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1.
James C. Kelley 《Mathematical Geology》1971,3(1):43-50
Increasing attention in recent years has been devoted to the application of statistical techniques in the analysis and interpretation of geologic and oceanographic data. Equally important, but less well explored, are methods for efficient experimental design. The theory of linear programming provides plans for optimal sampling of geologic and oceanographic phenomena. Of particular significance are solutions to problems of multivariate sampling. Often, a single field sample may be analyzed for a number of oxides, or a number of minerals, or a number of textural parameters. In general, these variables differ in the degree to which they are diagnostic of changes in the phenomenon of interest, and thus they must be known with different levels of precision if they are to be useful. Similarly, the variables differ in the ease with which they may be measured. If a sampling plan is to be most efficient, it must provide the requisite levels of precision for the minimum expenditure of time and effort. Sampling for a single variable may be optimized directly. Sampling for several variables simultaneously usually introduces special difficulties, but if the objective function can be generalized to hold for all variables, solutions can be determined even in this situation. 相似文献
2.
John C. Davis 《Mathematical Geology》1977,9(4):409-427
A probabilistic model for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence of oil, and the second reflecting the uncertainty associated with the estimation of geologic variables in areas of limited control. Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a training area judged to be geologically similar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates of the probability of success conditional upon geology. Uncertainty in perception of geological conditions may be estimated from the distribution of errors made in geologic assessment using the historical subset of control wells. These errors may be expressed as a linear function of distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram of the geologic variables used in the analysis: the two procedures will yield approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success of specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories from the mid-Continent area of the U.S.A.This paper was presented at Symposium 116.3, Quantitative Strategy for Exploration, held as part of the 25th International Geological Congress, Sydney, Australia, August 1976. 相似文献
3.
John C. Butler 《Mathematical Geology》1976,8(1):25-36
The application of R-mode principal components analysis to a set of closed chemical data is described using previously published chemical analyses of rocks from Gough Island. Different measures of similarity have been used and the results compared by calculating the correlation coefficients between each of the elements of the extracted eigenvectors and each of the original variables. These correlations provide a convenient measure of the contribution of each variable to each of the principal components. The choice of similarity measure (variance-covariance or correlation coefficient)should reflect the nature of the data and the view of the investigator as to which is the proper weighting of the variables—according to their sample variance or equally. If the data are appropriate for principal components analysis, then the Chayes and Kruskal concept of the hypothetical open and closed arrays and the expected closure correlations would seem to be useful in defining the structure to be expected in the absence of significant departures from randomness. If the data are not multivariate normally distributed, then it is possible that the principal components will not be independent. This may result in significant nonzero covariances between various pairs of principal components. 相似文献
4.
A common problem in experimental geochemistry is the derivation of equilibrium constants from solubility experiments. A simple method of deriving these equilibrium constants, multiple linear regression, often results in the appearance of negative values. This has been a significant obstacle to continuing research in this field. The problem occurs for the most part because of significant correlations among the “independent” concentration variables. These correlations are an inescapable result of the nature of the experiments and the physical model being fitted. Ridge regression is an appropriate modification to simple linear regression which overcomes this difficulty. Ridge regression results in a simple procedure to obtain physically plausible, yet statistically rigorous stability constants. Of course, other problems may further degrade the quality of derived equilibrium constants, e.g. uncertainty in activity coefficients and no purely statistical method can overcome these types of problems. However, ridge regression is an effective procedure to overcome the multicolinearity which is the main cause of negative equilibrium constants. We demonstrate the use of ridge regression with a general mathematical model and then illustrate its use in the determination of iron-chloro complex equilibrium constants from solubility studies of pyrite-pyrrhotite-magnetite in NaCl solutions at 250°C. Ridge regression may also be of use in other geochemical problems where one must estimate parameters with a physical interpretation and where the independent variables are significantly intercorrelated. 相似文献
5.
