DIFFERENTIATING CYCLICAL AND STOCHASTIC PROCESSES IN THE ROCK RECORD USING COMPUTER SIMULATIONS

Cyclicity is frequently reported from the sedimentary rock record. However, some previous investigations have compared patterns in the rock layer with what would be expected from random processes and postulated that cyclic-looking stratigraphic patterns can be explained mathematically as purely stochastic processes. This project simulated stratigraphic layers using computer-modeled cyclic processes and the resulting stratigraphic records were then tested against predictions generated by the purely stochastic (Poisson) process.

Stratigraphic column data and rock layer information were simulated using PHIL 5.4 Basin Analysis software (PetroDynamics Inc.). The simulations used carbonate deposition along a shallow, subsiding marine shelf. Water level change was simulated using one to six cycles of varying period and amplitude. The resulting stratigraphic sections were “sampled” along depositional gradients. A total of 8 simulated stratigraphic sections were generated. The thickness distributions of simulated cyclic records were then compared against random distributions of layers predicted by a Poisson distribution parameterized in terms of the number of layers per unit and the total thickness of the section. The quality of fit between the simulated thickness frequencies and those expected for the stochastic Poisson process was measured in terms of the Pearson's product-moment correlation.

For all simulations, the results indicate that cyclic processes can produce patterns that are indistinguishable from random processes. Consequently, the apparent stochasticity in the rock record is not a sufficient proof of a random, non-cyclic nature of the sedimentary record. However, further analyses subjecting simulated cyclic data to other tests of stochasticity (e.g., Markov Chain analysis) are required to affirm that the simulated cyclic records cannot be distinguished analytically from purely stochastic signals.