THICKENING AND OR THINNING UPWARD PATTERNS IN SEQUENCES OF STRATA - TESTS OF SIGNIFICANCE/

Geologists commonly purport that successions of strata show one or mor e thickening and/or thinning upward trends, often prompting colleagues to argue that the 'trends' are subjectively identified, unproven or n onexistent. Parametric and randomization tests are proposed to evaluat e the null hypothesis of random succession against a variety of altern ative postulates of trend. In place of test statistics in vogue that m erely compare each bed thickness with that of the beds immediately abo ve and below it, test statistics based on Kendall's S and Tau that mak e sequence-wide (or subsequence-wide) comparisons of bed thicknesses a re advocated. The test statistic used and the exact form of the test d epends on the alternative model considered: against the alternative of a single thickening (and/or thinning) upward trend, Kendall's S or eq uivalently Kendall's Tau are recommended. These statistics make pair-w ise comparisons of beds, comparing bed thicknesses with their position s in the vertical sequence. Against the alternative of trends in g sub sequences 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 indivi dual 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 includ e both thickening and thinning upward patterns). Tests can indicate th at a sequence has one or more subsequences which are nonrandom, but it will not indicate which. To test each subsequence for significance, t est each of g subsequences at a level of significance = alg, thus achi eving an overall, sequence-wide, level of significance = a. Against th e alternative g subsequences recognized post-hoc, i.e. purely on the b asis of observed thickness patterns, a family of test statistics are p roposed, each equal to the maximum value of the appropriate test stati stic (defined for subsequences recognized a-priori) that is attainable by partitioning the total sequence of beds into 1, 2,.... up to g sub sequences. Both same-type and mixed subsequences alternatives arise. E ach test proposed is applied to several different sequences, mostly tu rbidites.