Bayesian reasoning for evaluating interdependence and correlation of Cole-Cole model variables in spectral induced polarization measurements

This study investigates the dependency and correlation of the Cole-Cole model (CCM) parameters using Bayesian inference to invert spectral induced polarization (SIP) data. The aim is to improve the understanding of subsurface properties and provide a reliable interpretation of the estimated subsurface models by analyzing parameter interdependencies in detail. We present a novel 2.5D inversion framework specifically developed for spectral induced polarization (SIP) data. This approach leverages Python-based libraries and advanced statistical inversion techniques, employing an affine-invariant ensemble sampling-based Markov chain Monte Carlo (McMC) algorithm. To evaluate the efficacy of our methodology, we conduct synthetic modeling and McMC inversion across various subsurface scenarios, including a homogeneous Earth model, a two-layer medium, and a model containing two buried anomalies within a homogeneous background. Our methodology allows for the extraction of CCM parameters that represent electrical properties, providing a deeper insight into complex geological structures. Visualizations of McMC chains and corner plots illustrate the interdependencies among CCM parameters, demonstrating the convergence and reliability of parameter estimates. Through validation against synthetic models, we highlight the accuracy and effectiveness of our methodology. Overall, our study showcases the potential of Bayesian inversion in improving geophysical data interpretation and deepening our understanding of the interdependencies among CCM parameters in estimated models across a range of simplified geological scenarios.