Integrated Geometric-Stochastic Modeling of Metallogenic Systems: A Uniformization Approach via Moduli Space Dynamics

The stochastic modeling of ore body genesis in structurally complex terranes has historically been constrained by the fundamental limitations of Euclidean geometry. Conventional geostatistical methods, such as Kriging or Gaussian simulation, rely on the assumption of stationarity and isotropy—conditions that are fundamentally violated in high-grade metamorphic belts, complex hydrothermal breccia pipes, and orogenic gold systems where stress tensors induce significant curvature. This paper proposes a radical theoretical departure from traditional exploration geology. By conceptualizing the “Mineralized Crustal Volume” as a hyperbolic Riemann surface rather than a Cartesian grid, we introduce a rigorous mathematical formalism based on the dynamics of Moduli spaces. Drawing upon the asymptotic theorems of Mirzakhani regarding simple closed geodesics and the Weil-Petersson geometry studied by Wolpert and Schumacher, we derive a predictive law for vein density and ore localization. We postulate that the metallogenic potential of a prospect is a topological invariant, isomorphic to the symplectic volume of its underlying structural manifold. This work formally establishes the “Abhary-Riemann Conjecture” for blind exploration targeting, providing a deterministic bound on mineral endowment based purely on the topological genus of the host rock.

کلیدواژه ها:

Riemann Surfaces ، Moduli Spaces ، Weil-Petersson Volume ، Abhary-Mirzakhani Density Law ، Symplectic Geometry ، Structural Topology