介绍了一种线性模型参数回归分析方法-正交最小二乘法，并以电子探针微区分析技术分析环境样品的数据为例，对正交最小二乘法和经典最小二乘法的结果进行了详细比较。数据处理结果表明，当变自量和因变量都同时存在测量误差时（或自变量的测量误差与因变量的测量误差相比不能忽略时），正交最小二乘法获得的回归系数优于经典最小二乘法。对正交最小二乘法中的线性模型能解释的方差与经典最小二乘法中的相关系数的关系也进行了讨论。 相似文献
6.
回归分析是地质数据处理中应用最广的一种统计分析方法,尤其是其中的线性回归模型应用最广泛。模型中的变量,包括因变量和自变量,均被看作是线性的,但实际计算时,这些变量却可以看成是原始观测值的一种非线性的变换。 相似文献
7.
黄土的独立物性指标及其与湿陷性参数的相关性分析 总被引：1，自引：0，他引：1
黄土的湿陷性是其重要的工程特性,常用一维压缩应力条件下的湿陷系数、自重湿陷系数和湿陷起始压力等指标定量评价。影响黄土湿陷性的因素较多,包括土的粒度、密度、湿度等基本物理性质指标,且各因素之间并非完全独立,存在一定相关性。采用因子分析法,通过对西安地铁4号线黄土高台地和宝鸡-兰州高速铁路隧道黄土塬湿陷性黄土场地地层物性质指标的统计分析和相关性分析,首先确定了相对独立的含水比（含水率与液限之比）和孔隙比3个物性指标反映的两个因子。然后,依据湿陷性黄土场地的试验资料,通过多元线性回归分析,分别得到了两个场地黄土的自重湿陷系数、湿陷起始压力以及压缩模量与含水比和孔隙比之间的相关关系。最后,比较分析了两个场地黄土自重湿陷系数、湿陷起始压力和压缩模量计算值与实测值,验证了利用因子分析法寻找影响黄土湿陷性的独立因子,建立黄土湿陷性参数与独立影响因子之间相关关系的合理性和准确性。针对两个地区两类地貌单元湿陷性黄土场地,建立的黄土湿陷性参数的相关关系具有快速、准确的评价黄土湿陷性和黄土地基湿陷变形的实际意义。 相似文献
8.
On the estimation of the generalized covariance function 总被引：1，自引：0，他引：1
The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables. 相似文献
9.
E. L. Zodrow 《Mathematical Geology》1976,8(4):395-412
This is the first application of minimum residuals (minres),a type of factor analysis, in the study of hypersthene minerals from a mafic norite formation at the Strathcona Mine near Sudbury, Ontario. Minres, because it yields highest communalities for some variables, is preferred to other types of factoring solutions including a common factor model with Chayes' null correlations as factor input. Oblique rotation of factors is rejected as a model for statistical and geochemical reasons. A five oxide-variable model that reasonably well determines hypersthene is reduced by minres to a two-factor model which is statistically significant. Because of the small number of variables in the analysis, it is difficult to interpret the isolated factors in terms of specific geologic processes. The factors, however, even if surrogate, are linked with substitution phenomena in the hypersthene. 相似文献
10.
A logistic regression model is developed within the framework of a Geographic Information System (GIS) to map landslide hazards
in a mountainous environment. A case study is conducted in the mountainous southern Mackenzie Valley, Northwest Territories,
Canada. To determine the factors influencing landslides, data layers of geology, surface materials, land cover, and topography
were analyzed by logistic regression analysis, and the results are used for landslide hazard mapping. In this study, bedrock,
surface materials, slope, and difference between surface aspect and dip direction of the sedimentary rock were found to be
the most important factors affecting landslide occurrence. The influence on landslides by interactions among geologic and
geomorphic conditions is also analyzed, and used to develop a logistic regression model for landslide hazard mapping. The
comparison of the results from the model including the interaction terms and the model not including the interaction terms
indicate that interactions among the variables were found to be significant for predicting future landslide probability and
locating high hazard areas. The results from this study demonstrate that the use of a logistic regression model within a GIS
framework is useful and suitable for landslide hazard mapping in large mountainous geographic areas such as the southern Mackenzie
Valley. 相似文献
11.
