Matrix-Free Forward and Inverse Modeling of Gravity and Magnetic Data Using Terrain-Conforming Unstructured Hexahedral Meshes

To address the difficulty of terrain representation and the high storage cost of explicit sensitivity matrices in three-dimensional gravity and magnetic modeling and inversion, we propose a matrix-free framework based on terrain-conforming unstructured hexahedral meshes. Irregular topography is represented using eight-node deformed hexahedral elements, and element integrals are evaluated through isoparametric mapping and Gaussian quadrature. Precomputed Gaussian-point coordinates and Jacobian weights are shared by the forward and adjoint operators, enabling matrix-free evaluation of forward responses, adjoint actions, and Hessian–vector products without storing the full sensitivity matrix. An anomaly- and topography-guided adaptive parameterization further reduces the number of model parameters and Gaussian source points. Synthetic tests demonstrate numerical consistency with the conventional explicit-matrix method, substantial reductions in computation time and memory usage, and stable accuracy under pronounced terrain relief. Application to gravity data from the San Nicolás deposit recovers high-density anomalies consistent with the known massive sulfide body, confirming the effectiveness of the proposed method in complex terrain.