Time‐lapse inversion of self‐potential data through particle filtering

Abstract

In environmental sciences, comprehending the movement of subsurface contaminants is crucial for formulating effective remediation measures. The self‐potential (SP) method has become a common tool for delineating landfill contamination plumes. Contaminant diffusion or migration represents dynamic processes, with corresponding SP responses evolving over time. However, conventional SP interpretation approaches have predominantly relied on static single‐frame inversion, overlooking the temporal correlation in time‐series SP data and resulting in cumulative errors. To tackle this challenge, we introduce a novel method for time‐lapse inversion of SP data leveraging particle filtering. This approach recursively refines the priori state model through posteriori observations to achieve precise estimations of dynamic models. Specifically, a spherical polarization model is deployed to establish the state equations of underground contaminant diffusion and transport models, whereas the observation model is derived through forward modeling. The proposed method is validated using two synthetic examples and one lab‐measured dataset. The findings demonstrate the efficacy of the time‐lapse inversion algorithm in precisely estimating dynamic models, outperforming static single‐frame inversion based on the particle swarm optimization algorithm. The posteriori distribution of particles approximates a bell‐shaped distribution, with the true state closely positioned near the peak probability. Therefore, we affirm that conducting time‐lapse inversion of time‐series SP data through particle filtering is an effective and dependable approach for accurately estimating dynamic model states.