Geostatistical Mapping with Continuous Moving Neighborhood

An issue that often arises in such GIS applications as digital elevation modeling (DEM) is how to create a continuous surface using a limited number of point observations. In hydrological applications, such as estimating drainage areas, direction of water flow is easier to detect from a smooth DEM than from a grid created using standard interpolation programs. Another reason for continuous mapping is esthetic; like a picture, a map should be visually appealing, and for some GIS users this is more important than map accuracy. There are many methods for local smoothing. Spline algorithms are usually used to create a continuous map, because they minimize curvature of the surface. Geostatistical models are commonly used approaches to spatial prediction and mapping in many scientific disciplines, but classical kriging models produce noncontinuous surfaces when local neighborhood is used. This motivated us to develop a continuous version of kriging. We propose a modification of kriging that produces continuous prediction and prediction standard error surfaces. The idea is to modify kriging systems so that data outside a specified distance from the prediction location have zero weights. We discuss simple kriging and conditional geostatistical simulation, models that essentially use information about mean value or trend surface. We also discuss how to modify ordinary and universal kriging models to produce continuous predictions, and limitations using the proposed models.     

Direct Sequential Simulation and Cosimulation

Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of N _v variables without any transformation. A set of examples of direct simulation and cosimulation are presented.     

Accounting for Estimation Optimality Criteria in Simulated Annealing

This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be better conditioned to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning.     

Integration of Tracer Test Data to Refine Geostatistical Hydraulic Conductivity Fields Using Sequential Self-Calibration Method

On the basis of local measurements of hydraulic conductivity,geostatistical methods have been found to be useful in heterogeneity characterization of a hydraulic conductivity field on a regional scale. However,the methods are not suited to directly integrate dynamic production data,such as,hydraulic head and solute concentration,into the study of conductivity distribution. These data,which record the flow and transport processes in the medium,are closely related to the spatial distribution of hydraulic conductivity. In this study,a three-dimensional gradient-based inverse method-the sequential self-calibration (SSC) method-is developed to calibrate a hydraulic conductivity field,initially generated by a geostatistical simulation method,conditioned on tracer test results. The SSC method can honor both local hydraulic conductivity measurements and tracer test data. The mismatch between the simulated hydraulic conductivity field and the reference true one,measured by its mean square error (MSE),is reduced through the SSC conditional study. In comparison with the unconditional results,the SSC conditional study creates the mean breakthrough curve much closer to the reference true curve,and significantly reduces the prediction uncertainty of the solute transport in the observed locations. Further,the reduction of uncertainty is spatially dependent,which indicates that good locations,geological structure,and boundary conditions will affect the efficiency of the SSC study results.     

基于遗传算法的BP网络在黄河三门峡年径流量预测中的应用

提出了一种基于遗传算法(genetic algorithms,GA)的BP神经网络模型来进行径流量预测。此模型融合了遗传优化算法的全局寻优能力和BP神经网络的局部搜索的优势,有效地防止了网络陷入局部极小值,同时又保证了预测结果的精确性。仿真实验结果表明:在黄河三门峡1950~1985年年径流量预测方面,GA-BP模型预测的平均相对误差为5.67%,标准BP算法的模型平均预测误差为11.05%,说明提出的GA-BP径流量方法行之有效。     

Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

基于Stacking模型融合的深基坑地面沉降预测

为了提高机器学习对深基坑地面沉降的预测能力,本文提出了一种基于Stacking集成学习方式的多模型融合的地面沉降预测方法,并以深圳某深基坑为例,采用斯皮尔曼相关性系数对基坑地面沉降的影响因子进行筛选;运用筛选后的8个影响因子建立Stacking深基坑地面沉降预测模型,以验证该方法的适用性。结果表明：Stacking预测模型的平均绝对误差为0.34、平均绝对误差百分比为2.22%,均方根误差为0.13,相较于传统基模型（随机森林、支持向量机和人工神经网络）,Stacking预测模型的平均绝对误差、平均绝对误差百分比和均方根误差值皆为最小。     

Brittleness index predictions from Lower Barnett Shale well-log data applying an optimized data matching algorithm at various sampling densities

