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1.
ZOLTÁN SYLVESTER 《Sedimentology》2007,54(4):847-870
Turbidite bed thickness distributions are often interpreted in terms of power laws, even when there are significant departures from a single straight line on a log–log exceedence probability plot. Alternatively, these distributions have been described by a lognormal mixture model. Statistical methods used to analyse and distinguish the two models (power law and lognormal mixture) are presented here. In addition, the shortcomings of some frequently applied techniques are discussed, using a new data set from the Tarcău Sandstone of the East Carpathians, Romania, and published data from the Marnoso‐Arenacea Formation of Italy. Log–log exceedence plots and least squares fitting by themselves are inappropriate tools for the analysis of bed thickness distributions; they must be accompanied by the assessment of other types of diagrams (cumulative probability, histogram of log‐transformed values, q–q plots) and the use of a measure of goodness‐of‐fit other than R2, such as the chi‐square or the Kolmogorov–Smirnov statistics. When interpreting data that do not follow a single straight line on a log–log exceedence plot, it is important to take into account that ‘segmented’ power laws are not simple mixtures of power law populations with arbitrary parameters. Although a simple model of flow confinement does result in segmented plots at the centre of a basin, the segmented shape of the exceedence curve breaks down as the sampling location moves away from the basin centre. The lognormal mixture model is a sedimentologically intuitive alternative to the power law distribution. The expectation–maximization algorithm can be used to estimate the parameters and thus to model lognormal bed thickness mixtures. Taking into account these observations, the bed thickness data from the Tarcău Sandstone are best described by a lognormal mixture model with two components. Compared with the Marnoso‐Arenacea Formation, in which bed thicknesses of thin beds have a larger variability than thicknesses of the thicker beds, the thinner‐bedded population of the Tarcău Sandstone has a lower variability than the thicker‐bedded population. Such differences might reflect contrasting depositional settings, such as the difference between channel levées and basin plains. 相似文献
2.
Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data 总被引：13，自引：0，他引：13
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 相似文献
3.
This paper presents a methodological framework for inter‐instrument comparison of different particle‐size analysers. The framework consists of: (i) quantifying the difference between complete particle‐size distributions; (ii) identifying the best regression model for homogenizing data sets of particle‐size distributions measured by different instruments; (iii) quantifying the precision of a range of particle‐size analysers; and (iv) identifying the most appropriate instrument for analysing a given set of samples. The log‐ratio transform is applied to particle‐size distributions throughout this study to avoid the pitfalls of analysing percentage‐frequency data in ‘closed‐space’. A Normalized Distance statistic is used to quantify the difference between particle‐size distributions and assess the performance of log‐ratio regression models. Forty‐six different regression models are applied to sediment samples measured by both sieve‐pipette and laser analysis. Interactive quadratic regression models offer the best means of homogenizing data sets of particle‐size distributions measured by different instruments into a comparable format. However, quadratic interactive log‐ratio regression models require a large number of training samples (n > 80) to achieve optimal performance compared to linear regression models (n = 50). The precision of ten particle‐size analysis instruments was assessed using a data set of ten replicate measurements made of four previously published silty sediment samples. Instrument precision is quantified as the median Normalized Difference measured between the ten replicate measurements made for each sediment sample. The Differentiation Power statistic is introduced to assess the ability of each instrument to detect differences between the four sediment samples. Differentiation Power scores show that instruments based on laser diffraction principles are able to differentiate most effectively between the samples of silty sediment at a 95% confidence level. Instruments applying the principles of sedimentation offer the next most precise approach. 相似文献
4.
受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。 相似文献
5.
Undiscovered oil and gas assessments are commonly reported as aggregate estimates of hydrocarbon volumes. Potential commercial value and discovery costs are, however, determined by accumulation size, so engineers, economists, decision makers, and sometimes policy analysts are most interested in projected discovery sizes. The lognormal and Pareto distributions have been used to model exploration target sizes. This note contrasts the outcomes of applying these alternative distributions to the play level assessments of the U.S. Geological Survey's 1995 National Oil and Gas Assessment. Using the same numbers of undiscovered accumulations and the same minimum, medium, and maximum size estimates, substitution of the shifted truncated lognormal distribution for the shifted truncated Pareto distribution reduced assessed undiscovered oil by 16% and gas by 15%. Nearly all of the volume differences resulted because the lognormal had fewer larger fields relative to the Pareto. The lognormal also resulted in a smaller number of small fields relative to the Pareto. For the Permian Basin case study presented here, reserve addition costs were 20% higher with the lognormal size assumption. 相似文献
6.
