Markov Chain Monte Carlo inversion of Transient Electromagnetic

Transient electromagnetic methods (TEM) are widely used in the applications of near surface imaging in suburban environment. The complex field situation contribute the difficulty on the interpretation of TEM data. Conventional ly, nonlinear inverse methods estimate the conductivity depend on the observed data of TEM can only get the single earth model , which can't satisfy the need of evaluate the uncertainty of the high-dimensional geophysical problems. In the contrast, the probabilistic method has a better advantage on these inverse cases, and can obtain the huger deal of earth models to quantify non-uniqueness of TEM data to illustrate the uncertainty of the geophysical characters. In this work, we sample the Bayesian posterior probability density function from TEM data, using MCMC method based on the Metropolis-Hastings algorithm to estimate the parameters and quantify non-uniqueness of earth model. As a globally optimized heuristic probabilistic method, MCMC's unique algorithm construction avoids the complicated marginal integral calculation problem in Bayesian formula. Motivated by the reasonableness of the 1-D assumption for this application and the high computational cost of MCMC, we choose a 1-D parametriz ed layered medium, where the resistivity and thickness are poorly known a prior. Metropolis-Hastings (M-H) algorithm draw samples from the probability density of the model parameters and generate new candidate model from the proposed distribution with the acceptance probability α. This sample from the posterior distribution measures non-uniqueness in term of the range of layer thickness and resistivity consistent with the TEM observed data. Due to a lack of the priori information related to the parameter distribution, it is extremely difficult to determine the parameters' proposed distribution and accelerate the convergence rate. We use the previously generated fixed-quantity Markov chain elements to calculate the covariance matrix of the Gaussian proposed distribution. Then we adaptively updated the proposed distribution with the sampling process to accelerate convergence. We provide a synthetic model study, followed by inversions of real soundings. Both synthetic examples and field data inversion are used to verify the accuracy and stability of the algorithm .