The capability of accurately predicting mineralogical brittleness index(BI)from basic suites of well logs is desir-able as it provides a useful indicator of the fracability of tight formations.Measuring mineralogical components in rocks is expensive and time consuming.However,the basic well log curves are not well correlated with BI so correlation-based,machine-learning methods are not able to derive highly accurate BI predictions using such data.A correlation-free,optimized data-matching algorithm is configured to predict BI on a supervised basis from well log and core data available from two published wells in the Lower Barnett Shale Formation(Texas).This transparent open box(TOB)algorithm matches data records by calculating the sum of squared errors be-tween their variables and selecting the best matches as those with the minimum squared errors.It then applies optimizers to adjust weights applied to individual variable errors to minimize the root mean square error(RMSE)between calculated and predicted(BI).The prediction accuracy achieved by TOB using just five well logs(Gr,pb,Ns,Rs,Dt)to predict BI is dependent on the density of data records sampled.At a sampling density of about one sample per 0.5 ft BI is predicted with RMSE～0.056 and R2～0.790.At a sampling density of about one sample per 0.1 ft BI is predicted with RMSE～0.008 and R2～0.995.Adding a stratigraphic height index as an additional(sixth)input variable method improves BI prediction accuracy to RMSE～0.003 and R2～0.999 for the two wells with only 1 record in 10,000 yielding a BI prediction error of＞±0.1.The model has the potential to be applied in an unsupervised basis to predict BI from basic well log data in surrounding wells lacking mineralogical measure-ments but with similar lithofacies and burial histories.The method could also be extended to predict elastic rock properties in and seismic attributes from wells and seismic data to improve the precision of brittleness index and fracability mapping spatially.     

基于多变量LSTM神经网络的地下水水位预测

为解决以往模型未考虑地下水位相关影响因素的问题,探讨长短期记忆（LSTM）神经网络在地下水位预测中的应用,利用长短期记忆神经网络,采用多变量输入的方式,构建了基于多变量LSTM神经网络的地下水水位预测模型。以泰安市岱岳区J1号监测井为例,采用2001-2014年地下水水位动态监测资料与相关影响因素数据,利用多变量LSTM神经网络对2015-2016年地下水位进行预测,并与单变量LSTM神经网络和反向传播（BP）神经网络进行对比。研究结果表明：以相关影响变量为输入的BP神经网络无法考虑时序变化规律,预测均方根误差最大,为2.399 3;以地下水位为变量输入的单变量LSTM神经网络仅能根据时序变化作出相应预测,无法考虑相关变量影响,预测均方根误差为2.102 2;基于多变量输入的LSTM神经网络的预测精度显著高于单变量LSTM神经网络和BP神经网络,预测均方根误差最小,仅为1.919 1。总体上,多变量LSTM神经网络地下水位预测模型仅在某些峰值处误差较大,但总体预测效果较为理想。     

Influence of borehole quantity and distribution on lithology field simulation

This paper aims to study the influence of the number and distribution of drill samples on the simulation accuracy of the lithology field. This research mainly applies the variation function method in geo-statistics, and determines important indicators such as the variation, and then the lithology field is simulated by sequence index simulation. It is shown that(1) simulation error decreases with the increase of sampling density;(2) at the scale and complexity of this study, when the sampling density reaches 40/km^2, the average error of the lithology field simulation can be less than 2.0%;(3) in the study mode of examples, the simulation results of random sampling in the whole region are the most ideal, with an average error of 5.4%. The average error of the simulation results of the centralized sampling is about 10 times that of the random sampling method;(4) known from the influence analysis of the degree of study sample unevenness influence on the imitation results, under the same sample size, the simulation error decreases with the increase of the most adjacent index. When the nearest index reaches 1, the simulation error will be less than 6%, and the error variable range is within 3%.     

沁水盆地煤样静水压力下渗透率实验及模型分析

为研究沁水盆地煤样渗透率演化规律,构建了煤样渗透率测定的瞬态压力脉冲法实验装置,使用N2和CO2在实验室开展了3种试验条件的渗透率测定,应用Connell模型对实验结果进行分析,并讨论了模型预测值和实验值之间差别的原因。结果表明,（1）在恒定孔压变围压条件下渗透率随有效应力增大而减小;在等有效应力条件下,渗透率随孔压增大而减少;在恒定围压变孔压条件下,随孔压增大,渗透率呈先减小后变大的趋势。（2）运用Connell模型预测的恒定围压变孔压条件的渗透率值大于实验值,原因可能是由于裂隙压缩性系数和吸附应变系数存在估计误差。通过开展实验室渗透率实验和模型分析,对指导实验室内二氧化碳封存和气体驱替实验及其模拟研究具有借鉴意义。     

