Smoothing and Change Point Detection for Gamma Ray Count Data

Gamma ray detectors are used to measure the natural radioactivity of rocks. For a number of boreholes drilled at a site the gamma ray detector is lowered into each borehole and counts of gamma ray emissions at different depths are recorded as the instrument is gradually raised to ground level. The profile of gamma counts can be informative about the geology at each location. The raw count data are highly variable, and in this paper we describe the use of adaptive smoothing techniques and change point models in order to identify changes in the geology based on the gamma logs. We formulate all our models for the data in the framework of the class of generalized linear models, and describe computational methods for Bayesian inference and model selection for generalized linear models that improve on existing techniques. Application is made to gamma ray data from the Castelreagh Waste Management Centre which served as a hazardous waste disposal facility for the Sydney region between March 1974 and August 1998. Understanding the geological structure of this site is important for further modelling the transport of pollutants beneath the waste disposal area.     

Bayesian Mixture Modelling in Geochronology via Markov Chain Monte Carlo

In this paper we develop a generalized statistical methodology for characterizing geochronological data, represented by a distribution of single mineral ages. The main characteristics of such data are the heterogeneity and error associated with its collection. The former property means that mixture models are often appropriate for their analysis, in order to identify discrete age components in the overall distribution. We demonstrate that current methods (e.g., Sambridge and Compston, 1994) for analyzing such problems are not always suitable due to the restriction of the class of component densities that may be fitted to the data. This is of importance, when modelling geochronological data, as it is often the case that skewed and heavy tailed distributions will fit the data well. We concentrate on developing (Bayesian) mixture models with flexibility in the class of component densities, using Markov chain Monte Carlo (MCMC) methods to fit the models. Our method allows us to use any component density to fit the data, as well as returning a probability distribution for the number of components. Furthermore, rather than dealing with the observed ages, as in previous approaches, we make the inferences of components from the “true” ages, i.e., the ages had we been able to observe them without measurement error. We demonstrate our approach on two data sets: uranium-lead (U-Pb) zircon ages from the Khorat basin of northern Thailand and the Carrickalinga Head formation of southern Australia.     

Bayesian Modelling of Spatial Data Using Markov Random Fields, With Application to Elemental Composition of Forest Soil

Spatial datasets are common in the environmental sciences. In this study we suggest a hierarchical model for a spatial stochastic field. The main focus of this article is to approximate a stochastic field with a Gaussian Markov Random Field (GMRF) to exploit computational advantages of the Markov field, concerning predictions, etc. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a GMRF defined on a lattice. To estimate model parameters we adopt a Bayesian perspective, and use Monte Carlo integration with samples from Markov Chain simulations. Our methods does not demand lattice, or near-lattice data, but are developed for a general spatial data-set, leaving the lattice to be specified by the modeller. The model selection problem that comes with the artificial grid is in this article addressed with cross-validation, but we also suggest other alternatives. From the application of the methods to a data set of elemental composition of forest soil, we obtained predictive distributions at arbitrary locations as well as estimates of model parameters.     

Bayesian analysis of marked stress release models for time-dependent hazard assessment in the western Gulf of Corinth

We consider point processes defined on the space–time domain which model physical processes characterized qualitatively by the gradual increase over time in some energy until a threshold is reached, after which, an event causing the loss of energy occurs. The risk function will, therefore, increase piecewise with sudden drops in correspondence to each event. This kind of behaviour is described by Reid's theory of elastic rebound in the earthquake generating process where the quantity that is accumulated is the strain energy or stress due to the relative movement of tectonic plates. The complexity and the intrinsic randomness of the phenomenon call for probabilistic models; in particular the stochastic translation of Reid's theory is given by stress release models. In this article we use such models to assess the time-dependent seismic hazard of the seismogenic zone of the Corinthos Gulf. For each event we consider the occurrence time and the magnitude, which is modelled by a probability distribution depending on the stress level present in the region at any instant. Hence we are dealing here with a marked point process. We perform the Bayesian analysis of this model by applying the stochastic simulation methods based on the generation of Markov chains, the so called Markov chain Monte Carlo (MCMC) methods, which allow one to reconcile the model's complexity with the computational burden of the inferential procedure. Stress release and Poisson models are compared on the basis of the Bayes factor.     

Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models

Traditional approaches to develop 3D geological models employ a mix of quantitative and qualitative scientific techniques,which do not fully provide quantification of uncertainty in the constructed models and fail to optimally weight geological field observations against constraints from geophysical data.Here,using the Bayesian Obsidian software package,we develop a methodology to fuse lithostratigraphic field observations with aeromagnetic and gravity data to build a 3D model in a small(13.5 km×13.5 km)region of the Gascoyne Province,Western Australia.Our approach is validated by comparing 3D model results to independently-constrained geological maps and cross-sections produced by the Geological Survey of Western Australia.By fusing geological field data with aeromagnetic and gravity surveys,we show that 89%of the modelled region has>95%certainty for a particular geological unit for the given model and data.The boundaries between geological units are characterized by narrow regions with<95%certainty,which are typically 400-1000 m wide at the Earth's surface and 500-2000 m wide at depth.Beyond~4 km depth,the model requires geophysical survey data with longer wavelengths(e.g.,active seismic)to constrain the deeper subsurface.Although Obsidian was originally built for sedimentary basin problems,there is reasonable applicability to deformed terranes such as the Gascoyne Province.Ultimately,modification of the Bayesian engine to incorporate structural data will aid in developing more robust 3D models.Nevertheless,our results show that surface geological observations fused with geophysical survey data can yield reasonable 3D geological models with narrow uncertainty regions at the surface and shallow subsurface,which will be especially valuable for mineral exploration and the development of 3D geological models under cover.     

Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions

Soil pollution data collection typically studies multivariate measurements at sampling locations, e.g., lead, zinc, copper or cadmium levels. With increased collection of such multivariate geostatistical spatial data, there arises the need for flexible explanatory stochastic models. Here, we propose a general constructive approach for building suitable models based upon convolution of covariance functions. We begin with a general theorem which asserts that, under weak conditions, cross convolution of covariance functions provides a valid cross covariance function. We also obtain a result on dependence induced by such convolution. Since, in general, convolution does not provide closed-form integration, we discuss efficient computation. We then suggest introducing such specification through a Gaussian process to model multivariate spatial random effects within a hierarchical model. We note that modeling spatial random effects in this way is parsimonious relative to say, the linear model of coregionalization. Through a limited simulation, we informally demonstrate that performance for these two specifications appears to be indistinguishable, encouraging the parsimonious choice. Finally, we use the convolved covariance model to analyze a trivariate pollution dataset from California.     

Mineral Potential Mapping Using Bayesian Learning for Multilayer Perceptrons

Multilayer perceptrons (MLPs) can be used to discover a function which can be used to map from a set of input variables onto a value representing the conditional probability of mineralization. The standard approach to training MLPs is gradient descent, in which the error between the network output and the target output is reduced in each iteration of the training algorithm. In order to prevent overfitting, a split-sample validation procedure is used, in which the data is partitioned into two sets: a training set, which is used for weight optimization, and a validation set, which is used to optimize various parameters that can be used to prevent overfitting. One of the problems with this approach is that the resulting maps can display significant variability which stems from (i) the (randomly initialized) starting weights and (ii) the particular training/validation set partition (also determined randomly). This problem is especially pertinent on mineral potential mapping tasks, in which the number of deposit cells is a very small proportion of the total number of cells in the study area. In contrast to gradient descent methods, Bayesian learning techniques do not find a single weight vector; rather, they infer the posterior distribution of the weights given the data. Predictions are then made by integrating over this distribution. An important advantage of the Bayesian approach is that the optimization of parameters such as the weight decay regularization coefficient can be performed using training data alone, thus avoiding the noise introduced through split-sample validation. This paper reports results of applying Bayesian learning techniques to the production of maps representing gold mineralization potential over the Castlemaine region of Victoria, Australia. Maps produced using the Bayesian approach display significantly less variability than those produced using gradient descent training. They are also more reliable at predicting the presence of unknown deposits.     

基于自然伽马测井信号的维纳滤波法求取泥质含量

泥质含量是定性、定量评价储层属性的一个重要参数.研究经济、适用、高精度的储层泥质含量求取方法, 对储层的评价、预测含油气远景和计算储层油气储量意义明确.提出了测井自然伽马求取泥质含量的新原理, 认为测井自然伽马信号是地层自然伽马真值通过一个系统的卷积滤波输出.利用测井自然伽马信号和提取的自然伽马真值子波, 采用维纳滤波法求取测井系统逆因子函数, 根据逆因子函数, 用自然伽马测井信号做卷积直接计算泥质含量.本研究在中国西北某油气勘探区有岩心分析资料的K13井进行了试验, 求取的泥质含量精度比测井常规解释方法大幅提高, 在同一勘探区K11、S44、S4等井试验性应用, 效果良好.      

