Geology-exploration endowment models for simultaneous estimation of discoverable mineral resources and endowment

A new type of model, referred to as a geology-exploration endowment model, is proposed in this paper. These models differ from conventional ones in that they simultaneously estimate discoverable mineral resources and endowment by extracting and utilizing geoscience information from both geological features and exploration factors. Geological measurements describe mineral endowment, while exploration variables describe the completeness of exploration, and together, they explain discoverable resources. Without incorporation of exploration factors to geological-endowment models, the estimation of endowment is generally biased. This paper presents two variations of such hybrid nonlinear models: Poisson-logistic (PL) and exponential-logistic (EL) for estimation of number of mineral deposits or prospects based upon the Arps and Roberts' discovery process model and assumptions of endowment distributions. The PL model is obtained by assuming that endowment follows a Poisson distribution and that the probability of mineral occurrences ( 1) is a logistic function with geological arguments. The EL model is derived similarly, except that endowment is assumed to be exponentially distributed. The PL model is demonstrated on both a synthetic example and a case study of epithermal gold-silver vein deposits in the Walker Lake quadrangle of Nevada and California. A map containing the estimated numbers of gold-silver mineral occurrences potentially discoverable in the Walker Lake quadrangle is produced. The parameter estimates for the PL model based on the Levenberg-Marquardt iterative algorithm are validated by using several statistical measures, such as theT-statistic, Box's bias, and goodness of fit. Both a synthetic example and a case study suggest that the Box's bias measure is useful for validation of the nonlinear estimates.