Estimation of statistical parameters for censored lognormal hydraulic conductivity measurements

Field tests of hydraulic conductivity (e.g., injection test, pumping test, etc.) in low permeability formations are subject to censoring due to the detection limit of the instruments used. An iterative method of estimating the mean and variance of hydraulic conductivity data with a presumed log-normal distribution function is presented. This method accounts for the data that are actually below the lower detection limit (called truncated data) and thus gives distribution parameters that are more representative for the underlying distribution. The proposed method is then tested on two simulated normally distributed random datasets having different variances. The results show that the means and variances estimated by the proposed method are very accurate. Finally, the method is used to estimate the mean and variance of hydraulic conductivity data from single hole water injection tests in a fractured geological formation.     

Analysis and mapping of geochemical anomalies using logratio-transformed stream sediment data with censored values

There is lack of research and documentation of actual (as opposed to theoretical) benefits (e.g., mineral deposit discovery) of developments in compositional data analysis and imputation of censored values to mineral exploration geochemistry. In the present study, analyses of logratio- and ln-transformed stream sediment geochemical data containing ca. 30% of samples with censored values of a pathfinder element for the mineral deposit-type of interest yielded the following findings. Exclusion of those samples supports interpretation of multi-element anomalies reflecting the presence of mineralization. However, the multi-element anomaly maps obtained by exclusion of those samples are barely better than the multi-element anomaly maps derived by inclusion of those samples after replacing the censored values with 1/2 of detection limit or with imputed values. Logratio (i.e., alr, clr, or ilr) transformation, compared to ln-transformation, of stream sediment geochemical data does not improve mapping of pathfinder element anomalies reflecting the presence of mineralization. However, stream sediment geochemical data, excluding or including censored values (replaced with 1/2 of detection limit or with imputed values), should be clr- or ilr-transformed to enhance recognition of anomalous multi-element associations reflecting the presence of mineralization. The anomaly maps of multi-element associations derived from ilr-transformed data are better, albeit slightly, than the anomaly maps of multi-element associations derived from clr-transformed data. In the present study, the main benefit of either clr- or ilr-transformation, compared to either ln- or alr-transformation, of stream sediment geochemical data is the enhancement of anomalous multi-element associations reflecting the presence of mineralization. This is an important benefit because variations in trace element concentrations in regional-scale stream sediment geochemical data are mostly due to lithology and other factors (or processes) unrelated to mineralization. Further investigations of various exploration geochemical data are needed to demonstrate and document the actual (as opposed to theoretical) benefits of developments in compositional data analysis and imputation of censored values to mineral exploration.     

区域化探数据处理的几种分形方法

地球化学变量兼有随机性、确定性和区域结构性的特征,传统的数学方法难以精确地描述地球化学变量的空间分布规律,而新兴的分形几何是刻画空间不规则形体的一种比较有效的工具,且分维值可以表征空间不规则形体的确定性本质。基于分形原理,提出含量-总量法、空间分形插值法和分形趋势面法3种新的分形技术,应用于区域化探数据处理。在几个典型矿区应用后发现,上述分形方法不仅可以有效地模拟地球化学变量的空间分布特征,而且在保留原始有效异常信息的基础上可以更合理地区分地球化学变量的背景与异常,具有发现和强化弱异常信息的重要功效。     

A spatial analysis method for geochemical anomaly separation

One purpose of using statistical methods in exploration geochemistry is to assist exploration geologists in separating anomalies from background. This always involves two types of negatively associated errors of misclassification: type I errors occur when samples with background levels are rejected as background; and type II errors occur when samples with anomalous values are accepted as background. A new spatial statistical approach is proposed to minimize errors of total misclassification using a moving average technique with variable window radius. This method has been applied for geochemical anomaly enhancement and recognition as demonstrated by a case study of Au and Au-associated data for 698 stream sediment samples in the Iskut River area, northwestern British Columbia. Similar results were obtained using the fractal concentration-area method on the same data. By employing spatial information in the analysis, the process of selecting anomalies becomes less subjective than in more traditional approaches.     

