Studies of sequence in sediments using a simple mathematical device

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Abstract
This paper introduces a simple method for objectively analysing the arrangement of beds in sequences of alternating rock types. The number of times that different lithologies overlie one another in a section may be recorded in a table, termed the data array. The probability of one lithology overlying another in a section is a function of their frequency (i.e. the number of times that they occur), and the 'memory' of the depositional process. Since their frequency is known, from the data array, it is possible to calculate the number of times that different lithologies should be interbedded with one another if they were arranged at random. Comparison of these figures with the observed number of transitions (shown in the data array), picks out lithological transitions which occur more often than expected if they were randomly arranged. In such cases it can be said that one lithology has a good 'memory' for another. For example in the Coal Measures coal may have a good 'memory' for seat-earth. The results of these studies are presented on facies relationship diagrams. These record the most probable upward and downward transition for each lithology in a section and can be used to detect the modal and composite sequences. After testing for memory a corrected facies relationship diagram may be constructed showing those transitions which occur more often than expected assuming a random model. It is these transitions which must be considered when postulating the sedimentary process which controlled the deposition of a rock sequence. This method is applied to stratigraphical sections of the Paradox salt basin, U.S.A., Libyan Miocene shoreline deposits, fluviatile Torridonian (Pre-Cambrian) rocks of Scotland, and Yoredale (Lower Carboniferous) beds of northern England. All four cases show signs of memory in the vertical arrangement of their beds. The simplest examples show simple oscillatory motifs, both rhythmic (in the sense ABCABC) and cyclic (in the sense ABCBA). The more complex examples show arrangements due to up to three intertwined oscillations. The geological significance of these results is discussed.