Three-dimensional gravity inversion can be formulated as the minimization of a residual functional measuring the misfit between observed and predicted gravitational data. Due to the severely ill-posed nature of the inverse problem, stabilization requires dimensionality reduction and appropriate regularization strategies to obtain physically meaningful solutions [1–4]. This work presents a residual-based inversion framework grounded on geometric model reduction using prolate spheroids and rectangular prisms as elementary parameterizations of subsurface bodies. The forward problem is solved through closed-form analytical expressions of the gravitational attraction generated by both geometries, enabling efficient residual evaluation without volumetric discretization [5]. The inverse problem is addressed via global optimization, allowing the simultaneous estimation of density contrasts and geometric parameters. From a residual minimization perspective, geometric parameterization acts as an implicit regularization mechanism that constrains the solution space, reduces non-uniqueness, and improves model interpretability [4]. A comparative analysis is conducted to evaluate the behavior of the residual functional under both parameterizations. Synthetic experiments involving multi-body configurations and noisy data are used to assess convergence, stability, and sensitivity to initialization. Resolution capability and computational cost are also analyzed. Results indicate that prolate spheroidal models significantly reduce the dimensionality of the inverse problem while preserving data fit, whereas prismatic discretizations provide greater geometric adaptability at increased computational complexity. The proposed framework contributes to residual-minimization methodologies for nonlinear ill-posed inverse problems in gravitational modeling, extending recent ellipsoidal inversion strategies based on global optimization techniques [6].