如何利用Excel处理化探数据

利用Excel可以实现对化探数据多种项目的处理,如正态性检验;背景值及异常下限的确定;一元及多元回归分析;相关系数(R型聚类分析)以及一次趋势分析等,操作直观,目前在没有流行地质行业软件的情况下,不失为一种较为可取的选择。通过这种方法,可以较为简洁地实现对一定数量化探数据的处理,为地质找矿工作提供了化探方面的可靠依据。     

Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data

All variables of several large data sets from regional geochemical and environmental surveys were tested for a normal or lognormal data distribution. As a general rule, almost all variables (up to more than 50 analysed chemical elements per data set) show neither a normal or a lognormal data distribution. Even when different transformation methods are used more than 70 % of all variables in every single data set do not approach a normal distribution. Distributions are usually skewed, have outliers and originate from more than one process. When dealing with regional geochemical or environmental data normal and/or lognormal distributions are an exception and not the rule. This observation has serious consequences for the further statistical treatment of geochemical and environmental data. The most widely used statistical methods are all based on the assumption that the studied data show a normal or lognormal distribution. Neglecting that geochemcial and environmental data show neither a normal or lognormal distribution will lead to biased or faulty results when such techniques are used. Received: 21 June 1999 · Accepted: 14 August 1999     

基于GEOROC大数据分析地壳厚度地球化学指标

前人研究认为,火山岩中部分地球化学指标与岩浆弧地壳厚度之间存在一定的相关性,并通过统计主量元素K2O、Ca O和Na2O指标及微量元素Ce/Y、Sm/Yb、Dy/Yb、Sr/Y、La/Yb指标与地壳厚度之间关系,约束地质史上某些区域的地壳厚度发展和变化。本文基于GEOROC数据库,以Si O2含量57%和火山岩年龄23Ma为界,将全球火山岩数据分成年轻-壳源( 57%,23Ma)、年轻-幔源(57%,23Ma)、古老-壳源( 57%, 23Ma)和古老-幔源(57%, 23Ma)四个数据集,并通过核函数估计方法获得了各个地球化学指标与地壳厚度的归一化联合概率密度分布图。本文统计结果表明,年轻-幔源火山岩中的K2O含量分布与壳源火山岩呈现指数正相关关系、Ca O含量分布于地壳厚度呈现线性负相关关系,年轻-壳源火山岩中Ce/Y、La/Yb和Sm/Yb与现今地壳厚度有指数正相关关系。由以上5种地化指标建立的回归方程确定系数R2均大于0. 7,可以认为相关关系显著。本文认为幔源岩浆在穿透地壳到达地表过程中,地壳厚度控制了富K壳源物质进入地幔熔体和富Ca矿物结晶分异过程,导致了火山岩中K2O和Ca O含量的相关变化;而下地壳部分熔融形成的壳源岩浆,不同深度压力控制了残留相矿物比例,导致Ce/Y、La/Yb和Sm/Yb体现出与地壳厚度的相关性。本文建立的回归函数是基于大量数据概率密度分布的统计分析得出的,由于离群数据普遍存在,回溯历史地壳厚度变化需要大量数据统计支撑,否则难以获得可靠的结果。     

Variational method for objective analysis of scalar variable and its derivative

In this study real time data have been used to compare the standard and triangle method by performing the objective analysis of mean sea level pressure. In the standard method, derivative fields are obtained from the grid point data using finite difference scheme whereas in the triangle method, a set of non-overlapping triangles are formed from the observations and the scalar and the spatial derivatives are computed directly at the centroid of each of the non-overlapping triangles. These scalars and their derivatives are then mapped to uniform grids by using the standard method. It has been found that objectively analysed scalar field obtained using standard method is superior to the scalar field derived by the triangle method, whereas the derivative fields produced by triangle method are superior to the derivative fields produced using standard method. A variational objective analysis scheme has been developed and an experiment has been carried out with depression case of June (11–15) 2004. It is found that the new scheme (variational) is able to extract the better parts of both triangle and standard methods. The results of this study will be useful in carrying out diagnostic calculations that involve derivative estimates.     