Bayesian model selection for sand with generalization ability evaluation

Current studies have focused on selecting constitutive models using optimization methods or selecting simple formulas or models using Bayesian methods. In contrast, this paper deals with the challenge to propose an effective Bayesian-based selection method for advanced soil models accounting for the soil uncertainty. Four representative critical state-based advanced sand models are chosen as database of constitutive model. Triaxial tests on Hostun sand are selected as training and testing data. The Bayesian method is enhanced based on transitional Markov chain Monte Carlo method, whereby the generalization ability for each model is simultaneously evaluated, for the model selection. The most plausible/suitable model in terms of predictive ability, generalization ability, and model complexity is selected using training data. The performance of the method is then validated by testing data. Finally, a series of drained triaxial tests on Karlsruhe sand is used for further evaluating the performance.     

Markov Chain Monte Carlo Implementation of Rock Fracture Modelling

This paper deals with the problem of estimating fracture planes, given only the data at borehole intersections with fractures. We formulate an appropriate model for the problem and give a solution to fitting the planes using a Markov chain Monte Carlo (MCMC) implementation. The basics of MCMC are presented, with particular emphasis given to reversible jump, which is required for changing dimensions. We also give a detailed worked example of the MCMC implementation with reversible jump since our implementation relies heavily on this new methodology. The methods are tested on both simulated and real data. The latter is a unique data set in the form of a granite block, which was sectioned into slices. All joints were located and recorded, and the joint planes obtained by stacking strike lines. This work is important in the risk assessment for the underground storage of hazardous waste. Problems and extensions are discussed.     

On Modelling Discrete Geological Structures as Markov Random Fields

The purpose of this paper is to extend the locally based prediction methodology of BayMar to a global one by modelling discrete spatial structures as Markov random fields. BayMar uses one-dimensional Markov-properties for estimating spatial correlation and Bayesian updating for locally integrating prior and additional information. The methodology of this paper introduces a new estimator of the field parameters based on the maximum likelihood technique for one-dimensional Markov chains. This makes the estimator straightforward to calculate also when there is a large amount of missing observations, which often is the case in geological applications. We make simulations (both unconditional and conditional on the observed data) and maximum a posteriori predictions (restorations) of the non-observed data using Markov chain Monte Carlo methods, in the restoration case by employing simulated annealing. The described method gives satisfactory predictions, while more work is needed in order to simulate, since it appears to have a tendency to overestimate strong spatial dependence. It provides an important development compared to the BayMar-methodology by facilitating global predictions and improved use of sparse data.     

宁安盆地航空伽马能谱特征及铀成矿远景预测

利用最新的航空伽马能谱数据,分析了宁安盆地以及501铀矿床的航空伽马能谱特征。并利用铀转换参数(初始铀、活性铀、铀迁移系数)分析了本区的铀源条件,结合盆地基底、构造、岩相岩性、水文地质等成矿条件进行了铀成矿分析和远景预测。最终预测了3处铀成矿远景区段,对本区进一步找矿具有指导意义。     

GR320γ能谱仪人工核素面源刻度

介绍了GR320γ能谱仪人工核素面源刻度原理和方法、刻度实验过程以及对刻度结果的应用。通过人工核素小面源模拟大面源的刻度,得到人工核素137 Cs和60 Co面源的效率因子,使GR320γ能谱仪在进行环境放射性γ辐射水平调查中能够定量给出人工核素137 Cs和60 Co的面活度。对新疆某地航测异常的地面验证测量结果表明,该航测异常地表确实存在人工核素137 Cs,且GR320γ能谱仪测量的面活度结果与该异常就地HPGe谱仪的测量结果基本相符。此法可推广到其它型号的便携式γ能谱仪的刻度,也可扩展到其它人工核素面源的刻度。     

Bayesian Equivalent Sample Toolkit (BEST): an Excel VBA program for probabilistic characterisation of geotechnical properties from limited observation data

In site investigation, the amount of observation data obtained for geotechnical property characterisation is often too sparse to obtain meaningful statistics and probability distributions of geotechnical properties. To address this problem, a Bayesian equivalent sample method was recently developed. This paper aims to generalize the Bayesian equivalent sample method to various geotechnical properties, when measured by different direct or indirect test procedures, and to implement the generalized method in Excel by developing an Excel VBA program called Bayesian Equivalent Sample Toolkit (BEST). The BEST program makes it possible for practitioners to apply the Bayesian equivalent sample method without being compromised by sophisticated algorithms in probability, statistics and simulation. The program is demonstrated and validated through examples of soil and rock property characterisations.     

