STIGA-IFM: A Kinematically Constrained Inverse Framework for Multi-Seam Subsidence via Adaptive Super-Gaussian Kernels

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Abstract
The reliable prediction of mining-induced subsidence in deep multi-seam environments is fundamentally hindered by a kinematic contradiction: classical Influence Function Methods (IFMs) impose a Linear Shift-Invariant (LSI) Gaussian kernel that structurally cannot reproduce sharp shear boundaries, pillar relief, or trap-door failures, regardless of parameter tuning. This paper introduces the Spatio-Temporal Interaction and Geometrically Adaptive Influence Function Method (STIGA), a macroscopic phenomenological model of rock mass degradation that redefines the subsidence field as a Generalized Superposition Integral over a Linear Shift-Variant (LSV) medium. The influence kernel evolves endogenously from a diffusive Gaussian profile ($n=2$) to a shear-controlled Super-Gaussian piston ($n>2$) via the Hydraulic Radius ($R_h$), resolving the ``Soft Edge'' artifact without recourse to discontinuum mechanics. Multi-seam interactions are quantified through a Cumulative Extraction Density (CED) that couples surface deformation to the cumulative damage history of the rock mass. Although originally motivated by the need to supply continuous surface priors for numerical model calibration, where sparse, discontinuous monitoring points render the inverse problem under-determined, the calibrated framework proves to be a self-sufficient predictive engine. By anchoring constitutive variables to macroscopic geomechanical clusters, STIGA decouples geometric resolution from parameter dimensionality and generates physically valid continuous surfaces directly from the 3D mine schedule. A hybrid inverse strategy (CMA-ES, Huber Loss) is validated against a 20-year dataset from the \v{C}SM Mine, demonstrating that the framework reconstructs unrecorded subsidence, captures abrupt multi-seam shear ruptures, and outperforms classical literature-constrained models by an order of magnitude in volumetric fidelity.

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