多源异构地质数据集成方法应用研究

大数据技术的高速发展为地质数据挖掘与分析带来了新的机遇。借鉴大数据技术的思想,提出了一种多源异构的地质数据集成方法,为数据挖掘、地质数据信息化服务提供了技术基础。针对北京周口店研究区,建立了其野外地质三维综合信息平台,将各类地表、地质体、地质信息等结构、半结构、非结构数据集成到统一的平台系统中,实现了研究区域相关地质数据的集成管理、可视化浏览、查询与分析,为大数据方法在地质领域的应用提供了新的思路。     

Application of fractal content-gradient method for delineating geochemical anomalies associated with copper occurrences in the Yangla ore field,China

Fractal and multi-fractal content area method finds application in a wide variety of geological, geochemical and geophysical fields. In this study, the fractal content-gradient method was used on 1:10,000 scale to delineate geochemical anomalies associated with copper mineralization. Analysis of geochemical data from the Yangla super large Cu-Pb-Zn polymetallic ore district using the fractal content-gradient method, combined with other geological data from this area, indicates that ore-prospecting in the ore district should focus on Cu as the main metal and Pb-Zn and Au as the auxiliary metals. The types of deposits include (in chronological order) re-formed sedimentary exhalative (SEDEX), skarns, porphyries, and hydrothermal vein-type deposits. Three ore-prospecting targets are divided on a S–N basis: (1) the Qulong exploration area, in which the targets are porphyry-type Cu deposits; (2) the Zongya exploration area, where the targets are porphyry-type Cu and hydrothermal vein-type Cu-Pb polymetallic deposits; and (3) the Zarelongma exploration area, characterized mainly skarn-type “Yangla-style” massive sulfide Cu-Pb deposits. Our study demonstrates that the fractal content-gradient method is convenient, simple, rapid, and direct for delineating geochemical anomalies and for outlining potential exploration targets.     

利用地球化学资料评价水淹层方法研究:以大庆杏南油田为例

通过对水淹层地球化学资料的分析,总结出了不同程度水淹层的地球化学特征,提出了利用地球化学资料从定性识别到定量评价的水淹层评价思路,建立了水淹层水淹程度定性识别方法、剩余油饱和度和含水率定量评价模型.对储层物理性质、岩性、流体性质、水淹程度不同的108口井529层水淹层进行了评价,剩余油饱和度与经校正后的密闭取芯井岩芯分析剩余油饱和度非常接近,水淹级别、含水率与单层试油结果一致.证明利用地球化学资料评价水淹层方法是可行的,结果是可靠的,该方法有很好的推广应用前景.     

The loghyperbolic: An alternative to the lognormal for modeling oil field size distribution

The lognormal distribution is widely used to represent the distribution of deposit or reserve size of oil and gas fields. The purpose of this paper has been to investigate the potential usefulness of the loghyperbolic distribution as an alternative to the lognormal distribution. This hypothesis is tested using a set of data from the Denver basin. The results indicate that the loghyperbolic distribution shows a better fit to the empirical data than the lognormal distribution.     

关于数字地质图元数据编制方法若干问题的讨论

为实现空间数据共享,需要描述空间数据或数据集的内容、质量、状态和其他特性的数据,这就是元数据.以编制中国1∶50万数字地质图空间数据库元数据的实际经验,结合国内外已有的资料,分析了数字地质图空间数据库元数据的特点、用途和编制方法提出了进一步改进的建议.     

