Analysis of log-probability plots of recent Atlantic sediments and its analogy with simulated mixtures

The log-probability plots of some shallow to deep Atlantic sediments are analysed and compared with simulated mixtures of log-normal populations. The plots consist characteristically of two smoothly connected segments which display different slopes. The point of maximum curvature (PMC) between the two segments is shown to reflect the granulometric parameters (mean and sorting) and quantitative proportions of two mixed overlapping populations. This understanding is contrary to the concept which relies heavily on the break points of cumulative plots as indicating truncation of grain size distributions and therefore reflecting hydrodynamic processes. The particular behaviour of the cumulative plots from the Atlantic indicates fining of the two component populations with depth and distance from the shore, accompanied by an increasing dominance of the finer population. This behaviour is compatible with sorting processes which operate in sediments transported through individual grain movements, rather than through mass transportation or turbidity currents.     

Interpretation of grain-size distributions from measured sediment data, Platte River, Nebraska

Breaks in the slope of log-probability plots of cumulative grain-size distributions of bed material are compared with frequency distributions of bedload and suspended sediment over a range of discharges at two stations on the Platte River in south-central Nebraska. The break between suspension and intermittent suspension as determined from the bed-material curve coincides with the upper limit of the grain-size overlap between bedload particles and suspended-sediment particles, whereas the break between intermittent suspension and traction corresponds to the grain size at the lower limit of overlap of bedload particles and suspended-sediment particles. Although grain-size distributions of bedload change little with discharge, the size of the coarsest grains in suspension increases with increasing discharge. Thus, the length of overlap of bedload and suspended-sediment distributions increases with increasing discharge. The limits of grain-size overlap of bedload and suspended-sediment distribution curves associated with near-flood discharges most closely approximate the breaks in the bed material grain-size distribution.     

Determination of background and threshold in exploration geochemistry

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.     

堰塞湖沉积物粒度特征分析——以岷江上游叠溪古堰塞湖为例

对叠溪149个古堰塞湖沉积物样品作了物质组成分析、粒度参数计算和概率累积曲线的统计,结合有关资料对比分析了不同沉积环境中沉积物的粒度特征。结果显示湖相沉积上游段的沉积物主要是粉砂质砂和砂质粉砂,中游和下游段的沉积物较细,主要是黏土质粉砂和粉砂。受河流扰动的影响,湖相沉积上游段沉积物的粒径较粗,平均粒径在4～6φ之间,多为负偏度,峰态宽平,分选性差;中游和下游段的平均粒径在6～8φ之间,均为正偏度,峰态中等,沉积物的分选比上游段好。堰塞湖沉积物是由三个或四个粒度次总体组成,其中上游段沉积物含有4个次总体,中游和下游段含有3个次总体,受物源区的控制,上游段中推移总体的含量远大于中、下游段。这些特征均表明堰塞湖上游段沉积物的搬运方式和沉积环境与中、下游段明显不同。与其他环境中的沉积物相比,堰塞湖沉积物的截点偏细,跃移组分分选性最差。     

Computer program for presentation of grain-size data by the graphic method

A computer program is described for a Hewlett-Packard desk-top Calculator (Model 9820A)-Plotter (Model 9862A) which plots a histogram, frequency polygon and/or cumulative curve, as well as standard statistical parameters and percentages of gravel, sand, silt, and clay from raw weight data from a sediment grain-size analysis. The program utilizes the graphic method for calculating statistical parameters in contrast to other commonly used computer programs derived for the method of moments. This program is advantageous because (1) it is rapid, (2) it allows direct comparison with grain-size data in the literature which have been computed by the graphic method, (3) either a complete presentation of a distribution can be obtained on one sheet of paper or a series of cumulative curves or frequency polygons can be prepared on a single graph which is ready for publication photocopying, (4) automatic extrapolation of data points from a cumulative curve eliminates inconsistencies arising from manual extrapolation, and (5) the desk-top calculator is more convenient to use, eliminates punching of data cards, and can be operated by someone without a knowledge of computers and programming. Disadvantages of the program are: (1) some authors feel critical percentiles are more accurately read off cumulative curves plotted on a probability ordinate than on an arithmetic ordinate, (2) the cumulative curve is a series of straight-line segments, (3) the frequency polygon is not as accurate a representation of grain-size distribution as a frequency curve and (4) size class intervals for the histogram and frequency polygon are standardized at 0.5φ, even though gravel and mud fractions are analysed at whole φ intervals. For most studies, the advantages of the program outweigh the disadvantages.     