A logarithmic transformation may be used to improve the efficiency of estimates of the mean when observations follow the lognormal distribution. But if this transformation is applied to observations that follow another distribution, bias may be introduced. We consider some consequences of erroneously applying lognormal estimation theory and demonstrate that biased estimates may be obtained for certain classes of distributions. Illustrations of bias obtained in gold sampling are given. 相似文献
7.
大位移剪切下钙质砂破碎演化特性 总被引：1，自引：0，他引：1
为了揭示钙质砂在大位移剪切作用下的破碎及形状演化规律,对南海钙质砂进行了系列不同剪切位移下的环剪试验。首先,利用筛分和激光粒度分析获取试验后的颗粒粒径分布,分析颗粒分布变化情况;其次,通过粒径分布对破碎进行定量分析;最后,运用图像处理技术计算颗粒圆度和扁平度,分析了颗粒形状的变化情况。试验结果表明,在不同的竖向压力下,颗粒会达到不同的稳定级配,但达到稳定所需的剪切位移相同;经历大位移剪切后,出现粒径为0.01～0.075 mm钙质砂破碎严重的现象;随剪切位移的增加,颗粒的圆度和扁平度减小。针对细小颗粒破碎严重的现象,修正了相对破碎率;修正后的相对破碎率能考虑粒径为0.01～0.075 mm颗粒发生的破碎。剪切后的钙质砂颗粒更为规则,整体轮廓趋于圆形、表面更光滑。 相似文献
8.
Rock avalanches are a form of hazardous long-runout landslide and leave fragmented deposits of complex sedimentology that, if studied in detail, can provide insight into their emplacement processes. Complexity arises due to the myriad overlapping factors known to contribute to the final deposit fabric, such as source structures, lithology (i.e. material properties), topographic feedback, substrate interaction and emplacement processes (i.e. internal factors), as well as our reliance on (un)suitable exposures. Herein, we present sedimentological data from two carbonate rock avalanche deposits (Tschirgant in Austria and Flims in Switzerland), where changes in lithology can be eliminated from the causal equation due to their largely mono-mineralic composition. We further eliminated the effects of external influences such as topography or substrate interactions by detailed facies mapping of the deposit interior. Since sedimentary properties locally vary within less than 1-m2 outcrop area, emplacement processes are the only causes that remain to explain the different fabrics. Characteristic (fractal) grain size distributions of three distinctive sub-facies in the interior of these, and other, rock avalanche deposits—jigsaw-fractured, fragmented, and shear zone facies—can be linked to specific processes acting during emplacement. We suggest that a heterogeneously distributed and progressively increasing particle breakage in the moving granular mass best explains the ranges of fractal dimensions and associated features for the respective sub-facies, from simple breakage along pre-existing planes, through dynamic fragmentation which locally minimises coordination number, to zones of shear concentration. No exotic emplacement mechanisms (such as air-layer lubrication or fluidised substrates) are required to produce these features; continued, heterogeneous degrees of fragmentation of an initially intact source rock best explains the sedimentary record of rock avalanches. 相似文献
9.
Comparative study of aggregations under different dependency assumptions for assessment of undiscovered recoverable oil resources in the world 总被引：1，自引：0，他引：1
Robert A. Crovelli 《Mathematical Geology》1985,17(4):367-374
The U.S. Geological Survey assessed all significant sedimentary basins in the world for undiscovered conventionally recoverable crude-oil resources. Probabilistic methodology was applied to each basin assessment to produce estimates in the form of probability distributions. Basin probability distributions were computer aggregated to produce resource estimates for the entire world. Aggregation was approximated by a three-parameter lognormal distribution by combining the first three central moments of basin distributions. For purposes of experiment and study, world aggregation was conducted under four different sets of assumptions. The four cases are (1) dependent assessments of all basins, (2) dependent assessments within continental areas, but independent assessments among continental areas, (3) dependent assessments within countries, but independent assessments among countries, and (4) independent assessments of all basins. Mean estimate remained the same in all four cases, but the width of interval estimate formed using the 95th and 5th fractiles decreased with reduced dependency in going from first to fourth case. 相似文献
10.
