A Bayesian Depth-Confidence Model for Deep Orogenic Gold Exploration Using Logistic Survival Functions Calibrated to the Fault-Valve Mechanism

We develop a Bayesian posterior probability model for assessing the likelihood that a drill-core intercept of gold mineralization at depth belongs to a super-large (≥100 t Au) orogenic deposit system. Unlike previous exponential-decay formulations, we employ logistic survival functions calibrated to the fault-valve mechanism (Sibson, 1988; 2001), with physically motivated critical closure depths (Hc) that represent the statistical half-survival depth for each system class. All probabilities are defined within a unified probability space: a targeted exploration site with surface anomalies, where the prior P₀(Large) = 0.01 represents the empirical base rate. The model shows that at 2500 m depth, the posterior confidence is 65–100% (central: 97.3%), depending on the steepness parameter kS. The logistic formulation eliminates three vulnerabilities of exponential models: (1) zero-depth intercept bias, (2) conflation of modern depth with paleo-crustal position, and (3) circular reasoning via hard-coded decay constants. The critical closure depth Hc,S = 1000 m is derived from first principles: Hc = Hpaleo,crit − Δerosion ≈ 6000 − 5000 = 1000 m. Source code and data: https://github.com/Ruqing1963/bayesian-depth-confidence-model