Thickening and/or thinning upward patterns in sequences of strata: tests of significance
Thickening and/or thinning upward patterns in sequences of strata: tests of significance
复制标题
地层序列中向上加厚和/或变薄的模式：显着性检验
DOI：
10.1046/j.1365-3091.1998.00176.x
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发表时间：
1998
期刊：
影响因子：
3.5
通讯作者：
C. W. Harper
中科院分区：
文献类型：
--
作者：
C. W. Harper
地质学家通常声称，地层序列呈现出一种或多种向上增厚和/或变薄的趋势，这常常引发同行争论，认为这些“趋势”是主观认定的、未经证实的或根本不存在的。有人提出参数检验和随机化检验，以针对各种趋势的替代假设来评估随机序列的零假设。有人提倡使用基于肯德尔S和陶（Tau）的检验统计量，这些统计量对整个层序（或子层序）的地层厚度进行比较，以替代目前流行的仅仅将每层厚度与其紧邻的上下层厚度进行比较的检验统计量。所使用的检验统计量以及检验的确切形式取决于所考虑的替代模型：针对单一向上增厚（和/或变薄）趋势的替代假设，推荐使用肯德尔S或等效的肯德尔陶。这些统计量对地层进行成对比较，将地层厚度与其在垂直层序中的位置进行比较。针对先验识别的g个子层序中的趋势这一替代假设，例如那些被诸如半深海页岩厚层序等间断所分隔的子层序，所提出的检验统计量包括：为各个子层序计算的g个陶系数的加权和（如果据称子层序全部向上增厚或全部向上变薄），以及陶系数的绝对值或平方的加权和（如果据称子层序包括向上增厚和向上变薄两种模式）。检验可以表明一个层序有一个或多个非随机的子层序，但不会表明是哪些子层序。为了检验每个子层序的显著性，以显著性水平α/g对g个子层序中的每一个进行检验，从而实现整个层序的总体显著性水平为α。针对事后识别的g个子层序，即纯粹基于观测到的厚度模式，提出了一系列检验统计量，每个统计量等于通过将地层总层序划分为1、2、…直至g个子层序所能达到的适当检验统计量（为先验识别的子层序所定义）的最大值。会出现同类型和混合子层序的替代情况。所提出的每种检验都应用于几个不同的层序，其中大部分是浊积岩。
Geologists commonly purport that successions of strata show one or more thickening and/or thinning upward trends, often prompting colleagues to argue that the `trends' are subjectively identified, unproven or nonexistent. Parametric and randomization tests are proposed to evaluate the null hypothesis of random succession against a variety of alternative postulates of trend. In place of test statistics in vogue that merely compare each bed thickness with that of the beds immediately above and below it, test statistics based on Kendall's S and Tau that make sequence‐wide (or subsequence‐wide) comparisons of bed thicknesses are advocated. The test statistic used and the exact form of the test depends on the alternative model considered: against the alternative of a single thickening (and/or thinning) upward trend, Kendall's S or equivalently Kendall's Tau are recommended. These statistics make pair‐wise comparisons of beds, comparing bed thicknesses with their positions in the vertical sequence. Against the alternative of trends in g subsequences recognized a‐priori, e.g. those separated by breaks such as thick sequences of hemipelagic shale, test statistics proposed include: the weighted sum of the g Tau coefficients calculated for the individual subsequences (if subsequences are alleged to be all thickening or all thinning upward), and the weighted sum of the absolute value, or square, of the Tau coefficients (if subsequences are alleged to include both thickening and thinning upward patterns). Tests can indicate that a sequence has one or more subsequences which are nonrandom, but it will not indicate which. To test each subsequence for significance, test each of g subsequences at a level of significance = α/g, thus achieving an overall, sequence‐wide, level of significance = α. Against the alternative g subsequences recognized post‐hoc, i.e. purely on the basis of observed thickness patterns, a family of test statistics are proposed, each equal to the maximum value of the appropriate test statistic (defined for subsequences recognized a‐priori) that is attainable by partitioning the total sequence of beds into 1, 2,…. up to g subsequences. Both same‐type and mixed subsequences alternatives arise. Each test proposed is applied to several different sequences, mostly turbidites.