11.
J. A. Sanchidrián P. Segarra F. Ouchterlony L. M. López 《Rock Mechanics and Rock Engineering》2009,42(1):95-116
Summary Size distributions of fragments of crushed rock in conveyor belts and of blasted rock in a muckpile obtained by sieving are
compared with the size distributions obtained by digital image analysis of photographs of the same materials taken on-site.
Several calculation methods are tested, based on the raw distribution of fragment areas and on the volume-transformed ones.
The influence of the calibration of the system on the results and the performance of the system in a non-calibrated mode are
evaluated. The capacity of some distributions (Rosin-Rammler, Swebrec and lognormal) to fit the data in the coarse region
(where particles can be delineated, i.e. discriminated individually) and to extrapolate to the non-delineated fines (where
particles cannot be outlined and their contour delineated) is assessed. The error between the sizes measured and the sizes
of the reference distributions (determined by sieving) increases from the coarse to the fines region. The maximum error at
a given size depends primarily on its value relative to the fines cut-off (FCO) of the image analysis. In general, at sizes
greater than the FCO, where the system is able to delineate fragments reliably, both volume and surface-based, calibrated,
calculations can determine the sizes with maximum error expectancy of about 30%. Below the FCO, only the calibrated, volume
calculation maintains a maximum error of 30%, down to sizes of about one fourth the FCO, rapidly increasing for smaller sizes.
Where the calibration is done based on data above the FCO, errors can be large below this point, in excess of 80% at sizes
half the FCO. In the fines range (sizes smaller than 0.2 times the FCO) the maximum errors can be close to or greater than
100% for most of the calculations and function fittings. Of the distributions tested, all of them are acceptable at sizes
above the FCO; below that, the Swebrec function seems to adapt better towards the fines than the Rosin-Rammler and lognormal.
Correspondence: José A. Sanchidrián, Universidad Politécnica de Madrid, E.T.S.I. Minas, Rios Rosas 21, 28003 Madrid, Spain 相似文献
12.
An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage
The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na2SO4 contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.
相似文献13.
In order to reduce the maintenance costs of ballasted railway track and improve passenger comfort, the railway ballast particle breakage and its effect on track settlement need to be better understood. The failure process of individual railway ballast loaded between flat platens is simulated using the discrete element method, considering its irregular shape with the incorporation of parallel bonds. The tensile strength, the stress of a survival probability of 37% of samples, is obtained and compared with laboratory results from published literature for the verification of DEM simulations. The evolution to failure of the particle is understood from the stress-strain curve and progressive failure modes. The internal breakage mechanisms are analysed by tracking the accumulation of bond breakage number and the contact force distributions. 相似文献
14.
《Sedimentology》2018,65(6):1859-1874
Ripples are prevalent in aeolian landscapes. Many researchers have focused on the shape and formation of sand ripples, but few have studied the differences in the particle size of sand on crests and in troughs along bed, especially the variations caused by changes in friction velocity and the wind‐blowing duration. A particle size of 158 μm (d ) was used to create aeolian ripples in a wind tunnel under four friction velocities (u *) with different wind duration times (t ). Samples were collected from the surfaces of ripple crests and troughs, respectively, at seven sites, and particle sizes were measured using a Malvern Mastersizer 2000. The main results were: (i) The particle size distributions of sand in troughs are unimodal with slight variations of particle size parameters, including mean particle size, standard deviation, skewness and kurtosis, etc., under different conditions, while these particle size parameters of sand on crests change with friction velocity and deflation time. Moreover, some of the particle distribution curves for the sand on crests do not follow typical unimodal curves. (ii) With increasing friction velocity or deflation duration, the sand on the crests shows a coarsening process relative to those on the bed surface. The particle size of sand on crests at a 1 m bed increases linearly with friction velocity (d = 344·27 + 34·54 u *) at a given wind‐blowing duration. The particle sizes of sand on crests at 1 m, 2 m and 4 m beds increase with a power‐law relationship (d = a + t b, where a and b are fitting parameters) with deflation time at a given friction velocity. (iii) The probability cumulative curves of sand showed a three‐section pattern in troughs and on most of the crests but a four‐section pattern at crest locations due to increased influence by friction velocity and deflation time. The proportions of the sediment moved by suspension, saltation and creep in the three‐section pattern were within the ranges of 0·2% to 2·0%, 97·0% to 98·9%, and 0·8% to 3·0%, respectively. For the four‐section pattern, suspension accounted for 0·3% and 3·0%, and the proportion of creep increased with friction velocity and deflation time, while saltation decreased accordingly. Although these results require additional validation, they help to advance current understanding of the grain‐size characteristics of aeolian ripples. 相似文献
15.
