Abstract
The following notes provide a quantitative mathematical basis from which a three-dimensional (in space), time-dependent, numerical algorithm can be constructed to incorporate the basic processes of carbonate accumulation and diagenesis in relation to sea level variations, basement subsidence, wave base erosion, and fluid transportation (by bed load and suspended load) of eroded carbonates.
There are two major components to the modeling. First is to set up a geometry so that one has a basis from which to consider the problem. The geometry must include extraneous influences on carbonates such as: sea level variations, basement shape and motion, wind directions and current directions, etc. The second component is to provide dynamical process equations for carbonate growth, diagenesis, erosion, and transport within the framework of the geometric picture.
Once these two major components are addressed, one has then constructed a forward model, which allows one to insert parameter values and functional variations (with time and space) of basement, sea level, etc., in order to construct carbonate accumulations with time.
The third part of the problem is to use the forward model to: (a) predict observed carbonate accumulations accurately; and (b), once (a) is satisfied, to use the model patterns to suggest new observations that could then be made as a consequence of modeled behaviors consistent with observations.
This last part of the problem requires that: (c) an inverse method be used to determine parameters (and to find out which parameters are not well-determined): and (d) once minimal discord between predictions and observations is achieved, to then determine what new observations could be made to provide further confirmation and/or modification of model behaviors.
All four of these aspects are addressed here.