A three-dimensional (3D) numerical stratigraphic model has been built to simulate the development of microbial reefs on a Jurassic carbonate platform using fuzzy logic modeling methods. The flexibility of the model allows for the examination of a large number of variables. The relative importance of local environmental conditions and global changes on the frequency of reef development are examined relative to the temporal and spatial constraints from Upper Jurassic (Oxfordian) Smackover reef datasets from two Alabama oil fields. The fuzzy model simulates the deposition of reefs and carbonate facies by integrating local and global variables. Local-scale factors include basement relief, sea-level change, climate, latitude, water energy, water depth, background sedimentation rate, and substrate conditions. Regional and global-scale changes include relative sea-level change, climate, and latitude.
The model confirms preexisting theories that background sedimentation rate, water energy, substrate, relative sea-level change, and climate influenced the development of Jurassic reefs. Additionally, the model determines the degree of control each variable has on 'IF,' 'WHERE,' and 'WHEN' reefs develop. The variables that control 'IF' reefs develop are the global parameters of climate and amplitude of sea-level change. The model specifies that the variables that influence the lateral distribution of reefs (or 'WHERE' reefs occur) are substrate, water energy, and background sedimentation rate. The model also indicates a strong correlation between 'WHEN' reefs develop and the rate of sea-level rise. In all simulations, reefs initially develop in conjunction with the greatest rate of sea-level rise (i.e., the inflection point on the sea-level curve) and reach peak development before the time of deepest water.