Typically, datasets originated from mining exploration sites, industrially polluted and hazardous waste sites are correlated spatially over the region under investigation. Ordinary kriging (OK) is a well-established geostatistical tool used for predicting variables, such as precious metal contents, biomass, species counts, and environmental pollutants at unsampled spatial locations based on data collected from the neighboring sampled locations at these sites. One of the assumptions required to perform OK is that the mean of the characteristic of concern is constant for the entire region under consideration (e.g., there is no spatial trend present in the contaminant distribution across the site). This assumption may be violated by dalasets obtained from environmental applications. The occurrence of spatial trend in a dataset collected from a polluted site is an indication of the presence of two or more statistical populations (strata) with significantly different mean concentrations. Use of OK in these situations can result in inaccurate kriging estimates with higher SDs which, in turn, can lead to incorrect decisions regarding all subsequent environmental monitoring and remediation activities. A univariate and a multivariate approach have been described to identify spatial trend that may be present at the site. The trend then is removed by subtracting the respective means from the corresponding populations. The results of OK before and after trend removal are being compared. Using a real dataset, it is shown that standard deviations (SDs) of the kriging estimates obtained after trend removal are uniformly smaller than the corresponding SDs of the estimates obtained without the trend removal. 相似文献
12.
Quantitative approaches to data analysis in the last decade have become important in basin modeling and mineral-resource estimation. The interrelation of geological, geophysical, geochemical, and geohydrological variables is important in adjusting a model to a real-world situation. Revealing the interdependences of variables can contribute in understanding the processes interacting in sedimentary basins. It is reasonably simple to compare spatial data of the same type but more difficult if different properties are involved. Statistical techniques, such as cluster analysis or principal components analysis, or some algebraic approaches can be used to ascertain the relations of standardized spatial data. In this example, structural configuration on five different stratigraphic horizons, one total sediment thickness map, and four maps of geothermal data were copared. As expected, the structural maps are highly related because all had undergone about the same deformation with differing degrees of intensity. The temperature gradients derived (1) from shallow borehole logging measurements under equilibrium conditions with the surrounding rock, and (2) from non-equilibrium bottom-hole temperatures (BHT) from deeper depths are mainly independent of each other. This was expected and confirmed also for the two temperature maps at 1000 ft which were constructed using both types of gradient values. Thus, it is evident that the use of a 2-point (BHT and surface temperature) straightline calculation of a mean temperature gradient gives different information about the geothermal regime than using gradients from temperatures logged under equilibrium conditions. Nevertheless, it is useful to determine to what a degree the larger dataset of nonequilibrium temperatures could reflect quantitative relationships to geologic conditions. Comparing all maps of geothermal information vs. the structural and the sediment thickness maps, it was determined that all correlations are moderately negative or slightly positive. These results are clearly shown by the cluster analysis and the principal components. Considering a close relationship between temperature and thermal conductivity of the sediments as observed for most of the Midcontinent area and relatively homogeneous heat-flow density conditions for the study area these results support the following assumptions: (1) undifferentiated geothermal gradients, computed from temperatures of different depth intervals and differing sediment properties, cannot contribute to an improved understanding of the temperature structure and its controls within the sedimentary cover, and (2) the quantitative approach of revealing such relations needs refined datasets of temperature information valid for the different depth levels or stratigraphic units. 相似文献
13.
Wolfdietrich Skala 《Mathematical Geology》1977,9(5):519-528
This paper presents a mathematical model for simulating the distortion of correlation coefficients in percentage systems. Random variables from multivariate normal distributions with specified variance-covariance matrices are used to calculate correlations for both open and closed arrays. The relationships between these correlations and the dependence of the number of variables and the statistical parameters are examined. 相似文献
14.
