共查询到20条相似文献，搜索用时 31 毫秒
1.
Alan M. Jacobs 《Mathematical Geology》1971,3(3):227-238
Relative percentages of sand, silt, and clay from samples of the same till unit are not identical because of different lithologies in the source areas, sorting in transport, random variation, and experimental error. Random variation and experimental error can be isolated from the other two as follows. For each particle-size class of each till unit, a standard population is determined by using a normally distributed, representative group of data. New measurements are compared with the standard population and, if they compare satisfactorily, the experimental error is not significant and random variation is within the expected range for the population. The outcome of the comparison depends on numerical criteria derived from a graphical method rather than on a more commonly used one-way analysis of variance with two treatments. If the number of samples and the standard deviation of the standard population are substituted in at-test equation, a family of hyperbolas is generated, each of which corresponds to a specific number of subsamples taken from each new sample. The axes of the graphs of the hyperbolas are the standard deviation of new measurements (horizontal axis) and the difference between the means of the new measurements and the standard population (vertical axis). The area between the two branches of each hyperbola corresponds to a satisfactory comparison between the new measurements and the standard population. Measurements from a new sample can be tested by plotting their standard deviation vs. difference in means on axes containing a hyperbola corresponding to the specific number of subsamples used. If the point lies between the branches of the hyperbola, the measurements are considered reliable. But if the point lies outside this region, the measurements are repeated. Because the critical segment of the hyperbola is approximately a straight line parallel to the horizontal axis, the test is simplified to a comparison between the means of the standard population and the means of the subsample. The minimum number of subsamples required to prove significant variation between samples caused by different lithologies in the source areas and sorting in transport can be determined directly from the graphical method. The minimum number of subsamples required is the maximum number to be run for economy of effort. 相似文献
2.
Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry 总被引：1，自引：0，他引：1
A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used. 相似文献
3.
4.
Dipankar Pathak 《Geostandards and Geoanalytical Research》2023,47(1):185-197
Isotope dilution (ID) is a widely used analytical technique to determine elemental abundance to a high degree of accuracy and precision, using a spiked isotope tracer. This technique also enables efficient correction of the inevitable phenomenon of analytical mass fractionation during mass spectrometric analysis. It is also used to determine stable isotope variations of an element in a sample relative to a reference material, using tracers enriched in two isotopes (popularly known as the double spike method). Isotope dilution data reduction can be performed in Microsoft® Excel™ using different algorithmic approaches. Additional software such as iolite and MATLAB® offer algorithm implementations to perform these calculations. These are however limited to use within particular laboratories/research groups, or either require additional cost-bound software or some degree of knowledge in computer programming languages for use, or all of these. To ease this situation, a graphical user interface-based software is proposed (here named Parmanu-Gunak, meaning Atom-Calculator in Sanskrit text) to invert both single and double spiked isotope data, with the aim of making it a standard tool for ID data reduction. Examples of Nd and Mo isotopes are used to demonstrate the robustness of the program. 相似文献
5.
Methods used for the estimation of analytical precision commonly suffer from two deficiencies which give rise to misleading results. These are: (1) the methods take no account of changes in absolute or relative error over the concentration range, and (2) they tend for other reasons to produce optimistically-biassed results. The difficulties can be avoided by the correct use of duplicate determinations. One method presented allows precision parameters to be estimated. The other gives rise to a simple control chart for use in geochemical analysis. 相似文献
6.
地应力测量的误差处理及精度评定 总被引：4，自引：3，他引：1
本文从地应力测量数据误差处理的角度阐述了地应力计算的最小二乘法,对地应力测量精度评定方法进行了改进。采用协方差传播律进行误差计算,使精度评定的结果更加准确。利用应力的坐标变换关系,推导出应力与应力分量之间的微分关系,使主应力的精度计算更加简便。提出了主应力的偏用误差概念及其计算方法,使主应力方向的精度评定更加真实客观。 相似文献
7.