在常规应力水平下颗粒发生破碎是钙质砂有别于其他砂土的重要性质之一,且由于颗粒破碎的存在,使用传统的本构模型无法很好地模拟钙质砂的力学行为。因此本文以最为普及的本构模型之一--邓肯-张E-B模型为基础,对其进行颗粒破碎方面的修正以得到一个能用于钙质砂的本构模型。具体方法为:首先本文采用Hardin提出的相对破碎Br这一指标来度量颗粒破碎的大小。之后研究分析得出了颗粒破碎对邓肯-张模型参数(内摩擦角φ、割线模量E50及体积模量B)的影响规律。然后通过颗粒破碎与输入能量之间的关系将各状态下无法直接确定的相对破碎Br与可确定的应力-应变状态联系起来。最终得到了一个考虑颗粒破碎的钙质砂修正邓肯-张E-B模型。为验证模型的准确性及适用性,本文还使用该模型对4种不同粒径范围且试验围压不同的钙质砂的三轴排水行为进行了模拟。结果表明拟合效果较好,模型能适用于各种不同粒径范围的钙质砂,并且在颗粒破碎较大的情况下明显优于传统邓肯-张模型。 相似文献
16.
珊瑚砂是一种含钙极高的海洋生物成因材料,具有高棱角性、形状不规则、易破碎等特点。通过珊瑚砂的高压一维蠕变试验,研究颗粒破碎引起颗粒分布曲线和形状因子的演化规律。借助于高速动态图像的激光粒度粒形仪器,从统计学的角度分析试验前后颗粒形状随压力演化的关系,发现颗粒的形状因子,如长宽比、球形度和凹凸度等,随压力增加而逐渐增加。不同粒径的颗粒形状因子均向一个窄幅范围趋近,说明颗粒破碎具有无尺度性和自相似性的分形特性,分形维数随压力增加而逐渐增大,且趋近分形破碎极限。采用Hardin和Einav的方法计算相对破碎量,发现在两种计算方法下相对破碎量与压力呈幂函数关系,且幂指数相同。相对破碎量随时间增加的现象并不明显,说明在高压力下颗粒破碎主要为压缩破碎,且颗粒细化滑移填充孔隙引起的变形是造成蠕变的主要原因。 相似文献
17.
A method is proposed to calculate the distribution of energy during the quasi-static confined comminution of particulate assemblies. The work input, calculated by integrating the load-displacement curve, is written as the sum of the elastic deformation energy, the breakage energy and the redistribution energy. Experimental results obtained on samples subjected to compression stresses ranging between 0.4 and 92 MPa are used to calibrate the model. The elastic energy stored in the samples is obtained by simulating the compression test on the final particle size distributions (PSDs) with the discrete element method and by extracting the contact forces. A PSD evolution law is proposed to account for particle breakage. The PSD is related to the total particle surface in the sample, which allows calculating the breakage energy. The redistribution energy, which comprises the kinetic energy of particles being rearranged and the friction energy dissipated at contacts, is obtained by subtracting the elastic energy and breakage energy from the work input. Results show that: (1) at least 60% of the work input is dissipated by particle redistribution; (2) the fraction of elastic deformation energy increases, and the fraction of redistribution energy decreases as the compression stress increases; (3) the breakage energy accounts for less than 5% of the total input energy, and this value is independent of the compressive stress; (4) the energy dissipated by redistribution is between 14 and 30 times larger than the breakage energy. 相似文献
18.
