Markov Chain Analysis of Computer-Simulated Limestone Sequences

In the hopes of proving that the Markov property of a marine stratigraphic sequence is controlled by its position relative to basin margins, a computer-simulated sequence was generated and tested. The computer manufactures a sequence of 1,000 sedimentation units (beds), each positioned by a sea-level transgression-regression subroutine that may be systematic, random, or systematic-random. The facies-distribution pattern at each sea-level stand is controlled by the variation of five facies components (micrite, spar, fossils, coated grains, and oolites). At each of 200 points along the sea floor, the proportion of each of these components is calculated, and a facies identification number is assigned to that point. The result is a data array of 1,000 rows (beds) by 200 columns (columnar sections). Each columnar section is then analyzed for its Markov property, and a test value is computed. The test value is then plotted as a function of relative shoreline position.

The major conclusion is that there is no relationship between the Markov property of a stratigraphic sequence and its position relative to basin margins.