区域大地水准面的确定是GPS测量常需解决的问题。目前确定大地水准面的方法主要包括重力法、GPS水准几何法及组合法,其中组合法因其精度和可靠性都较高,常用于计算高精度区域大地水准面。高精度的大地水准面模型是组合法确定区域大地水准面的关键。在我国,EGM2008全球重力场模型精度和分辨率均高于此前的所有模型,研究基于该模型的组合法大地水准面精化具有重要的实践意义。笔者以吉林大学兴城教学实习基地物探实验区为例,基于实测重力数据、EGM2008重力场模型和GPS水准数据,采用组合法精化了区域大地水准面,比较了组合法大地水准面模型和无重力实测数据的几何法大地水准面模型的精度差异,分析了该方法在物探测量中的适用性。结果表明,实验区组合法大地水准面模型精度最高达到1.2 cm,并且误差分布区间较小,总体上精度和可靠性高于对比的几何方法,并且组合法和几何法获取的两种大地水准面模型均能满足大比例尺物探测量要求。EGM2008模型精度较高,故平坦地区使用组合法时,高密度的实测重力数据可能带来高频扰动,有可能降低EGM2008重力场模型本身的精度,所以重力数据采集过程中要顾及重力点的密度和空间分布。本文方法更适用于地形复杂的地区。 相似文献
8.
Parameters and their error intervals numerically estimated for the observed light curve of the binary eclipsing system YZ Cas as well as for one-, two-, three-, and four-parameter functions, and the associated parameters and their error intervals numerically estimated. The error intervals are calculated using differential corrections method, Monte-Carlo simulations, and confidence areas. We study the error intervals and the reliability of the techniques used. 相似文献
9.
Craig Loehle 《Mathematical Geology》2005,37(2):127-140
Timeseries of estimated temperature have been combined to create global or hemispheric climate series over periods exceeding 1000 yr. The data used in these studies, however, may be subject to dating errors. It is shown that when timeseries with dating error are combined, the noise in the data smoothes periodic signals but leaves linear trends intact. This means that the effect of dating error of sample data in a timeseries reconstruction is to smooth out any signals (waves, cycles) that may be present. The purpose of this study was to develop signal extraction methods that will work for this type of historical data. The method used was nonlinear estimation of sample series where dating error has been added by Monte Carlo sampling. Several algorithms were tested for handling the dating error problem. Results were that using nonlinear model fitting, the periods of signals can be identified even from the averaged data. In a second stage of the estimation procedure, the cycle magnitudes can be estimated. Very good fits were achieved for two example cases. Temperature estimation error (white noise due to the use of proxies) was also considered and the method was extended to cover this case with quite good results. Using the new estimation methods, the information inherent in multiple series can be used to overcome the problem of dating error. 相似文献
10.
《International Geology Review》2012,54(4):293-303
York's (1969) method of regression, determining the best-fit line to data with errors in both variables using a least-squares solution, has become an integral part of isotope geochemistry. Although other methods agree with York's best-fit line (e.g., maximum likelihood), there is little agreement on the standard-error estimates for slope and intercept values. The reasons for this are differing levels of approximation used to compute the standard error, doubts concerning procedures for determining a confidence interval once the standard error has been estimated, and a typographical error in the original publication. This paper examines York's method of regression and standard errors of the parameters of a best-fit line. A very accurate method for determining the standard error in slope and intercept values is introduced, which eliminates the need to multiply the standard-error estimate by the goodness-of-fit parameter known as MSWD. In addition, a derivation of a fixed-intercept method of regression is introduced, and interpretations of MSWD and use of the t-adjustment in confidence intervals are discussed. The accuracy of the standard-error computations is determined by comparing the results to slope and intercept statistics generated from several thousand Monte Carlo regressions using synthetic 40Ar/39Ar inverse isochron data. 相似文献
11.