Using Multitemporal Remote Sensing Imagery and Inundation Measures to Improve Land Change Estimates in Coastal Wetlands 总被引：1，自引：0，他引：1
Remote sensing imagery can be an invaluable resource to quantify land change in coastal wetlands. Obtaining an accurate measure
of land change can, however, be complicated by differences in fluvial and tidal inundation experienced when the imagery is
captured. This study classified Landsat imagery from two wetland areas in coastal Louisiana from 1983 to 2010 into categories
of land and water. Tide height, river level, and date were used as independent variables in a multiple regression model to
predict land area in the Wax Lake Delta (WLD) and compare those estimates with an adjacent marsh area lacking direct fluvial
inputs. Coefficients of determination from regressions using both measures of water level along with date as predictor variables
of land extent in the WLD, were higher than those obtained using the current methodology which only uses date to predict land
change. Land change trend estimates were also improved when the data were divided by time period. Water level corrected land
gain in the WLD from 1983 to 2010 was 1 km2 year−1, while rates in the adjacent marsh remained roughly constant. This approach of isolating environmental variability due to
changing water levels improves estimates of actual land change in a dynamic system, so that other processes that may control
delta development such as hurricanes, floods, and sediment delivery, may be further investigated. 相似文献
15.
Cascading regressions is a technique for predicting a value of a dependent variable when no paired measurements exist to perform a standard regression analysis. Biases in coefficients of a cascaded-regression line as well as error variance of points about the line are functions of the correlation coefficient between dependent and independent variables. Although this correlation cannot be computed because of the lack of paired data, bounds can be placed on errors through the required properties of the correlation coefficient. The potential meansquared error of a cascaded-regression prediction can be large, as illustrated through an example using geomorphologic data. 相似文献
16.
Robert A. Crovelli 《Mathematical Geology》1988,20(8):955-972
The geologic appraisal model that is selected for a petroleum resource assessment depends upon purpose of the assessment, basic geologic assumptions of the area, type of available data, time available before deadlines, available human and financial resources, available computer facilities, and, most importantly, the available quantitative methodology with corresponding computer software and any new quantitative methodology that would have to be developed. Therefore, different resource assessment projects usually require different geologic models. Also, more than one geologic model might be needed in a single project for assessing different regions of the study or for cross-checking resource estimates of the area. Some geologic analyses used in the past for petroleum resource appraisal involved play analysis. The corresponding quantitative methodologies of these analyses usually consisted of Monte Carlo simulation techniques. A probabilistic system of petroleum resource appraisal for play analysis has been designed to meet the following requirements: (1) includes a variety of geologic models, (2) uses an analytic methodology instead of Monte Carlo simulation, (3) possesses the capacity to aggregate estimates from many areas that have been assessed by different geologic models, and (4) runs quickly on a microcomputer. Geologic models consist of four basic types: reservoir engineering, volumetric yield, field size, and direct assessment. Several case histories and present studies by the U.S. Geological Survey are discussed.This paper was presented at Emerging Concepts. MGLIS-87, Redwood City, California, 13–15 April 1987. 相似文献
17.
