Discovery process modeling—A sensitivity study

Lognormal discovery process modeling characterizes oil and gas discovery as sampling from a lognormal parent distribution with probability proportional to size and without replacement. In this article, we present a sensitivity study that is based on simulated discovery sequences with different assumptions regarding discovery efficiency, exploration status, and the shape of the parent field size distribution. The results indicate that lognormal discovery process modeling provides good overall estimates of the lognormal parameters if the parent field size distribution is lognormal. If the parent field size distribution is Pareto, an underestimation of the play potential may occur if a lognormal discovery process model is applied. Failure of the likelihood value converging to a maximum is more frequent when sample size is small and/or discovery efficiency is low.     

Pareto–Lognormal Modeling of Known and Unknown Metal Resources

Recently, large worldwide databases with statistics on amounts of metal in mineral deposits have become available. Frequently, most metal is contained in the largest deposits for a metal. A major problem in meaningful modeling of the size–frequency distributions of the largest deposits is that they are very rare. Until now it was rather difficult to establish the exact form of their size–frequency distribution. However, because of the new very large databases it can now be concluded that two commonly used approaches (lognormal and Pareto) thought to be mutually incompatible in the past, are both correct with a high probability. One approach does not necessarily exclude validity of the other. Patiño-Douce (Nat Resour Res 25(1):97–124, 2016b) has shown that metal tonnage frequency distributions for worldwide metal deposits are approximately lognormal with similar standard deviations (σ) of log-transformed data. In this paper, it is assumed that worldwide metals satisfy both lognormal and Pareto models simultaneously. Copper and Au are taken for example for comparison with results previously obtained for these two metals in the Abitibi area of the Canadian Shield. Worldwide there are 2541 Cu deposits approximately satisfying a lognormal distribution. Total amount of Cu in these deposits is 2.319 × 10⁹ tons of Cu. However, the 45 largest deposits, which together contain 1.281 × 10⁹ tons of Cu, satisfy a Pareto distribution. If their lognormal model would apply in the upper tail as well, these 45 largest deposits should have contained only about 0.076 × 10⁹ tons of Cu. It is shown in detail for Cu that the best statistical model for Cu deposits is a worldwide Pareto–lognormal model in which the basic lognormal size–frequency distribution is flanked by two juxtaposed Pareto distributions for the largest and smallest Cu deposits, respectively. Both Pareto distributions smoothly change into the central lognormal by means of bridge functions that can be determined separately. The worldwide Pareto–lognormal model also was found to be applicable to several other metals, especially Ag, Ni, Pb, and U. For Au, the model does not work as well for the upper tail Pareto distribution as it does for the other metals taken for example.     

乌鲁木齐河洪水频率分析

本文通过对乌鲁木齐河年最大洪峰流量实测资料与历史洪水资料的分析，选定了正态分布，对数正态分布，三参数对数正态分布，Ｇｕｍｂｅｌ分布，Ｐｅａｒｓｏｎ－Ⅲ型分布和对数Ｐｅａｒｓｏｎ－Ⅲ型分布等６种线型，利用极大似然法对各种分布函数的参数进行了最优估计。     

历史文献中气候信息的评价

本文对我国史料中所载气候信息进行了评价。结论是:①对于史料所载的某一气候事件,我们将其状态分辨取越细,所获取的信息越少;②在分析过程中,对误差要求低些,所获取的信息反而高些;③就已记录的气候事件而言,官方组织的记载所提供的气候信息最多,私人笔札次之,方志类书最次。     

U.S. department of the interior U.S. geological survey: Fractal lognormal percentage analysis of the U.S. geological survey’s 1995 national assessment of conventional oil and gas resources

The U.S. Geological Survey periodically makes appraisals of the oil and gas resources of the Nation. In its 1995 National Assessment the onshore areas and adjoining State waters of the Nation were assessed. As part of the 1995 National Assessment, 274 conventional oil plays and 239 conventional nonassociated-gas plays were assessed. The two datasets of estimates studied herein are the following: (1) the mean, undiscovered, technically recoverable oil resources estimated for each of the 274 conventional oil plays, and (2) the mean, undiscovered, technically recoverable gas resources estimated for each of the 239 conventional nonassociatedgas plays. It was found that the two populations of petroleum estimates are both distributed approximately as lognormal distributions. Fractal lognormal percentage theory is developed and applied to the two populations of petroleum estimates. In both cases the theoretical percentages of total resources using the lognormal distribution are extremely close to the empirical percentages from the oil and nonassociated-gas data. For example, 20% of the 274 oil plays account for 73.05% of the total oil resources of the plays if the lognormal distribution is used, or for 75.52% if the data is used; 20% of the 239 nonassociated-gas plays account for 76.32% of the total nonassociated-gas resources of the plays if the lognormal distribution is used, or for 78.87% if the data is used     

Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning

One of the major sources of uncertainty associated with geographical data in GIS arises when they are the outcome of a sampling process. It is well known that when sampling from a spatially autocorrelated homogeneous surface, stratification reduces the error variance of the estimator of the population mean. In this study, we evaluate the efficiency of different spatial sampling strategies when the surface is not homogeneous. When the surface is first-order heterogeneous (the mean of the surface varies across the map), we examine the effects of stratifying it into first-order homogeneous zones prior to the usual stratification for a systematic or stratified random sample. We investigate the effect of this form of spatial heterogeneity on the performance of different methods for estimating the population mean and its error variance. We do so by distinguishing between the real surface to be surveyed (?), the sampling frame (?) including the choice of zoning, and the statistical estimators (Ψ). The study shows that zoning improves estimator efficiency when sampling a heterogeneous surface. Systematic comparison provides rules of thumb for choice of sample design, sample statistics and uncertainty estimation, based on considering different spatial heterogeneities on real surfaces.     