An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points

This paper presents an efficient Bayesian back-analysis procedure for braced excavations using wall deflection data at multiple points. Response surfaces obtained from finite element analyses are adopted to efficiently evaluate the wall responses. Deflection data for 49 wall sections from 11 case histories are collected to characterize the model error of the finite element method for evaluating the deflections at various points. A braced excavation project in Hang Zhou, China is chosen to illustrate the effectiveness of the proposed procedure. The results indicate that the soil parameters could be updated more significantly for the updating that uses the deflection data at multiple points than that only uses the maximum deflection data. The predicted deflections from the updated parameters agree fairly well with the field observations. The main significance of the proposed procedure is that it improves the updating efficiency of the soil parameters without adding monitoring effort compared with the traditional method that uses the maximum deflection data.     

The Use of Gamma Ray Spectrometry as an Aid for Uranium Exploration in Kab Amiri Area,Central Eastern Desert,Egypt

High‐resolution gamma ray spectrometry was exploited to locate the potential radioactive targets at Kab Amiri granite pluton, Central Eastern Desert, Egypt. The Kab Amiri pluton forms a concentric granitic body of monzogranite to syenogranite composition intruded into mafic‐ultramific rocks. To identify and detect anomalous concentrations of natural radioactive elements in the study area, contour maps of equivalent uranium (eU ppm), equivalent thorium (eTh ppm), potassium (K%) and their geochemical ratios (eU/Th, eTh/K and eU‐eTh/3.5) as well as standard deviation map of uranium were constructed and interpreted. Qualitative and quantitative interpretations of the spectrometric survey data revealed the presence of seven radioactive anomalies in the south of the studied area. These anomalies could be related to the prevailing faulting directions NE and ENE fault trends. The southernmost anomalous zone is related to high episyenitization and uranium concentrations. It exhibits a sharp increase in the eU concentrations reaching 370 ppm resulting in a high eU/eTh ratio reaching 4.5 and characterized by oval shape trending in the NE direction. Constructing the contour map of the (eU‐eTh/3.5) was helpful in defining the trends of uranium migration and enabling the delineation of the limit between the negative contours (leaching) and positive contours (deposition).     

利用自然伽马测井数据计算地层泥质含量

阐述了利用自然伽马测井数据,采用相对值法定量计算地层泥质含量的方法。用CorelDRAW绘图软件绘制泥质含量曲线。通过在研究区中的应用,证实了该方法的可靠性,为研究区地层泥质含量计算提供了可靠的依据。     

The Tornquist Zone, a north east inclining lithospheric transition at the south western margin of the Baltic Shield: Revealed through a nonlinear teleseismic tomographic inversion

From July 1996 to August 1997 the TOR project operated 130 seismographs in North Germany, Denmark and South Sweden, with the aim of collecting signals from local, regional and teleseismic earthquakes. This data set is particularly interesting since the seismic antenna crosses the most significant geological boundary in Europe, the Tornquist Zone, which in the northern part is the border between the Baltic Shield and the younger European lithosphere. Previous studies have shown significant physical changes in the crust and upper mantle across this transition zone, including two independent teleseismic tomographic studies of the TOR data set. But these two studies disagree on the orientation of the slope of the transition. Both studies used an iterative linearized inversion method. We will in this work Preprint submitted to Elsevier Science 27 July 2005 present an inversion based on Bayesian statistics, where the solution space is examined in order to study a very large number of tomographic solutions and to examine the solution uniqueness and uncertainty. The method is applied to measurements of 3345 relative teleseismic P-phase travel times from 48 teleseismic earthquakes with good azimuthal coverage with respect to the great circle arc of the TOR array. We find the lithospheric transition to be a north east inclination of around 30° to 45° off vertical.     

空间数据仓库元数据的结构体系

给出了空间数据仓库元数据的基本概念，说明了空间数据仓库元数据的相关技术．重点论述了空间数据仓库元数据的结构体系是由11类信息组成，它们分别是空间数据标识信息、区域范围信息、邻接信息、表示信息、数学基础信息、数据集内容信息、质量信息、分发信息、安全信息、联系信息和时间信息，并设计出了空间数据仓库元数据的组织结构。     

Tests on Application of Soil Magnetic and Integrated Gamma Ray TLD and TC Methods to the Exploration of Sandstone-Type Uranium Deposits

This paper introduces the test results of the soil magnetic survey and the integrated gamma-ray TLD and TC methods for sandstone-type uranium exploration and describes the prospecting mechanism. The tests have proved that these approaches have yielded good results on classifying the sedimentary fades, defining the redox transitional zones and reflecting deep mineralization information. They may probably become new methods on searching for sandstone-type uranium deposits.