用MAPGIS二次开发绘制物探电法原始数据图

将物探电法的测点数据及测点的大地直角坐标按每条测线上测点由西向东的顺序 ,以统一编号、线号、点号、横坐标、纵坐标、测点数据为字段建成MicrosoftAccess数据库。根据制图比例尺和测点的大地直角坐标逐个计算数据库中所有测点在图纸上的坐标值 ,绘制测点位置子图 ,并在测点位置沿垂直测线方向向东移动 1/ 2测点数据注释的字符宽度 ,并以测点位置为圆心顺时针旋转 6 0°的位置绘制测点数据注释。按照上述方法 ,以MicrosoftVC + + 6 0为工具 ,利用MAPGIS 6 1地理信息系统二次开发技术 ,编制数据处理程序 ,实现电法原始数据图的微机制图     

Hilbert-semblance method for acoustic logging data processing

We suggest a method of multi-element low-frequency acoustic logging data processing which combines advantages of the semblance and phase velocity processing (PVP) techniques, namely, the interference resistance in the former and better accuracy in the latter. The new method is based on point (windowless) semblance by the Hilbert transformation. The introduced concept of phase semblance makes it possible to estimate the signal distribution semblance and the phase. Also suggested are an algorithm for preliminary estimation of formation S-wave slowness from signal group power variations and improved forms of processed data imaging.     

An inverse method to determine the optimal stress from imperfect fault data

An inverse method is developed to determine the optimal stress inversion from imperfect fault data. It is specifically designed to process fault data at variable division—either with observed slip directions or with observed fault/slip senses or with both. The method has the flexibility of processing data with a few fault/slip senses incorrectly determined—a case we occasionally meet in the field. A vast number of artificial 10-datum examples are processed to illustrate the reliability of the method and to examine the effects of the data set at variable division on stress estimation. The results show that the precision of solution decreases with the increase in either of two factors, the percentage of the data limited to slip sense and the range of measurement error, both resulting in a broader dispersion of estimated stress vectors relative to the assigned stress vector in the sigma space. Thus, in order to keep the dispersion within a range of 5° requires the percentage of data for which only slip sense is known to be less than about 20%. This in turn allows for a measurement error range in the data of 10° in real space, much larger than real measurement errors. We believe that the proposed method would be of practical value for stress inversion of fault/slip data.     

地震资料信噪比估算方法改进

在存在相关干扰的地震资料中,用以往的方法估算信噪比(Signal-to-Noise),往往存在较大的误差。这里提出了利用F-K滤波分离相关干扰,然后用相关时移法估算有效信号,再利用有效信号与总干扰之能量比来计算信噪比。通过模型实验和实际资料试算证实,这种改进的信噪比估算方法,对于存在有相关干扰的资料,能够较准确地估算出真实信噪比。     

化探综合异常图定量编制方法及应用

现阶段以单元素异常图为基础编制的综合异常图,只能定性地圈定出综合异常范围,并没有考虑异常点元素彼此之间的叠加贡献,不能定量评价综合异常。研究发现,该类图件不论在图面表达形式还是在应用效果中均存在诸多不足。明确了"平均衬度法"的概念,提出利用平均衬度法编制综合异常图的思路和方法,即以原始分析数据为基础,利用平均衬度定量表达综合异常范围,编制形成平均衬度综合异常图。对比结果表明,平均衬度法对综合异常的圈定效果优于累加衬度法和综合衬度法。平均衬度综合异常图特别适合1:5万化探普查资料的开发研究,由于圈定的范围小、浓集中心明显,适合准确布置地表探矿工程,并可以节约勘查成本,提高找矿命中率。     

A mathematical model for orientation data from macroscopic conical folds

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.     

广义S变换时频分析在广域电磁法数据处理中的应用

广义S变换是一种可逆的局部时频分析方法,是短时傅里叶变换和小波变换的延伸和推广。利用广义S变换对广域电磁时间序列数据进行分析,除了可以划定噪声区域便于实施滤波去噪之外,还可以提高数据频谱分析精度。针对广域电磁数据特点,基于广义S变换提出了适合广域电磁法的广义S变换处理流程,进行了信号的仿真实验。同时,也对广域电磁法实测数据进行了处理,高信噪比数据的处理结果证实了广义S变换的有效性和准确性。强干扰数据处理的结果表明,获取的信号质量比基于傅里叶变换的传统方法有明显提高。处理效果表明,提出的方法适用于广域电磁法数据处理。