Thickness and spatial distributions of clastic dykes, northwest Sacramento Valley, California

The geometry and distribution of the clastic dykes of the Ono district, North Sacramento Valley are examined within stream sections. Five traverses along dry stream beds provide good exposure allowing the spacing, thickness and geometry of the dykes to be recorded. The spatial and thickness distribution of the dykes are considered using cumulative frequency plots, allowing a visual estimation of a best fit distribution. Dyke thickness conforms best to a log-normal distribution. There is also a characteristic minimum dyke thickness in a traverse and this is attributed to the minimum aperture that a fluid with sand clasts is able to exploit. Dyke spacing, however, shows a good correlation with a power-law distribution for four traverses, suggesting that there is a mechanistic control on the spatial distribution. Plotting dyke thickness against minimum dyke spacing reveals that thin dykes do not generally intrude in isolation. Unlike veins and igneous dykes, clastic dykes continue to provide preferential pathways for fluid flow, subsequent to their intrusion, thus inhibiting intrusion in the area surrounding a pre-existing dyke. A combination of this process and dyke branching provides the best model for the observed spatial and thickness distribution of clastic dykes seen in the Ono district, California.     

粒度分布数据的计算机光滑插值绘线方法

以一种单调光滑的分段插值函数为基础，在计算机上实现了光滑的粒度分布累积频率曲线和频率分布曲线的绘制。这一方法为编制软件在计算机上实现粒度分析数据高效高质量的系统处理提供了基础，为粒度分布特征的普遍表述向更精确、更全面的方向深化提供了途径。     

Submarine fan environment inferred from turbidite thickness distributions

Recent studies of turbidite bed thickness distributions have demonstrated power-law as well as log-normal statistical distributions. The different distributions may reflect different fan processes and environments and, therefore, could be used as a quantitative method to help identify those environments, including those devoid of sequential patterns. The cumulative distributions of well-known turbidite deposits spanning a range of interpreted fan subenvironments are used to illustrate the potential correlation between cumulative distribution and environments. Assuming that power-law distributions may, for some systems, be the primary input signal, one-dimensional modelling allows semi-quantitative characterization of the effects of different fan processes such as erosion and bed amalgamation. Environments indicative of different fan processes may be characterized based on the degree to which processes have acted as a 'filter' to modify the assumed power-law distribution systematically. This model of the effect of fan processes on the power-law distribution is used to help to account for bed thickness distributions observed in several field sites.     

成矿元素品位有序数据集自仿射分形方法应用性评价

自仿射分形的Hurst指数是分析地质剖面数据的有利参数。以大尹格庄金矿不同勘探线刻槽取样所得的金品位序列为例，评价Hurst指数的几种估算方法在地质剖面数据分析中的适用性。取相同尺度，全部数据集的增量标准偏差法统计散点呈波状变化，部分数据集的曲线长度变换法统计散点的后半部分呈波状变化,全部数据集的重标极差分析法统计散点线性拟合较好。结果显示增量标准偏差法对尺度要求较为苛刻，适于巨量数据的统计；曲线长度变换法应用性较广，所得Hurst指数反映品位的空间变化强度；重标极差分析法稳定性最好，其Hurst指数反映了品位变化相依性。      

几种土壤累积粒径分布模型的对比研究

土壤粒径分布是最基本的土壤物理性质。作为许多预测模型的输入参数,准确描述土壤的粒径分布是保证模拟质量的前提。评价了对数正态分布、三次样条、逻辑生长、改进逻辑生长以及van Genuchten方程等经验模型在描述土壤粒径分布中的适用情况。结果表明,改进的逻辑生长曲线模型预测效果最好,而广泛采用的对数正态分布的结果最差。其它3种模型的效果介于两者之间。根据5种粒径分布模型的模拟结果,利用分形方法来预测土壤水分特征曲线也得到了类似的结论。     

