Inverse Gravimetric Problem Solving via Prolate Ellipsoidal Parameterization and Particle Swarm Optimization

Ruben Escudero González, Zulima Fernández Muñiz (), Antonio Bernardo Sánchez and Juan Luis Fernández Martínez
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Ruben Escudero González: Departamento de Tecnología Minera, Topografía y Estructuras, Universidad de León, 24006 Leon, Spain
Zulima Fernández Muñiz: Grupo de Problemas Inversos, Optimización y Aprendizaje Automático, Departamento de Matemáticas, Universidad de Oviedo, 33007 Oviedo, Spain
Antonio Bernardo Sánchez: Departamento de Tecnología Minera, Topografía y Estructuras, Universidad de León, 24006 Leon, Spain
Juan Luis Fernández Martínez: Grupo de Problemas Inversos, Optimización y Aprendizaje Automático, Departamento de Matemáticas, Universidad de Oviedo, 33007 Oviedo, Spain

Mathematics, 2025, vol. 13, issue 12, 1-23

Abstract: We present a method for 3D gravity inversion using ellipsoidal parametrization and Particle Swarm Optimization (PSO), aimed at estimating the geometry, density contrast, and orientation of subsurface bodies from gravity anomaly data. The subsurface is modeled as a set of prolate ellipsoids whose parameters are optimized to minimize the misfit between observed and predicted anomalies. This approach enables efficient forward modeling with closed-form solutions and allows the incorporation of geometric and physical constraints. The algorithm is first validated on synthetic models with Gaussian noise, successfully recovering complex multi-body configurations with acceptable uncertainty. A statistical analysis based on multiple PSO runs provides interquartile ranges (IQRs) to quantify inversion stability. The method is then applied to a real microgravity dataset from the Nirano Salse mud volcanoes (northern Italy) using a field acquisition strategy previously described in the literature. Unlike earlier studies based on commercial software, our inversion uses the ellipsoidal–PSO framework. The best-fitting model includes four ellipsoids (two low- and two high-density), reproducing the main features of the observed Bouguer anomaly with a prediction error of 20–25%. The inferred geometry suggests that fluid migration is controlled by fault-related damage zones rather than shallow reservoirs. This method is robust, interpretable, and applicable to both synthetic and real cases, with potential uses in geotechnical, volcanic, and hydrogeological studies.

Keywords: gravity inversion; uncertainty quantification; model reduction; ellipsoidal parameterization; particle swarm optimization; anomaly detection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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