ESTIMATING INTERCEPTION PROBABILITY FOR UNEXPLORED CAVE SYSTEMS

If a previously unknown cave has been encountered by drilling or other discovery, how does the probability of encountering that same cave decline with horizontal distance from the first discovery? To estimate the probability, it may be reasonable to borrow statistics from a nearby, fully mapped cave system, or from cave systems developed in similar geologic and hydrologic environments (leading to similar generic cave patterns and intensities of passage development).

Correlation analysis results for known cave systems, derived from standard cave maps, can be reformatted to yield plots of encounter probability versus horizontal radius from a first encounter. As an initial test, I have evaluated 14 North American cave systems with diverse environment and pattern. A number of these examples are derived from the southeastern US and adjacent Gulf basin. Plots for the caves approximately fit power functions for radii up to 0.2-0.5 of greatest cave extent, beyond which probability values tail off rapidly. Power function exponents vary from -0.2 to -1.1. These exponent values sort well by cave pattern, with a notably high typical value of -1.0 for single-passage caves, a notably low value of -0.2 for network mazes, and intermediate values for branchwork, anastomotic maze, and ramiform caves. For some cases, most notably single passage and ramiform caves, the plot form is more complex, with slope that notably breaks, fitting two power functions of significantly different exponent for two different ranges of radius. In such cases the exponents derived for larger radii are higher, ranging from -1.2 to -1.8.

Initial testing for statistical similarity of nearby caves of different size, such as the Burnsville Cove cave group in Virginia, suggests a persistence of overall plot form. Nevertheless, exponent values for comparable plot sections can vary significantly. This suggests that specific geologic environment, rather than simple proximity, deserves most attention in the selection of known cave analogs for statistical passage distribution in unexplored caves.