东亚季风强弱变化及其对初夏我国东部地区降水的影响

本文通过对东亚季风系统的分析,发现东亚季风存在3-4年左右的长期振荡.这类振荡与赤道东太平洋海面温度变化有相互作用,形成一个相互反馈的耦合振荡过程.据此提出海温通过季风系统的变化影响初夏我国东部地区降水分布的可能长期天气过程.     

THE NONPARAMETRIC ANALYSIS OF VARIANCE AND MULTIPLE COMPARISONS PROCEDURES IN GEOGRAPHY*

Geographers employing the parametric F statistic in analyses of variance should consider that it can be highly sensitive to departures from normality. The Friedman and Kruskal-Wallis tests offer geographers nonparametric alternatives to the analysis of variance, for k dependent and independent samples respectively. Associated with the tests are little known methods for examining ordered alternatives and making multiple comparisons between samples, thereby permitting in-depth analysis of sample data. Both tests and these latter procedures are illustrated by examples drawn from population and urban retailing geography.     

The statistical distribution of magnetotelluric apparent resistivity and phase

The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the Gauss–Markov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

北太平洋海面温度的年变化型及区划

本文用主成分分析方法,根据1949—1987年北太平洋286个格点的月平均海面温度资料,求得北太平洋海面温度的12种年变化型。讨论了前三种年变化型(占总方差的95%)的特点。分别计算了前三种年变化型对各格点的贡献率,再根据贡献率的空间分布图,将北太平洋海面温度分成八个区域,每个区域海温都有各自的统计特征。     

Seasonal Response of Mean Monthly Streamflow to El Niño/Southern Oscillation in North Central Florida

The southeastern United States, including Florida, has been identified as a region of homogeneous response to the El Niño/Southern Oscillation (ENSO) climatic anomaly, in which mean monthly precipitation and discharge during winter is above or below normal following the onset of the warm (El Niño) or cold (La Niña) phase of ENSO, respectively. However, this understanding of the response is expanded through a study of the effects of the ENSO phenomenon on the probability distributions of mean monthly streamflows of the Santa Fe river. The Santa Fe river basin is situated between one region, which experiences the greatest proportion of annual streamflow during winter, and another where the largest percentage of annual flow occurs during late summer. The basin experiences both winter and summer peaks in precipitation and (subsequent) streamflow and may therefore display responses to ENSO during each season. A two-parameter lognormal distribution is employed to model these streamflows during warm and cold phases of ENSO. Increases in both the mean and the variance detected during warm phase winters are compatible with previous observations. Increases in variance apparent during cold phase summers have not been previously identified. These results, which have considerable bearing upon predictions of high and low flow probabilities during the year, suggest that the response in streamflow is not spatially homogeneous across the state.     

POLITICAL GEOGRAPHY AND THE CITY IN THE 1990s

In Amsterdam, a large number of rental units were converted to condominiums during the 1970s. Local housing officials observed this process with alarm and tried (in vain) to put an end to conversion. Given the tight housing market, they feared that a decrease in the number of available rental units would impede a fair distribution of housing. They also assumed that proper maintenance of the dwellings would not take place. But their arguments were not based on a solid evaluation. Recent research results demonstrate that sub-markets exist within the condominium sector, and that in each of these the effects of conversion are different. While this study identifies problems at the lower end of the market, the conversion of more expensive units coincides with an improved matching of households and dwellings and with an upgrading of the housing stock.     

地理信息系统和遥感技术支持下的山地环境梯度分析方法研究*

文章提出了一种地理信息系统和遥感技术支持下的环境梯度分析方法。应用该方法可将研究区域的TM遥感影像经遥感图像处理和分类得到该地区的植被类型分布图,充分应用地理信息系统强大的空间信息管理和分析功能,将各环境因子分布图分别与植被类型分布图进行叠加分析得到各种植被类型与各环境因子关系的向量表达式,进而建立符合环境梯度分布的植被空间分布模型。在此基础上,综合各环境因子分布图与植被类型分布图进行叠加分析和植被群落空间分布制图。该方法曾应用于贺兰山环境梯度分析并得到较满意的结果。     

New Method of Fitting Pareto–Lognormal Size-Frequency Distributions to Worldwide Cu and Zn Deposit Size Data

