Inverse Gravimetric Problem Solving via Ellipsoidal Parameterization and Particle Swarm Optimization

Detecting underground cavities using gravity measurements is a challenging inverse problem characterized by non-uniqueness, instability, and sensitivity to noise. Classical inversion approaches based on domain discretization often lead to highly underdetermined problems that require strong regularization. In this work, we propose a model reduction strategy that represents subsurface cavities as prolate ellipsoids embedded in a homogeneous background, significantly reducing the number of free parameters and improving computational efficiency. The inverse problem is solved using Particle Swarm Optimization (PSO), which allows both optimization and thorough exploration of the parameter space, enabling direct uncertainty quantification without the need for explicit regularization. Synthetic experiments with added Gaussian noise demonstrate that the method accurately recovers the location, size, orientation, and density contrast of anomalies, while capturing the anisotropic nature of model uncertainty. A synthetic case study simulating water-filled karstic cavities is also presented to illustrate the method’s potential for realistic scenarios. The results underscore the advantages of combining geometric model reduction with swarm-based global optimization in gravity inversion, particularly when model simplicity, computational efficiency, and uncertainty assessment are critical.