Water in Zibo City,China

In this paper, the hydraulic characteristics of the fracture-karst aquifer and the distribution patterns of petrochemical contaminants are studied. Then, a numerical model using the mixed Eulerian-Lagrangian approach is constructed to predict the distribution and transport of petrochemical compounds in groundwater. The results of numerical modelling and sensitivity analysis show that it may be a workable way for aquifer remediation to combine contamination sources control and capture zone establishment.     

基于建筑信息模型技术的盾构隧道结构信息模型建模方法

为解决隧道工程建设各阶段之间的信息交流和数据共享困难的问题,前期在工业基础类（industry foundation classes,简称IFC）标准的基础上实现了盾构隧道建模数据模型。在此基础上,提出基于建筑信息模型（building information modeling,简称BIM）技术的盾构隧道结构信息模型建模方法。根据扩展的盾构隧道结构信息模型的IFC表达,提出了单个管片块建模方法和隧道线路解算流程和步骤。在此基础上,进行盾构管片拼装与隧道建模,建立了盾构隧道建模流程和参数化建模方法,形成了基于BIM技术的盾构隧道结构信息模型建模方法。最后,通过实例验证了建模方法的可行性。工程应用表明,通过借鉴和引入BIM技术,建立基于统一IFC数据标准的盾构隧道结构信息模型,可以实现盾构隧道信息的无损交换与充分共享,从而进一步验证了前期提出的基于IFC的盾构隧道建模数据模型的正确性。研究成果可为隧道数值计算分析提供初始模型,为实现隧道三维可视化模型和分析计算模型的无缝对接提供基础。     

A New Methodology for Singularity Modelling in Flow Simulations in Reservoir Engineering

In this paper, numerical methods for flow simulation in the well vicinity are discussed. Flux truncation errors are analyzed on gridblocks near the well. Due to the singularity of the well, standard numerical schemes are not efficient for near well flow simulations. To improve simulation accuracy, a new methodology, using a change of coordinates to make near well pressure linear, is presented for the singularity modelling. Based on this new approach, two numerical schemes, a two-point flux approximation scheme and a multi-point one, are proposed. These schemes are accurate for the near well modelling and are suitable for any kinds of gridblocks.     

http://www.sciencedirect.com/science/article/pii/S1674987111000508

This paper presents the results of a set of numerical models focussing on structural controls on hydrothermal mineralization.We first give an overview of natural phenomena of structurally-controlled ore formation and the background theory and mechanisms for such controls. We then provide the results of a group of simple 2D numerical models validated through comparison with Cu-vein structure observed near the Shilu Copper deposit(Yangchun,Guangdong Province, China) and finally a case study of 3D numerical modelling applied to the Hodgkinson Province in North Queensland(Australia).Two modelling approaches,discrete deformation modelling and continuum coupled deformation and fluid flow modelling,are involved.The 2D model-derived patterns are remarkably consistent with the Cu-vein structure from the Shilu Copper deposit,and show that both modelling approaches can realistically simulate the mechanical behaviours of shear and dilatant fractures.The continuum coupled deformation and fluid flow model indicates that pattern of the Cuveins near the Shilu deposit is the result of shear strain localization,development of dilation and fluid focussing into the dilatant fracture segments.The 3D case-study models(with deformation and fluid flow coupling) on the Hodgkinson Province generated a number of potential gold mineralization targets.     

On the time scales of nonlinear instability in miscible displacement porous media flow

In this paper, we analyze the time scales associated with instable fingering induced by density contrasts in miscible displacement porous media flow. We perform numerical simulations of a two-dimensional domain with boundaries that are closed to flow and identify the three regimes of the dynamics, namely the development of a stable diffusive boundary layer, the onset and growth of instabilities, and the fully nonlinear dynamics. Special focus is given to the onset of the fully nonlinear regime. The results are generic in the sense that there are no parameters in the non-dimensional model problem. Large ensembles are studied and an error estimate is given based on the combined effect of numerical errors and sampling errors. The nonlinear time scales show a dependence on the size of initial perturbations. We estimate this size for three formations used for CO₂ storage and find that the onset of enhanced convective mixing is considerably delayed compared with the linear onset time.     

Probabilistic calibration of a coupled hydro-mechanical slope stability model with integration of multiple observations

Multiple types of responses, such as displacements, ground water level, pore water pressures, water contents, etc., are usually measured in comprehensive monitoring programmes for rainfall-induced landslide prevention. In this study, a probabilistic calibration method for coupled hydro-mechanical modelling of slope stability is presented with integration of multiple types of measurements. A numerical example of a soil slope under rainfall infiltration is illustrated to compare the effects of single and multiple types of responses on parameter estimation and model calibration. The results show that the soil parameters can be estimated with less uncertainty and total uncertainty bounds are narrower with multiple types of responses than with a single type of response. Model calibration based on multiple types of responses can compromise different responses and hence the means and standard deviations of model error are the smallest. A feasible correlation coefficient between soil modulus and permeability can be obtained from model calibration with multiple types of responses and single type of response as long as the responses include displacement data.     