A Nonstratified Model for Natural Fractal Curves

The stratified structure of Koch curves limits their value as models of nonstratified curves typical in nature, which may nevertheless have statistically self-similar character. Richardson plots for basic and randomized Koch curves are marked by strong, scale-periodic disruptions, and compare poorly with the smoothly sloping, compact Richardson plots derived for some natural, irregular curves. These disruptions relate to the heirarchies of dominant element sizes created in the discrete steps of Koch curve construction, with element vertices acting as attractors for divider steps. We have developed a curve-generation algorithm that adds individual bend elements to a line segment in a nonstratified manner, explicitly following the self-similar limit relation of curve length (L) to added line segment length (r). Values that may be specified include curve fractal dimension (D) and bend element shape (angle of inclination for the added segments). The procedure allows combinations of fractal dimension and element shape, which encompass the range of D values encountered for natural fractal curves. The nonstratified construction method provides useful standard curves for testing and norming of geometric analysis methods commonly applied to complex natural features. In a preliminary test of a multisampling divider method algorithm, the resulting Richardson plots consistently diverge from linear form, and are likely to lead to an overapproximation of D value.     

等温剩磁获得曲线的累积对数高斯模型在泥河湾盆地磁组分识别中的运用

基于饱和等温剩磁(SIRM)获得曲线遵循累积对数高斯模型(CLG)的假设，利用改进的CLG模型分析，成功地对采自泥河湾河—湖相层上部的许家窑剖面样品所含的主要载磁组分进行了分离；结合先前的岩石磁学结果，进一步验证了高矫顽力的赤铁矿和低矫顽力的磁铁矿／磁赤铁矿为许家窑样品的主要载磁矿物，并对各磁组分对SIRM的贡献进行了定量估算；对CLG模型的优缺点和实用性进行了探讨；结合剩磁矫顽力曲线特征，尝试提出了X参数的概念。     

大中型水库坝前年最高水位统计变化特性分析

根据全国１６０座大中型水库的实际观测资料,对坝前年最高水位的变化特性进行了较系统的分析研究。结果表明：年最高水位为独立随机变量,概率分布多为负偏,可由三参数对数正态表征。参数由概率权重矩法估计。     

温度对土体微孔隙特征影响的试验研究

采用烘干法和冻干法分别对深圳土和重塑膨润土进行干燥制样,利用压汞试验得到的累积进汞量曲线,对土体进行了孔隙尺度划分,分析了土体采用不同温度烘干和冻干法干燥制样后孔隙分布存在的差异性,得出了制备压汞试验用土样时,冻干法优于烘干法这一结论。     

Description and hydraulic interpretation of grain size cumulative curves from the Platte River system

Log-probability plots of grain-size distribution from the Platte, North Platte, and South Platte rivers are composed of four or five straight line segments. The line segments are grouped, dividing each curve into three regions. These regions are interpreted as subpopulations moved by different transport mechanisms. Consideration of the criterion for suspension and calculation of shear velocities associated with dominant discharges support this interpretation. The grain size cumulative curves are similar to each other but distinct from curves of fluvial systems transporting only fine-grained material, the difference being the presence of a subpopulation of grains moved in traction transport. One of two possible relationships seems to exist between the grain-size distributions and flow conditions within the Platte River system. Estimated shear velocities derived by varying flow conditions within reasonable limits predict a range of grain sizes within which the break between the intermittent suspension and traction loads should occur. This break appears to be associated with intermediate shear velocities if truncated normal distributions are assumed; but if overlapping distributions are assumed, the ‘break'is associated with estimated maximum shear velocities.     

累计磁极性偏转及其在发电机模型评估中的应用

地磁板性反转纪录通常用代表两种极性的黑白间隔所组成的极性柱来表示。这里引入累计磁极性偏转曲线,作为描述地磁极性反转记录的一种新方法。通过组合整个地质时期地磁极性间隔的长度所获得的这种曲线,使人们更容易想象任一时期内地磁场极性的偏转,以及磁场的滞后性质,它同时提供了一种评估地磁发电机模型的有效手段。本文通过实例论述：如何运用累计磁极性偏转方法,评估无量纲参数和信噪比两者的变化及其对磁极性偏转、极性带长度和极性变化频率的影响。     

