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The nature of shallow-water carbonate lithofacies thickness distributions

¹ Shell International Exploration and Production, PO Box 60, 2280AB Rijswijk, Netherlands

View larger version (27K): [in this window] [in a new window]   Figure 1. Cumulative frequency plots. A: Cambrian–Ordovician strata from measured section in Nopah Range, Utah, USA (section 56; see the GSA Data Repository [see footnote 1]). B: Cretaceous Aptian–Albian strata logged at Sierra de el Abra, San Louis Potosi, Mexico (section 11; GSA Data Repository). Both show sampled cumulative normalized frequency distribution plotted against theoretical exponential cumulative normalized frequency distribution calculated for the same thickness L and number of lithofacies units n. In each case, maximum difference between two distributions, D, is marked by vertical line terminated by two squares. Distributions in B are broadly similar, leading to a lower value of D relative to example in A, where the curves show a marked difference in shape. Significance level p, calculated from the Kolmogorov–Smirnov test, is also shown in each case, along with µ, the sample mean lithofacies unit thickness.

View larger version (14K): [in this window] [in a new window]   Figure 2. A: Frequency of Kolmogorov–Smirnov test significance probability p values, categorized by degree to which they refute the null hypothesis that sample lithofacies thickness distribution is indistinguishable from an exponential distribution. Plot shows that just more than half of the 56 outcrop sections deviate markedly from an exponential lithofacies thickness distribution, that 16 of the examples are well matched by an exponential model, and that the nature of the remaining 12 is more uncertain. B: Frequency plot of the non-exponential cases classified according to how observed curve differs from an exponential. Type 1 has relatively few thin and intermediate thickness lithofacies units, and too many thick units. Type 2 has too few thin units, and too many intermediate and thick units. Type 3 has too many thin units, and too few thick. Type 4, of which there is only one case, has too few thin and thick units, and too many intermediate thickness units.

View larger version (32K): [in this window] [in a new window]   Figure 3. Examples of Type 1, Type 2, and Type 3 observed lithofacies unit thickness distributions. A: Type 1 curves have too few thin and intermediate units, and too many thick units. B: Type 2 curves have too few thin and too many intermediate and thick units. C: Type 3 curves have too many thin units and too few thick units. Lithofacies thicknesses are plotted as cumulative frequency curves, with a matching theoretical exponential distribution in each case, and the point of maximum difference D for each marked with two squares joined by a vertical line. See Figure 1 for explanation of variables.