Indicator Kriging without Order Relation Violations

Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified.     

泛克立格法和指示克立格法在地球化学探矿中的应用

泛克立格法是一种非平稳随机函数的最佳线性无偏估计方法，作者将之用于处理区域地球化学探矿数据，给出被测元素的估计值，漂移植和涨落值，后者为评估元素区域北景和异常特性提供了有用信息，作者用非参数地质统计学的指示克立格法对化探元素含量进行异值的分析及大于各级下限值的概率估计。     

基于多元线性回归的航空重力梯度测量自身梯度校正

航空重力梯度勘探中,载体自身产生的重力梯度效应对于超高精度的重力梯度仪而言是一种严重的干扰。由于载体结构复杂,用常规的载体建模并正演难以精确去除这种干扰。本文从统计学角度出发,用多元线性回归来处理自身梯度效应,不需要对载体模型做出任何假设与近似,用纯数据驱动的方式来校正自身梯度的干扰。回归诊断与模型仿真验证了这种校正方式有较高的准确性,并且当实际的转角落在地面标定的范围内时具备预测能力。     

基于回归克里格方法和sentinel 2B遥感数据的澴河流域土壤总磷空间分布信息提取

土壤总磷空间分布是准确掌握流域农业面源污染状况的关键,而遥感技术因其便利性在土壤面源污染调查中的潜力亟待探索。本文以澴河流域土壤总磷分布为例,分析了土壤总磷的光谱特性,发现总磷含量与土壤光谱反射率呈负相关,其中红外光谱（700~1800nm）表现更加明显;并以土壤总磷光谱计算数据作为环境辅助因子,取样点数据作为主要因素,运用回归克里格地统计方法成功提取了澴河流域土壤总磷空间分布信息,将结果与实测数据对比,其ME值为0.08,MAE值为0.48,RMSE值为0.69,预测精度较协同克里格和反距离权重法有明显提高。本方法既保留了地统计分析方法的精度,又具备处理高密度样本的能力,为土壤属性的空间插值提供了一种可行的获取方法。     

地下水出流单断沙关系的回归分析

阐述回归分析理论，根据南洞1：1站8年的实测输沙率成果资料作回归分析。从而了解和认识地下水出流的泥沙在横向和垂向上的分布规律及各垂线单沙与断沙之间的相关系数、回归效果、回归误差的多少。掌握泥沙的变化规律，对该地区的工、农业用水，城市用水，水资源的合理化利用和保护有着十分重要的意义。     

灰色线性回归组合模型在北京地面沉降分层预测中的应用

灰色系统理论GM(1,1)模型,应用于地面沉降模拟和预测中只能分析数据的指数变化规律。对于地面沉降发展过程中,存在的线性关系不能有效地反映。本文利用灰色组合模型中的第一类灰色组合模型即GM(1,1)与线性回归模型相融合。选取北京东部某地面沉降监测站2004～2012年的分层监测数据建立模型,计算出各监测层位沉降的数学模型,并以此预测各监测层位地面沉降量。结果表明：利用灰色线性回归组合模型在对地面沉降进行分层模拟和预测是可行的。在已有数据的基础上,利用数学模型进行沉降模拟时,两种模型的精度均很高,但通过模型预测未来一年沉降量时,灰色线性回归组合模型的精度,要远高于普通均值GM(1,1)模型。     

Regression diagnostics and robust regression in geothermometer/geobarometer calibration: the garnet-clinopyroxene geothermometer revisited

Abstract The calibration of geothermometers and geobarometers should involve not only the determination of the parameters in the equation used, but also the uncertainties on, and the correlations between, these parameters. This necessitates the use of a technique such as least squares. Given the poor performance of least squares in the presence of outliers in the data, techniques for identifying outliers for exclusion—regression diagnostics, and techniques for handling data which include outliers—robust regression and jackknifing, are essential. These techniques are summarized and their importance is emphasized, and they are applied to the calibration of the garnet-clinopyroxene Fe-Mg exchange geothermometer.
The experimental data of Raheim & Green (1974) and Ellis & Green (1979) are explored using regression diagnostics to discover outliers in the data. After exclusion of the two influential outliers found, a new geothermometer equation for garnet-clinopyroxene Fe-Mg exchange is derived using robust regression and based on all the data: thus, T (K) = 2790 + 10 P + 3140x_ca,g/1.735 + In K _D where T is in Kelvin and P is in kbar. This equation, as might be hoped, is essentially identical to that of Ellis & Green (1979). Equations for calculating the uncertainty in a calculated temperature, contributed by uncertainties in the calibration, are also derived.     

