Regularized fruit fly optimization for robust inversion of self-potential data

Abstract

Self-potential surveying constitutes a widely applied passive geophysical technique in environmental and near-surface investigations, including groundwater assessment, mineral exploration, and subsurface fluid characterization. Quantitative interpretation of self-potential data requires solving nonlinear inverse problems that are inherently ill-conditioned and highly sensitive to measurement uncertainty, often leading to unstable or non-unique parameter estimates. This study presents a reproducible inversion framework that integrates Tikhonov regularization with the fruit fly optimization algorithm (FOA) to achieve stable and computationally efficient parameter recovery. The proposed scheme embeds the swarm-based search process within a regularized objective function, thereby explicitly addressing ill-posedness and noise amplification while preserving global exploration capability. The framework is rigorously evaluated through synthetic benchmarks involving single and multiple subsurface sources under variable noise contamination (0%, 5%, and 15), achieving NRMSE values as low as 0.000391 under noise-free conditions and maintaining stable recovery up to 15% noise (NRMSE = 0.1117). In multi-source scenarios, the framework successfully resolves a ten-parameter search space with an NRMSE of 0.0005681 under noise-free conditions and 0.0741 under 10% noise. Comparative benchmarking against particle swarm optimization (PSO), genetic algorithm, and the bat algorithm confirms that FOA consistently achieves superior convergence precision and lower misfit values, with an average execution time of 0.64 s and NRMSE of 0.00408 under noise-free conditions compared to PSO (NRMSE = 0.00768). Application to three field datasets—the Bavarian Woods graphite deposit (Germany) and two copper ore bodies in Turkey—further validates the framework, with recovered source depths (e.g., 31.39 m) aligning closely with independent drilling constraints (~ 30 m) and dynamically estimated shape factors (q = 0.74–1.07) enabling accurate morphological classification of ore bodies. The resulting system provides a transparent, uncertainty-aware, and transferable modeling tool suitable for automated SP inversion and broader environmental geophysical applications.