Nonlinear Dynamics in Stratigraphic Modeling: Order from Chaos?

Abstract

The cyclic nature of the lithostratigraphic record is clear to the most casual observer. Major facies associations such as red beds, passive margin wedges, and carbonate platforms reappear throughout the record. At finer scales, bed thickness, color, grain size, elemental composition, gamma-ray response, permeability, and porosity all show cyclicity. The cause is of interest in both forward and inverse modeling contexts. The search for a driving mechanism has concentrated recently on cyclic input signals such as insolation (Milankovitch cycles), and eustasy (Vail cycles). An alternative approach is to ask why the stratigraphic record tends to oscillate around a few relatively stable states and whether the transitions between states are predictable. A systems approach accepts that insolation and eustatic signals can be isolated neither from each other nor from many other Earth processes. They form interdependent components in a dynamic system. Such systems tend to generate their own information as a result of feedback relationships and they may either amplify or suppress any input signals. Many stratigraphic process models employ linear combinations of input parameters. We suspect that stratigraphic relationships may result more from coupling among system variables and from lag times in (for instance) isostatic response to loading. Patterns suchmore » as the widely observed four- to five-fold bundling of primary bedding rhythms thus could be system generated, rather than system amplified. We hope to demonstrate the principles of such an approach, with modeling applications at all scales from reservoir to basin.« less