基于主成分和半参数的大坝变形监测回归模型

主成分分析在一定程度上可以解决大坝变形监测回归模型因子间的复共线性,然而当提取的主成分信息不充分时,主成分回归用于大坝安全预测可能失效。提出以主成分分析提取的主成分作为半参数回归的参数分量,剩余成分和模型误差作为未知的非参数分量对主成分回归进行补偿,建立一种基于主成分和半参数的大坝变形监测混合回归模型。利用某大坝实测资料进行建模分析,结果表明该混合模型能克服回归因子间的复共线性,避免半参数回归补偿最小二乘估计中法矩阵的病态性,比传统的主成分回归和逐步回归模型具有更好的拟合和预报精度。     

Excel回归分析及其在矿井瓦斯涌出量预测中的应用

回归分析方法是处理变量之间相关关系的有利工具,在很多领域都有应用。介绍了多元线性回归分析的数学原理,以及用MicrosoftExcel工作表进行多元回归分析的多种方法。在应用实例中用常村矿井的钻孔实测数据,演示了Excel多元线性回归各种方法的分析过程。     

基于逻辑回归模型的化探异常信息识别研究——以克拉玛依地区为例

化探数据对矿产资源勘查工作有着重要作用,其中比较关键的工作就是从化探数据中识别矿床相关的化探异常信息.在化探异常信息识别工作中也发展出了较多的技术,但是它们大多针对单变量进行分析.为了对多变量化探数据进行分析并识别金矿相关的地球化学异常信息,笔者将逻辑回归模型用于研究区化探数据分析,通过研究区内对金矿预测比较有价值的16种元素的逻辑回归建模及模型应用,发现逻辑回归是一种有效的化探多变量数据分析和建模技术,研究结果显示,笔者建立的逻辑回归模型不仅可以有效识别已知金矿区的地球化学异常信息,而且对那些还未发现矿床的区域具有预测作用,能够为矿产资源勘查工作重点区域的选择提供指导.     

断陷湖盆中强制湖退沉积作用及其成因机制

断陷湖盆中相对湖平面下降引起的湖退作用称之为强制湖退作用。强制湖退作用时期若存在沉积物供给盆地,将加速湖退作用,并形成一套具有明显前积结构的强制湖退前积体。强制湖退前积体的顶积层不发育,地震剖面上具斜交前积反射结构。强制湖退前积体的顶界面为层序界面,且伴随有下切谷的形成。气候变化、构造抬升和边界断层的幕式断陷活动引起的盆地缓坡带基底差异沉降运动均可引起断陷湖盆中相对湖平面的下降,也是引起强制湖退作用的三大成因机制。强制湖退前积体具有良好的油气成藏条件,是隐蔽油气藏有利勘探目标。     

Applicability of the ACE algorithm for multiple regression in hydrogeology

This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (J Am Stat Assoc 80:580–619, 1985) for estimating the transformations of a response and a set of predictor variables in multiple regression problems in hydrogeology. The proposed nonparametric approach can be applied easily for estimating the optimal transformations of different hydrogeological data to obtain maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. The advantages and applicability of this new approach to solve different multiple regression problems in hydrogeology or in Earth Sciences are illustrated by means of theoretical investigations and case studies. It is demonstrated that the ACE method has certain advantages in some fitting problems of hydrogeology over the traditional multiple regression. Based on our knowledge, this is the first application of the ACE algorithm to analyze and interpret groundwater data.     

大型水电站厂区三维地应力场回归反演分析

岩体初始地应力场是地下洞室围岩稳定与支护结构设计所需要的基本因素之一,初始地应力场是否可靠将直接影响到工程设计与施工的可靠性与安全性。结合某水电站厂区的地质条件及地应力实测资料,引入灰色控制系统理论,采用三维有限元法和采用静态的三因素灰色计算模型GM(0, 3)对厂区岩体初始应力场进行回归反演分析。计算结果表明,厂区存在较大的水平向地质构造作用,岩体的地应力由自重和构造应力叠加而成。实测点的计算应力值与实测值在量值上和方向上都较为接近,表明经过回归得到的地应力场是合理的,从而获得地下厂房厂区初始应力场较为合理的分布规律,为地下厂房的开挖模拟及稳定性分析提供了合理的初始应力场。     

Fuzzy and Multiple Regression Modelling for Evaluation of Intact Rock Strength Based on Point Load, Schmidt Hammer and Sonic Velocity

Summary. Uniaxial Compressive Strength (UCS), considered to be one of the most useful rock properties for mining and civil engineering applications, has been estimated from some index test results by fuzzy and multiple regression modelling. Laboratory investigations including Uniaxial Compressive Strength (UCS), Point Load Index test (PL), Schmidt Hammer Hardness test (SHR) and Sonic velocity (V_p) test have been carried out on nine different rock types yielding to 305 tested specimens in total. Average values along with the standard deviations (Stdev) as well as Coefficients of variation (CoV) have been calculated for each rock type. Having constructed the Mamdani Fuzzy algorithm, UCS of intact rock samples was then predicted using a data driven fuzzy model. The predicted values derived from fuzzy model were compared with multi-linear statistical model. Comparison proved that the best model predictions have been achieved by fuzzy modelling in contrast to multi-linear statistical modelling. As a result, the developed fuzzy model based on point load, Schmidt hammer and sonic velocity can be used as a tool to predict UCS of intact rocks.     

