Enhanced uncertainty quantification in geophysical inversion using Langevin Transitional MCMC

Geophysical inversion is essential for deriving subsurface physical properties from indirect geophysical measurements and has a wide range of applications in natural resource exploration, including both mineral and hydrocarbon prospecting. Markov Chain Monte Carlo (MCMC) sampling, a widely used Bayesian inference technique, is popular in this field because it provides uncertainty quantification. However, conventional MCMC methods often experience slow convergence and high computational costs. To overcome these challenges, we developed the Langevin Transitional Markov Chain Monte Carlo (LTMCMC) method that employs gradient-based proposals to boost sampling efficiency in geophysical inversion. Tested on a complex benchmark function and applied to both synthetic and field magnetotelluric data, LTMCMC converges faster and estimates parameters more accurately than standard TMCMC. This approach successfully identifies key transitions in subsurface resistivity and accurately delineates the subducting Cocos Plate boundary, all while delivering robust uncertainty quantification. Although there are minor smoothing effects, our results indicate that LTMCMC effectively balances computational speed with reliable uncertainty assessment, paving the way for further improvements with refined priors and applications in higher-dimensional settings.