Bayesian inversion with Markov chains - II. The one-dimensional DC multilayer case

In this paper, we will report on the application of Bayesian inference to D C resistivity inversion for 1-D multilayer models. The posterior probabilit y distribution is explored through a Markov process based upon a Gibbs's sa mpler. The process would lead to unrealistic estimates without additional p rior information, which takes the form of a second Markov chain where the t ransition kernel corresponds to a smoothness constraint. The outcomes are p osterior marginal probabilites for each parameter, as well as, if required, joint probabilities for pairs of parameters. We will discuss the main prop erties of the method in the light of a theoretical example and illustrate i ts capabilities with some field examples taken from various contexts.