Dynamical Systems Theory of Gulf Coast Shelf-Clinoform Stratigraphy
Water depth and sediment bottom slope are fundamental variables for defining the state of sedimentary environments and sedimentation rates in shelf-slope clinoform depositional settings such as the Gulf Coast. A two-dimensional dynamical system of differential equations for the state variables water depth (w) and bottom slope (m) is solved with prescribed inputs (control variables) of subsidence, compaction, and eustatic seal-level change (?). The dynamical system represents sedimentation at a single location on shelf, shelf break, or slope environments with sedimentation rate (?) controlled by depth and slope. The sedimentation rate function in the modeling decreases linearly with depth to represent sediment starvation in deeper environments. The sedimentation rate depends nonlinearly on bottom slope with maximum rates at low slopes and moderate slopes. The subsidence function is linear with rates of 0.01 to 0.1 m/ky to represent passive-margin conditions. The eustatic sea-level function is time dependent and assigned with periodic functions of specified amplitude and frequency. The nonlinear terms of the system make up an autonomous dynamical system and represent effects of autogenic stratigraphic processes in changing the water depth and bottom slope. The dynamical system is driven by the non-autonomous time-dependent forcings (allogenic processes) caused by subsidence and eustatic change. The simulations show cyclic evolution of water depth and bottom slope with time. The water depth is affected by eustatic level and the effects on the solutions increase with amplitude. The solutions exhibit positive Lyapunov exponents, indicating the solutions are chaotic. During rapid eustatic change, deepening cycles show sensitive dependence on initial conditions.
AAPG Search and Discovery Article #90167©2013 GCAGS and GCSSEPM 63rd Annual Convention, New Orleans, Louisiana, October 6-8, 2013