Eugene C. Rankey 《Sedimentology》2016,63(7):2190-2216
Although the general criteria for recognition and environmental interpretation of different carbonate facies are well‐established, a predictive understanding of the areal extent and spatial patterning of facies bodies and why they might organize into facies belts or facies mosaics is poorly constrained. To explore patterns and process dynamics of facies on isolated carbonate platforms, quantitative analysis of thematic maps derived from remote sensing images of 27 Holocene atolls of the Paracel and Spratly chains in the South China Sea explores variability within and among platforms. On these systems, most annular shelf‐margin reefs are less than 500 m wide on both chains; inboard of the reefs, reef sand aprons range up to 500 m (Spratlys) and 1000 m (Paracels) wide. Around individual platforms, Spratly Chain sand apron widths are wider to the north‐west, whereas apron widths in the Paracel Chain are more symmetrical; collectively, data indicate log‐normal width‐exceedance probability distributions. Platform‐interior patch reefs include area‐exceedance probability distributions and gap size distributions (lacunarity) consistent within chains, but distinct between the chains. To understand the processes underlying distinct distributions, simulations explored distinct growth scenarios. Results suggest that differences may represent distinct process classes: proportional growth processes with multiplicative random effects (reef sand aprons – belts), versus non‐linear, size‐proportional growth of randomly aged and distributed elements (patch reefs – mosaics). The probabilistically distinct sizes and spatial patterns of geomorphic elements within these general process classes are interpreted to represent ‘variations on themes’ related to the different impacts of tropical storms, winter cold fronts and circulation in each chain. The results highlight fundamentally different growth patterns impacting the sizes and distribution of facies belts and mosaics on isolated carbonate platforms. Because these types of bodies ultimately construct stratigraphy, the themes could be applied to understand and predict variability in the architecture of subsurface reservoir analogues. 相似文献
19.
Ida Lykke Fabricius 《Sedimentology》2020,67(7):3451-3470
Chalks originate as Cretaceous to Recent pelagic or hemipelagic calcareous ooze, which indurate via burial diagenesis to chalk and limestone. Because they accumulate in pelagic settings with high environmental continuity, chalks may form thick formations and even groups. For this reason, and because chalks have a simple mineralogy (low magnesium calcite, silica and clays), they are ideal for the study of diagenetic processes including the depth-related decrease of porosity. It is the aim of this study to illustrate how the evaluation of in situ elastic strain can help in understanding these processes including the interplay between stress-controlled diagenetic processes and processes furthered by thermal energy. Petrophysical core and well data can be used for analyses of how porosity reduction via pore collapse and pressure dissolution is related to in situ elastic strain. The data in question are: depth, density of overburden, pore pressure, ultrasonic P-wave velocity and dry density/porosity. The analysis reveals that the transition from ooze to chalk is associated with high elastic strain and consequent pressure dissolution at calcite–particle contacts causing contact cementation. The transition from chalk to limestone is also associated with high elastic strain, especially at clay–calcite interphases causing development of stylolites via pressure dissolution, and consequent pore-filling cementation. Following each transformation the elastic strain drops rapidly. The observation of this diagenesis-related pattern in elastic strain of the sedimentary rock is novel and should not only be helpful in understanding the porosity development in sedimentary basins, but also add basic scientific insight. 相似文献
20.
Gilles Bourgault 《Mathematical Geosciences》2014,46(7):841-868
A multivariate probability transformation between random variables, known as the Nataf transformation, is shown to be the appropriate transformation for multi-Gaussian kriging. It assumes a diagonal Jacobian matrix for the transformation of the random variables between the original space and the Gaussian space. This allows writing the probability transformation between the local conditional probability density function in the original space and the local conditional Gaussian probability density function in the Gaussian space as a ratio equal to the ratio of their respective marginal distributions. Under stationarity, the marginal distribution in the original space is modeled from the data histogram. The stationary marginal standard Gaussian distribution is obtained from the normal scores of the data and the local conditional Gaussian distribution is modeled from the kriging mean and kriging variance of the normal scores of the data. The equality of ratios of distributions has the same form as the Bayes’ rule and the assumption of stationarity of the data histogram can be re-interpreted as the gathering of the prior distribution. Multi-Gaussian kriging can be re-interpreted as an updating of the data histogram by a Gaussian likelihood. The Bayes’ rule allows for an even more general interpretation of spatial estimation in terms of equality for the ratio of the conditional distribution over the marginal distribution in the original data uncertainty space with the same ratio for a model of uncertainty with a distribution that can be modeled using the mean and variance from direct kriging of the original data values. It is based on the principle of conservation of probability ratio and no transformation is required. The local conditional distribution has a variance that is data dependent. When used in sequential simulation mode, it reproduces histogram and variogram of the data, thus providing a new approach for direct simulation in the original value space. 相似文献