Multi-chain Bayesian inversion of Probability Integral Method parameters from InSAR measurements

The Probability Integral Method (PIM) is a widely used technique for predicting surface displacements caused by underground mineral extraction. Precisely inverting the physical parameters of the PIM is essential to ensure the accuracy of displacement prediction. In recent years, it has become a promising way to invert the PIM parameters using interferometric synthetic aperture radar (InSAR) observations. However, nearly all existing studies invert the PIM parameters using deterministic nonlinear optimization methods, resulting in local optimal solutions and difficulty in quantitative uncertainty assessment. This letter proposes a new probabilistic method for inverting the PIM parameters from InSAR observations. A Bayesian inference was adopted to reduce the probability of obtaining the local optimal solutions. By incorporating prior knowledge, the Bayesian inversion framework with a multi-chain Markov chain Monte Carlo algorithm was then used to invert the PIM parameters and quantitatively assess the uncertainties of the parameter estimates. Simulations and real data tests indicate that the accuracy of the PIM parameters inverted by the proposed method is on average 83% and 29% higher than the parameters estimated by a conventional genetic algorithm and a single-chain Bayesian inversion algorithm.