成土母岩营养元素含量与柑桔产量的关系

以柑桔园成土母岩,土壤中营养元素含量为自变量,柑桔产量为因变量建立了多元回归方程,运用这些方程对规划区进行了产量预后,此外,对营养元素影响柑桔产量的作用机制也进行了初步探讨。     

Quantifying TiO_2 Abundance of Lunar Soils:Partial Least Squares and Stepwise Multiple Regression Analysis for Determining Causal Effect

Partial least squares(PLS) regression was applied to the Lunar Soil Characterization Consortium(LSCC) dataset for spectral estimation of TiO2.The LSCC dataset was split into a number of subsets including the low-Ti,high-Ti,total mare soils,total highland,Apollo 16,and Apollo 14 soils to investigate the effects of interfering minerals and nonlinearity on the PLS performance.The PLS weight loading vectors were analyzed through stepwise multiple regression analysis(SMRA) to identify mineral species driving and...     

Application of Partial Least Squares Regression in Multimodal Integrated Forecasting of Water Vapor and Surface Air Temperature

The use of a new multi model integration method of Partial Least Squares regression (PLS) can completely eliminate the multicollinearity features to improve multi model’s integrated forecasting results of the humidity and temperature. Based on the four centers’ ensemble forecast results, namely, the European Center for Medium-Range Weather Forecasts (ECMWF), Chinese Meteorological Administration (CMA), the Japan Meteorological Agency (JMA) and the UK Met Office (UKMO), we built a 2012 multi mode (25°~60°N, 60°~150°E) 24 ~168 hours forecast time (interval 24 hours) multi model for humidity and temperature and used the four methods, like ensemble average (BREM) for eliminating the deviation, a simple set of average (EMN), Super Ensemble (SUP) and Partial Least Squares regression (PLS) for ground temperature multi model integration. We used the Root-Mean-Square Error (RMSE) and anomaly correlation coefficient (cor) to determine the effect of more modes of integration and to predict a short course of cold. The two prediction results showed that the Partial Least Squares regression (PLS) was the best multi model integrated method, more superior than the other three single modes and compared with the other three methods, it showed better prediction performance, which has certain value and application prospect.     

济宁市翟村铁矿小体重值与磁性铁品位的回归分析

利用济宁市翟村铁矿勘查过程中取得的体重测试值与磁性铁品位数据进行了回归分析,得出回归方程为y＝2．74＋0．026x,经显著性、精度检验并结合实际实践,证明该一元回归方程具有显著性,预测精度较高。可以用该方程预测翟村铁矿区小体重值。     

A Combined Weight of Evidence and Logistic Regression Method for Susceptibility Mapping of Earthquake-induced Landslides: A Case Study of the April 20, 2013 Lushan Earthquake,China

The Ms 7.0 Lushan earthquake triggered a huge number of landslides. Landslide susceptibility mapping is of great importance. Weight of Evidence (WoE) and Logistic Regression (LR) methods have been widely used for LSM (Landslide Susceptibility Mapping). However, limitations still exist. WoE is capable of assessing the influence of different classes of each factor, but neglects the correlation between factors. LR is able to analyze the relationship among the factors while it is not capable of evaluating the influence of different classes. This paper proposes a combined method of LR and WoE for LSM, taking advantage of their individual merits and overcoming their limitations. An inventory of 1289 landslides was used: 70% were random-selected for training and the remaining for validation. 11 landslide condition factors were employed in the model and the result was validated using Receiver Operating Characteristic (ROC) curve. The results showed that the LR-WoE model had a better accuracy than the LR model, producing an area below the curve with values of 0.802 success and 0.791 predictive, higher than that of the LR model (0.715 success and 0.722 predictive). It is therefore concluded that the combined method of WoE and LR can provide a promising level of accuracy for earthquake-induced landslide susceptibility mapping.     

基于信息量、逻辑回归及其耦合模型的滑坡易发性评估研究:以青海沙塘川流域为例

滑坡易发性定量评估是预测滑坡发生空间概率的重要手段,基于统计分析原理的评估方法目前在国内外应用最为广泛,且不同评估方法的对比研究逐渐成为热点。以青海沙塘川流域黄土梁峁区为例,剖析了信息量模型和逻辑回归模型在滑坡易发性评估中的优越性和局限性,并探索提出基于二者的耦合模型。考虑坡度、坡向、起伏度、岩性、与干流距离、与支流距离和植被指数等7个影响因素,对比分析了基于信息量、逻辑回归及二者耦合模型的滑坡易发性评估的技术流程及结果。3种模型的成功率分别为:耦合模型成功率(78. 9%)>信息量模型成功率(71. 8%)>逻辑回归模型成功率(70. 8%)。在沙塘川流域黄土滑坡的易发性评估中,信息量和逻辑回归模型的表现基本相当,但信息量-逻辑回归耦合模型的成功率明显提升。该研究结果可为黄土高原区滑坡易发性定量评估提供借鉴。