煤层气钻井固相物污染特征及评价

针对钻井过程中储层裂隙发育情况不明,防漏堵漏方法和材料选择困难的问题,结合实际井史资料,提出了一种基于神经网络的储层裂缝宽度预测方法。首先通过相关性分析,对储层裂缝宽度的主要相关因素进行分析并对其进行排序,选取了泵压、钻井液排量以及钻速等7种主要相关因素作为输入参数并利用附加动量算法和变学习率算法对模型收敛速度进行提升,同时对模型结构进行优选。其次利用遗传算法(GA)和Adaboost算法对BP神经网络(BPNN)进行优化,克服了其易陷入局部极小值的问题,提升了模型的预测精度。最后建立了Adaboost-GA-BP神经网络预测模型对储层裂缝宽度进行预测研究,同时对比分析了模型的预测精度。结果表明,相关参数与储层裂缝宽度的相关性由高到低依次为漏失速度与漏失量、泵压、钻井液排量、钻速、井深、塑性黏度和钻井液静切力。另外,附加动量算法和变学习率算法使得训练结束时训练数据的绝对误差和降低了27%,显著提升了模型性能,同时通过GA算法优化模型的权值和阈值以及利用Adaboost算法进行集成优化进一步提升了预测精度,建立的Adaboost-GA-BP神经网络储层裂缝宽度预测模型误差和相关系数分别为18%和0.98,与随机森林等其他模型相比,模型的预测精度高,可为勘探开发过程中的裂缝宽度计算以及堵漏方案的制定提供一定的指导。

     

基于ABC-GRNN组合模型的露天矿边坡变形预测

准确预测露天矿边坡变形是有效实现边坡临灾预警的重要保证,针对传统边坡变形预测方法无法表征和综合分析边坡变形受多种因素的影响,提出一种露天矿边坡变形的人工蜂群(ABC)算法优化广义回归网络(GRNN)组合预测模型(ABC-GRNN)。在此预测模型中,综合考虑了影响露天矿边坡变形的5个因素：开采扰动、降雨量、降雨持续时间、温度以及湿度。以山西中煤平朔安家岭露天矿为例,通过遗传算法改进BP神经网络(GA-BPNN)、支持向量机(SVM)等人工智能算法与实测变形数据进行预测效果对比分析。结果表明：ABC算法能够快速帮助GRNN寻优获取合适的传递参数,并对变形进行有效的预测。ABC-GRNN组合预测模型,将预测结果的平均绝对误差292.9 mm、平均绝对百分比误差0.691 3%及均方根误差338.9 mm分别降低到25 mm、0.043 3%和29.5 mm,说明该模型具有更高的预测精度;ABC-GRNN模型比其他模型收敛速度快,只经过7步的迭代,即可得到最小的均方误差。与其他预测模型相比较,本文模型的预测精度更高、泛化能力更强、收敛速度更快,有较高的实用价值。     

A method for assessing local variation among scattered measurements

Automatic triangulation of scattered locations permits analysis of local variation in a dependent variable through calculation of a roughness index. This is approached by treating triangles of the triangulation (including the dependent variable) as vectorial structures, and accumulating at each data point the vector sum of the cluster of triangles surrounding it. The roughness index is defined as the complement of the ratio of the area of a triangle cluster to the area of component triangles as projected onto a gradient plane defined by their vector sum. The roughness index provides a measure of consistency of data values relative to surrounding observations and can be interpreted as a local index of reliability of interpolation.     

Influence of borehole quantity and distribution on lithology field simulation

This paper aims to study the influence of the number and distribution of drill samples on the simulation accuracy of the lithology field. This research mainly applies the variation function method in geo-statistics, and determines important indicators such as the variation, and then the lithology field is simulated by sequence index simulation. It is shown that (1) simulation error decreases with the increase of sampling density; (2) at the scale and complexity of this study, when the sampling density reaches 40 /km2, the average error of the lithology field simulation can be less than 2.0%; (3) in the study mode of examples, the simulation results of random sampling in the whole region are the most ideal, with an average error of 5.4%. The average error of the simulation results of the centralized sampling is about 10 times that of the random sampling method; (4) known from the influence analysis of the degree of study sample unevenness influence on the imitation results, under the same sample size, the simulation error decreases with the increase of the most adjacent index. When the nearest index reaches 1, the simulation error will be less than 6%, and the error variable range is within 3%.     

