STOCHASTIC AND DETERMINISTIC 3D MODELING OF CARBONATE ISLAND KARST

The speleogenesis of flank margin caves was tentatively modeled using GOCAD. Salt Pond Cave from Long Island, Bahamas, was used as a reference because of its characteristic morphology and large size. A three dimensional model of this cave was constructed from survey data. The resulting cave model and the overlying topography were used to build a fresh-water lens surface that would be used in simulating virtual flank margin cave development. The lens was generated as for a simple, heterogeneous carbonate island, with a 1:40 ratio between the height of the lens above sea level and the depth below sea level. The maximum dimensions for horizontal and vertical growth of caves and the probability of development of voids in different areas of the lens were defined for the margin of the lens. These properties were transferred to a stratigraphic grid of ~1m³ cells that was previously intersected with the lens surface. The G3 Object Modeling tool (a GOCAD plug-in devised at TOTAL), which uses a stochastic simulation technique that allows the creation of equal-probable models, was utilized to generate virtual flank margin caves in the resulting grid region. The simulation of cave growth was performed in several phases by populating the lens region with dissolution voids as constrained by the defined properties. The computer-generated caves are comparable in size and morphology with caves observed in the field. Each simulated phase produces not only the expansion of individual caves but also linking of neighboring voids. The model demonstrates that often only a small connection is necessary to link adjacent voids and provide the jump in size from one category to another. This jump in size is not linear because the probability of a cave intercepting neighboring voids increases as the cave gets larger. The model also shows that connections do not always occur and that it is highly probable that significant voids could exist but not be open to the surface. The computer simulation results support the results obtained from statistical analysis of field data, which show that caves of a certain size form by the aggregation of lesser voids. The model presented here is both stochastic and deterministic in that it generates dissolution voids with equal probability of appearance but under tight constraints of location and horizontal and vertical expansion.