Soil–water characteristic curve (SWCC) contains the fundamental information needed for describing the mechanical behavior of unsaturated soil. Some parameters such as air-entry value, slope at the inflection point, residual water content and residual suction are commonly used to describe the SWCC and other associated properties such as shear strength and permeability. Currently these parameters are determined using the graphical method which can be subjective and time consuming. Equations for determining these parameters are proposed and the relationships between SWCC parameters and fitting parameters are discussed in this paper. These equations can be used for computational analyses to replace the conventional graphical method in providing consistent results. 相似文献
12.
近年来人们往往利用GPS数据来确定大地高,但大地高不同于正常高,为此,利用多项式拟合与地球重力场模型相结合的数学方法,使GPS所测大地高通过这些数学模型直接转换为具有厘米精度的正常高,将该方法得到的正常高与单独利用多项式拟合和地球重力场模型得到的结果进行了比较,其差值的标准差为±38 cm。 相似文献
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14.
粉末压片制样-X射线荧光光谱法测定铁矿石中锌砷锰 总被引：1，自引：1，他引：0
应用X射线荧光光谱仪测定铁矿石中的锌、砷、锰含量,采用粉末压片法制样,并研究了制样的条件,确定了仪器最佳参数,建立了标准曲线。经国家实物标准铁矿石样品验证,测定值与标准值吻合,三元素的偏差均小于±0.007%;精密度试验表明相对标准偏差(n=10)均小于2.80%。大量实验数据表明,压片制样-X射线荧光光谱法测定锌、砷、锰元素的精密度高,准确可靠。该方法在检测准确度和分析速度上可以满足钢厂生产要求。 相似文献
15.
G.R. Parslow 《Journal of Geochemical Exploration》1974,3(4):319-336
The graphical methods of analysing bi-modal frequency distributions are reviewed. The effects of inflection point position, curvature of the sigmoid, polymodality, and graphical and analytical precision are found to be important and are discussed in detail. The optimum method is a cumulative plot on log-probability paper with the two component distributions (linear) being asymptotic to the sigmoid tails and having a symmetry with each other about the inflection point. The method is illustrated with five natural examples to emphasise its advantages and limitations. 相似文献
16.
LHS方法在边坡可靠度分析中的应用 总被引：8，自引：0，他引：8
Monte Carlo（MC）法在目前边坡可靠度分析中是一种相对精确的方法,应用广泛,受问题限制的影响较小,适应性很强,其误差仅与标准差和样本容量有关。但其精度受随机抽样的可靠性和模拟次数制约,收敛速度慢,影响了实际使用。在极限平衡方法的基础上,用拉丁超立方抽样（Latin hypercube sampling,LHS）方法代替MC法的随机抽样,考虑边坡参数的变异性和相关性进行边坡可靠度分析。讨论了LHS法、MC法中可靠指标的各种计算方法,建议以破坏概率、安全系数均值和标准差作为评价指标。算例显示LHS法较MC法效率上有很大改善：较少的抽样样本就能反映参数的概率分布,可靠度分析收敛快,不需要大量的模拟,因此,值得在边坡可靠度分析中推广应用。也将工程上常用的均匀设计和正交设计用于边坡可靠度分析,结果表明,正交设计结果和中心点法比较接近,而均匀设计得到的结果则是不可靠的。 相似文献
17.
Analysis of the precision of the illite 'crystallinity'technique shows that machine errors are <5%, while intra- and inter-sample errors are variable but are up to 12% and 14%, respectively (1σ). Consideration of this error analysis shows that the isocryst approach, which involves close contouring (e.g. 0.03 Δ2°) of illite 'crystallinity'data, has a very low degree of confidence (<0.5) and thus is not regarded as statistically valid. If contouring is to be undertaken with a high degree of confidence (>0.8) it is necessary that contours should be at intervals of 0.1 ΔΘ2°, which is equivalent to subdivision of the anchizone into upper and lower units. Where previous interpretations have relied upon an isocryst method of contouring at less than 0.1 ΔΘ2° the conclusions must be regarded as unsubstantiated.