When properly calibrated, Holocene pollen data provide an important source of quantitative information about Holocene climates. Multiple linear regression of modern climate and pollen data allows the development of statistical calibration functions that transform percentages of certain pollen types into quantitative estimates of climatic variables, and these functions, when applied to Holocene pollen data, yield estimates of climatic variables for past times. Confidence intervals for the climatic variables provide estimates of the statistical errors. These interval estimates are based upon the following statistical assumptions: (1) the regression model is appropriate; (2) the errors in measuring the climate variables are independent, normally distributed and have constant variance; and (3) no outliers are present. We outline the steps to be followed in calculating calibration functions, including (1) selecting the calibration region; (2) selecting a pollen sum; (3) analyzing scatter diagrams of a given climate variable against each pollen type; (4) deleting outliers and transforming pollen data; (5) performing the regression; and (6) testing the appropriateness of the statistical assumptions. We used available computer programs for most of this study. In addition, we developed new software to compute the Moran statistic to test for spatial autocorrelation among the regression residuals, using the dual of the Voronoi diagram to describe the spatial relationships among the sites. In order to illustrate the sequence of procedures, we used data from the lower peninsula of Michigan to develop a calibration function for July mean temperature and then used Holocene pollen data from central lower Michigan to estimate past temperatures. 相似文献
18.
粘土矿物X射线衍射相定量分析方法与实验 总被引：12，自引：0，他引：12
粘土矿物的物相定量分析在地质研究中有着广泛的应用。本概述了该方法的原理和特点，并讨论了实验中要注意的问题，在对实验结果做了分析之后认为：用x射线衍射方法解决粘土矿物的物相定量问题，虽然只能给出半定量的结果，但是它简单、快捷、重复性好，且有行业标准为依据，仍不失为一种地质研究中常规的物相定量分析方法。 相似文献
19.
A number of growth models have been developed and used in an attempt to project the historical pattern of oil activities to some estimate of their upper limit. Techniques are outlined for the estimation of parameters of the logistic and Gompertz curves. Factor analysis indicated a close relationship between production and demand, whereas annual discoveries and discoveries classified by year of discovery tended to comprise unique factors which were indifferent to changes in time. The growth models projected relatively high values for ultimate demand and production in comparison to the figures for ultimate reserves. Inasmuch as these trends seemed to be occurring independently, some reconciliation of the results was necessary. Using the highest projections of estimates for reserves suggests that over 420 billion barrels of oil in place will eventually be discovered in the United States, with perhaps 200 billion barrels of this eventually to be proved in the form of reserves. Projections for production were higher, corresponding to a trend indicating high levels in demand for crude oil. The only credible long-term estimate of demand was given by a bounded exponential growth model, in which ultimate cumulative demand for crude oil would reach about 416 billion barrels. These figures imply that over 150 billion barrels of oil would be imported into the United States from 1970 to 2070. Provided the time pattern for one of the variables has been determined, then estimates of the other variables probably would be facilitated because of the high interrelationship between variables. Models are suggested in which accurate pivotal forecasting in the short term might be possible—assuming the particular future trend in some of the independent variables has been predetermined.Research Council of Alberta Contribution No. 596. 相似文献
20.
Satoshi Yamamoto 《Mathematical Geology》1993,25(7):867-879
Modern marine sediments can be classified into terrigenous, hemipelagic, and pelagic types according to the distances from the land for the sites recovered and in terms of lithological characteristics of sediments. Ancient cherts are the best sedimentary rocks to reconstruct ancient depositional environments and hemipelagic and pelagic cherts can be identified in terms of lithologic and stratigraphic characteristics. However, geochemical characteristics of modern sediments and ancient cherts can discriminate them into these three types. Particularly, the degree of correlation between Fe and Mg in clay minerals is the most effective criterion for the classification, because the concentration of pelagic clay minerals in which the Fe/Mg ratio is constant may become indices for the classification into the three types. The correlation coefficient and goodness-of-fit to a certain regression line were used as indices of the classification and calculated for several sets of modern sediments and ancient cherts totalling to more than 400 samples. The correlation coefficients and the student-t values for the coefficients become better classification indices than the goodness-of-fit andF-values of the analysis of variance. Goodness-of-fit andF-values can be only used as subsidiary indices for the main classification indices of the correlation coefficients. The classification on the basis of the degree of correlation between Fe and Mg is effective and this approach can be used for other major chemical elements such as Al, K, and Na, if some sequential values of chemical analyses are available. 相似文献