Earlier methods of fitting Pareto–lognormal distributions to large samples of worldwide metal deposit size data are improved by using a sliding window method for estimating upper-tail Pareto coefficients and constructing best-fitting lognormal Q–Q plots with their corresponding probability-density curves. Lower-tail Pareto distributions are fitted to some extent as well. Copper and Zn deposits of the world are taken as example in this paper. Three principal statistical laws resulting in the basic lognormal with two Pareto tails are thought to underlie the generation of Pareto–lognormals for amounts of metal in primarily hydrothermal ore deposits. Historical trends in mining and exploration are thought to create an excess of smaller deposits with respect to the basic lognormal that decreases steadily with increasing deposit size until it changes into a deficit slightly before median size is reached. This deficit decreases for the largest metal deposit sizes for which the upper-tail Pareto and extrapolated basic lognormal show similar size frequencies again. The Pareto–lognormal model can also be used to describe metal size-frequency distributions for smaller geographically coherent regions on the continents. A new version of the original model of de Wijs is considered to help explain why regional Pareto–lognormal distributions with lesser logarithmic variances and Pareto coefficients can be combined to form worldwide size-frequency distributions of the same type.     

Seasonal Response of Mean Monthly Streamflow to El Niño/Southern Oscillation in North Central Florida

The southeastern United States, including Florida, has been identified as a region of homogeneous response to the El Niño/Southern Oscillation (ENSO) climatic anomaly, in which mean monthly precipitation and discharge during winter is above or below normal following the onset of the warm (El Niño) or cold (La Niña) phase of ENSO, respectively. However, this understanding of the response is expanded through a study of the effects of the ENSO phenomenon on the probability distributions of mean monthly streamflows of the Santa Fe river. The Santa Fe river basin is situated between one region, which experiences the greatest proportion of annual streamflow during winter, and another where the largest percentage of annual flow occurs during late summer. The basin experiences both winter and summer peaks in precipitation and (subsequent) streamflow and may therefore display responses to ENSO during each season. A two-parameter lognormal distribution is employed to model these streamflows during warm and cold phases of ENSO. Increases in both the mean and the variance detected during warm phase winters are compatible with previous observations. Increases in variance apparent during cold phase summers have not been previously identified. These results, which have considerable bearing upon predictions of high and low flow probabilities during the year, suggest that the response in streamflow is not spatially homogeneous across the state.     

云南雨季开始期的特征以及与南海季风和印度季风开始期的可能关系

应用EOF、Morlet小波分析方法对云南雨季开始期的时空特征及多尺度周期变化特征进行分析,使用相关分析初步分析印度季风和南海季风开始期与其关系.结果表明：（1）云南雨季开始期的EOF第一模态表明全省雨季开始期一致偏早（晚）,EOF第二模态表明滇中及以东、滇东北、滇东南、滇西南部分地区与滇西、滇西北、滇南大部分地区雨季开始期反相变化的空间分布特征.（2）云南雨季开始期存在着明显的周期性波动,连续小波变换分析表明云南雨季开始期存在2～4年和5～7年的振荡周期.（3）南海季风开始期与云南雨季开始期相关不好,印度季风开始期与云南雨季开始期存在很好的相关性.     

THERMAL CONVECTION IN THE INTERIOR OF THE EARTH

The paper deals with thermal convection in the shell of the earth, caused by various assumed zonal temperature perturbations. One temperature perturbation here treated is that due to the difference in the temperature distribution under a continental crust made up of 10 km. of granite on top of 20 km. of basaltic material and a sub-oceanic crust consisting of 25 km. of basalt. The kinematic viscosity v was assumed to be 3 × 1021, as estimated recently by N. A. Haskell from a study of the uplift of Fennoscandia after the ice load. It is found that when g, ν, p and a, the coefficient of volume expansion, are constant, the velocities and their gradients are proportional to the amplitude of the temperature perturbation and to (ag/ν), while the stresses are independent of the viscosity. The velocities are found to be of the order of I cm./year. The shearing stress exerted by the convective substratum on the crust is of the order of 10⁷ dyn./cm.², while the normal stresses are about 10 times larger. The crust is pushed upwards under the warmer (continental) regions and pulled downwards under colder (oceanic) regions. The maximum stress-difference occurs at the bottom of the crust over the centre of the oceans or continents. The surface inequalities are nearly compensated.     

ROBUST PRINCIPAL COMPONENT ANALYSIS BY PROJECTION PURSUIT

Principal component analysis (PCA) is a widely used technique in chemometrics.The classical PCAmethod is,unfortunately,non-robust,since the variance is adopted as the objective function.In thispaper,projection pursuit (PP) is used to carry out PCA with a criterion which is more robust than thevariance.In addition,the generalized simulated annealing (GSA) algorithm is introduced as anoptimization procedure in the process of PP calculation to guarantee the global optimum.The resultsfor simulated data sets show that PCA via PP is resistant to the deviation of the error distribution fromthe normal one.The method is especially recommended for use in cases with possible outlier(s) existingin the data.     

长江淮河海河流域降水与南水北调的关系

本文以农田需水量作为供水余缺的标准,分析长江、淮河、海河流域降水的年内年际变化与季节需水的关系,论证了南水北调的必要性和引江济海的合理性。