Centrifuge separation of clay fractions (based on a Stokes'law application) gives separations in which a significant, but variable, percentage of grains have long axes greater than the size calculated. For the typical <2-μm fraction utilized, some 20% of grains lie in the 2–4-μm range, although the proportion is not believed to have a significant effect upon 'crystallinity'values. The formula is applicable for grain-sizes down to 0.5 μm. Illite 'crystallinity'values on samples prepared by an ultrasonic disaggregation method show a small increase on those prepared by ball mill crushing. The differences are minimal at the epi/anchizone level but increase to some 10% at the anchizone/diagenetic level. The effect on grade determinations is again thought to be minimal and indicates that concern over unsuitability of the ultrasonic disaggregation method is unfounded. 相似文献
Centrifuge separation of clay fractions (based on a Stokes'law application) gives separations in which a significant, but variable, percentage of grains have long axes greater than the size calculated. For the typical <2-μm fraction utilized, some 20% of grains lie in the 2–4-μm range, although the proportion is not believed to have a significant effect upon 'crystallinity'values. The formula is applicable for grain-sizes down to 0.5 μm. Illite 'crystallinity'values on samples prepared by an ultrasonic disaggregation method show a small increase on those prepared by ball mill crushing. The differences are minimal at the epi/anchizone level but increase to some 10% at the anchizone/diagenetic level. The effect on grade determinations is again thought to be minimal and indicates that concern over unsuitability of the ultrasonic disaggregation method is unfounded. 相似文献
18.
In classical plasticity there are clear mathematical links between the dissipation function and the consequent yield function and flow rule. These links help to construct constitutive equations with the minimum of adjustable parameters. Modelling granular materials, however, requires that the dissipation function depends on the current stress state (frictional plasticity) and this changes the mathematical structure—altering the links and invalidating the associated flow rule. In this paper we show, for a large family of dissipation functions, how much of the structure remains intact when frictional dissipation is included. The surviving links are examined using straightforward physically based graphical insight and well‐established mathematical techniques leading to a central result, which provides a mathematical justification for the procedural features of hyperplasticity. This should allow hyperplasticity to be used more widely and certainly with increased confidence. As an example of the effectiveness of the general method, two specific dissipation functions are constructed from the simple physical concepts of sliding friction and granule damage. One is based on a Drucker–Prager cone and the other a Matsuoka–Nakai cone, both incorporate kinematic hardening and a compactive cap. In each Case a single smooth yield function with consistent flow rules is produced. The computational usefulness of an inequality derived in the paper is demonstrated in the generation of the figures showing yield surfaces and flow directions by means of a simple maximization procedure. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
19.
地面多基线数字摄影测量在冰川测量中的应用 ——以博格达峰黑沟8号冰川为例 总被引：2，自引：1，他引：1
冰川的监测一直是冰川学研究的重要内容, 2008年对天山东段博格达峰南坡的黑沟8号冰川末端进行了地面多基线数字摄影测量, 获取了该冰川末端的影像, 以及与之相配套的控制信息. 在Lensphoto多基线数字摄影测量系统中, 测得了冰川末端的0.11 km2 DEM数据. 采用同期测量的GPS数据检验得知, 摄影测量所得DEM数据在高程上的平均误差为1.92 m, 标准偏差为3.47 m. 地面旋转多基线数字摄影测量是一种非常有效的冰川测量手段, 可以在典型冰川测量和冰川重要部位(例如冰川末端、 冰崖等)的测量中发挥作用. 相似文献
20.
W. E. Bardsley 《Mathematical Geology》1983,15(6):649-658
The effect of random error on age reliability is investigated with respect to the externaldetector method of fission-track dating. Obtaining confidence limits to age is shown to be equivalent to obtaining confidence limits for products and ratios of Poisson expectations. Attention is drawn to the relevant methodology for calculating exact confidence limits, and some simple approximations to these limits are suggested for use when the number of track counts is large. 相似文献