Fuzzy finite element analysis of a foundation on an elastic soil medium

One of the important factors that lead to errors in settlement predicitions is the degree of precision in obtaining the soil parameters. Most mathematical methods for reliability modelling offered to date in the area of geomechanics are based on the classical probabilistic approach, in which soil properties are treated as random variables. In this paper, a model based on the theory of fuzzy sets is presented to take account of the uncertainty in the soil behaviour. This proposed method considers the elastic modulus and Poisson's ratio as two fuzzy numbers in the elastic matrix. An example is given to show the possibility distributions of the displacements and the stresses at some locations in the soil medium. By means of a fuzzy inference scheme, the total possibility distributions or total membership functions of the finite element results may be obtained by considering the estimated error resulting from the mesh discretization.     

A multidisciplinary procedure to evaluate and optimize the efficacy of hydraulic barriers in contaminated sites: a case study in Northern Italy

In the last decades, hydraulic barriers have been activated in a large number of polluted sites with the aim of preventing groundwater pollution outside the contaminated area. From a regulatory point of view, there is the need of evaluating the efficacy of these barriers. For this reason, the goal of the present study is to apply a coupled experimental modelling approach aimed at evaluating the efficacy of the barrier and providing management strategies. In particular, a case study in Italy is investigated. The study case is of main interest because of its complexity due to a heterogeneous aquifer and the presence of surface water that interacts with the below aquifer. The study has been carried out through the experimental characterization of the aquifer system (coupling the classic stratigraphic techniques with the results of radiocarbon dating, as well as through pumping and injection tests) and its hydrogeological behaviour (by means of hydraulic- and the stream-head measurements, as well as some isotopic investigations), and the implementation of a numerical model (through MODFLOW 2005). The results show the effectiveness of the coupled experimental modelling approach to analyse and simulate the hydrodynamics within the test aquifer system, as well as to evaluate the efficacy of the hydraulic barrier. Based on the results of the numerical model, easy solutions were designed to manage the barrier.     

大地电磁响应数值计算中结点分布的最优化问题

首次提出用广义逆理论解决数值计算中结点分布的最优化问题。由于文章的目的仅在于提出和说明这种方法的概念,所以只考虑一种典型的一维大地模型,并叙述了广义逆理论在这种应用中的基本关系。结果表明这种算法可给出最佳的结点分布。雅可比矩阵,奇异值和对应的特征向量的分析,可以从本质上理解不同电性层中结点分布对数值计算精度的影响,对设计数值模型具有很重要的指导意义。本文的结果对二维和三维复杂模型的数值计算具有重要的参考意义。     

河流型水库垂向二维水沙数学模型

在垂向二维水动力模型的基础上,叠加了泥沙模型,建立了垂向二维泥沙模型,该模型的主要特点是水动力模型采用斜压模式,可以模拟由于水库水温度分布时空变化对其水动力结构及泥沙沉降速度的影响;泥沙模型采用分步法求解,简化了计算;独立求解粘性泥沙及非粘性泥沙的沉降速度及水土界面交换通量;运用经验公式估算泥沙及水动力模型参数,弥补了资料不足的缺点。最后运用实测资料对所建泥沙模型进行了有效性验证,结果表明:悬沙模拟值与实测值相对误差较小,时空分布特征相似;同时,模型能较为准确反映由于水库出入流引起的库首与库尾水温及泥沙分布特征。     

实验室尺度高地温梯度模拟地层的实现方法研究

地热井与周围热储层的传热过程对地热井产热性能研究有重要意义。由于实际工程中在地热井周边布置测点较难,无法获取地热井周围热储层的参数变化,进而为地热热储模拟结果提供验证,故以往大多地热热储模拟仅将地热井作为源项处理,未考虑地热流体和储层的耦合流动换热。实验室条件下的模拟试验方便布置测点,可为热储-井筒耦合流动传热模型提供试验验证,其中如何实现实验室尺度下有温度梯度的模拟地层是试验研究的关键,目前尚未有类似研究。基于传热学基本原理,研究了实验室条件下有较高温度梯度多孔地层的快速实现方法,通过确定模拟热储层和热储盖层几何尺寸、优选填充多孔介质和实现恒定温度的模拟热储层,设计了一套实验室尺度下有高温度梯度的模拟地层系统,通过分层加热与边界动态热补偿方法,较快实现了热储层温度分别为60,65,70°C下模拟地层的线性温度分布,采用有限体积法得到的数值模拟与试验结果的相对误差在±2.5%范围内,二者吻合较好。文章设计搭建的模拟地层系统可为开展地热井筒-热储耦合模拟试验提供条件,进而为开发的地热热储-井筒耦合传热数值软件提供试验验证。