The dynamic economic evaluation method of shale gas resources

At present, most shale gas exploration and development areas in China are difficult to provide sufficient and effective production data to support economic evaluation, since they are still in the initial stage of low exploration level. In addition, ecological and environmental factors are not taken into account in the evaluation process, which does not meet the needs of green energy development of China. Aiming at above problems, the dynamic economic evaluation method of shale gas resources based on calculus principle is proposed. The Arps hyperbolic decreasing curve model will be used in the evaluation of single shale gas well production, which can evaluate single well production of shale gas by fitting the existing dynamic production data to generate the production decreasing curve. Therefore, the variation regularity of the cumulative production of single well shale gas within the study area can be obtained by the model mentioned above. According to the variation regularity of the cumulative production obtained from the Arps hyperbolic decreasing curve model, the recovery period of single well cost, ultimate economic life and the ultimate economic resource can be evaluated dynamically by analyzing the variation regularity of the cumulative sales revenue and cumulative input cost of single shale gas well. Then the evaluation result can be further extend to the whole evaluation areas, in order to analyze shale gas resources ’ economic value in evaluation regions under different shale gas price conditions. The results of the above evaluation methods are not only conducive to improving the economic benefits of relative shale gas development enterprises, but also provide a basis for the national energy strategy deployment.© 2019 China Geology Editorial Office.     

标准U形断面渠槽水面线的计算模型

用常规的分段求和法完成标准U形断面渠槽水面线计算不但存在误差累积而且计算工作量大、效率低。依据优化拟合理论,以标准剩余差最小为目标函数,在工程适用参数范围内,经拟合计算获得了由一个简化通用算式替代原积分中的分段且不可积函数,并通过积分获得了该种断面水面线的解析计算模型,且由于正、负拟合误差的相互抵消,使最终计算成果的精度进一步提高。利用该模型完成标准U形断面水面线计算可使求解过程大大简化,工作效率明显提高,具有实用推广意义。     

Asymptotic Dykstra�CParsons Distribution, Estimates and Confidence Intervals

The sample Dykstra?CParsons (DP) coefficient, the most popular heterogeneity static measure among petroleum engineers, may exhibit significant sampling errors. Moreover, approximations of its probability distributions (uncertainty estimates) are only available for specific families of permeability models (e.g., log-normal). The cited probability distributions allow for the specification of confidence intervals and other inferences for the theoretical DP, which will be useful for reservoir screening purposes, or to establish if a more detailed study is justified. This paper presents the development of an asymptotic approximation of the distribution of the sample Dykstra?CParsons coefficient, which is independent of the permeability probability distribution. The effectiveness (bias and confidence intervals) of the proposed approach is demonstrated using analytical and field case studies and by comparing the results gleaned with those obtained using a well-known parametric approximation, under different scenarios of reservoir maturity levels (i.e., number of wells) and different degrees of deviation from the log-normal probability density function assumption. The results show that, in the vast majority of the case studies, the proposed approach outperformed the parametric approximation; in particular, our approach resulted in a significant reduction of the bias and the confidence intervals always including the theoretical DP coefficient. In addition, an excellent agreement was observed between the asymptotic cumulative distribution of the DP coefficient and the corresponding empirical distribution for sample sizes as small as one hundred, which suggests that high success rates can be obtained when reservoirs are classified according to the asymptotic DP coefficient.     

Geochemical baseline of trace elements in the sediment in Dexing area,South China

A baseline might be used as a point of reference to monitor change from some specific data without concern for whether the baseline determination is natural or has been changed by human activity. We selected 326 sediment samples from Dexing area, South China, and analyzed for 17 chemical elements. The geochemical baseline was predicted with the method of the normalization procedure combined with the relative cumulative frequency curve. The results indicate Al was the best reference element for the normalization procedure among four potential reference elements (Al, Fe, Ti, and Mn). The baseline value range obtained from the normalization procedure method included both the regional geochemical background of the sediment and the median value of the measured contents. The median value of baselines obtained from relative cumulative frequency method was lower than that obtained from normalization procedure method. In contrast to the geochemical patterns of heavy metals in 1987, the spatial distribution of anomalies sprawled in 2004 in study area, especially for Cu, Pb, Zn, Cd, As, Fe, and Cr.