Improved hydrograph prediction through subsurface characterization: conditional stochastic hillslope simulations

Subsurface heterogeneity is one of the largest sources of uncertainty associated with saturated hydraulic conductivity. Recent work has demonstrated that uncertainty in hydraulic conductivity can impart significant uncertainty in runoff generation processes and surface-water flow. Here, the role of site characterization in reducing hydrograph prediction bias and uncertainty is demonstrated. A fully integrated hydrologic model is used to conduct two sets of stochastic, transient simulation experiments comprising different overland flow mechanisms: Dunne and Hortonian. Conditioning hydraulic conductivity fields using values drawn from a simulated synthetic control case are shown to reduce both mean bias and variance in an ensemble of conditional hydrograph predictions when compared with the control case. The ensemble simulations show a greater reduction in uncertainty in the hydrographs for Hortonian flow. The conditional simulations predict surface ponding and surface pressure distributions with reduced mean error and reduced root mean square error compared with unconditional simulations. Uncertainty reduction in Hortonian and Dunne flow cases demonstrates different temporal signals, with more substantial reduction achieved for Hortonian flow.     

Generation of Aquifer Heterogeneity Maps Using Two-Dimensional Spectral Texture Segmentation Techniques

Numerical models that solve the governing equations for subsurface fluid flow and transport require detailed quantitative maps of spatially variable hydraulic properties. Recently, there has been great interest in methods that can map the spatial variability of hydraulic properties such as porosity and hydraulic conductivity (permeability). Presently, only limited data on natural permeability spatial structure are available. These data are often based on extensive discrete sampling in outcrops or boreholes. Then methods are used to interpolate between data values to map aquifer heterogeneity. Interpolation methods often mask critical local or intermediate scale heterogeneities. As sediment texture is directly correlated with many hydraulic properties we developed two new texture segmentation algorithms based on a space-local two-dimensional wavenumber spectral method known as the S-Transform. Existing texture segmentation algorithms could not delineate the subtle and continuous texture variations that exist in natural sediments. The S-Transform algorithms successfully delineated geologic structures and grain size patterns in photographs of outcrops in a glacial fluvial deposit; thus, no interpolation methods were required to produce continuous two-dimensional maps of texture facies. The S-Transform method is robust and is insensitive to changes in light intensity, and moisture variations. This makes the algorithm particularly applicable to natural sedimentary outcrops. The effectiveness of our methods are tested by correlating measured relative grain sizes in the images with actual grain size measurements taken from the sedimentary outcrops.     

Predicting Threshold Exceedance by Local Block Means in Soil Pollution Surveys

Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK), Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores.     

基于核最小二乘模型的矿产靶区预测

地质统计单元的含矿性与地质找矿证据之间存在复杂的非线性关系,建立这种复杂关系的多元非线性统计模型并预测矿产靶区,对矿产勘查具有重要指导意义。以核函数为理论工具,在核最小二乘原理基础上提出了矿产靶区预测的核最小二乘模型;在GDAL数字图像输入输出函数库和CLAPACK线性代数软件包基础上,用VC++语言开发了面向栅格数据的矿产靶区预测核最小二乘模型算法程序,并把模型应用于新疆阿勒泰地区的矿产靶区预测研究。在MapInfo中生成包含100×151个网格统计单元的栅格图层,把栅格化后的15种找矿证据图层转化成100×151×15的数字图像数据立方体,用自行开发的程序计算每个网格统计单元的核最小二乘判别得分。结果表明,网格统计单元判别得分的高值区与已知矿床（点）的空间分布基本一致。     

Spatial prediction of soil water content in karst area using prime terrain variables as auxiliary cokriging variable

In karst areas, accurately measuring and managing the spatial variability of soil water content (SWC) is very critical in settling numerous issues such as karst rocky desertification, ecosystem reconstruction, etc. In these areas, SWC exhibits strong spatial dependence, and it is a time and labor consuming procedure to measure its spatial variability. Therefore, estimation of this kind of soil property at an acceptable level of accuracy is of great significance. This study was conducted to evaluate and compare the spatial estimation of SWC by using ordinary kriging (OK) and cokriging (COK) methods with prime terrain variables, tending to predict SWC using limited available sample data for a 2,363.7 km² study area in Mashan County, Guangxi Zhuang Autonomous Region, Southwest China. The measured SWC ranged from 3.36 to 26.69 %, with a mean of 17.34 %. The correlation analysis between SWC and prime terrain variables indicated that SWC showed significantly positive correlation with elevation (r is 0.46, P < 0.01), and significantly negative correlation with slope (r is ?0.30, P < 0.01); however, SWC was not significantly correlated with aspect in the study area. Therefore, elevation and slope were used as auxiliary data together for SWC prediction using COK method, and mean error (ME) and root mean square error were adopted to validate the prediction of SWC by these methods. Results indicated that COK with prime terrain variables data was superior to OK with relative improvement of 28.52 % in the case of limited available data, and also revealed that such elevation and slope data have the potential to improve the precision and reliability of SWC prediction as useful auxiliary variables.