We here establish basic inversion framework in a Bayesian context, with introduction of measures of data fit and model suitability. We introduce Bayes’ theorem and identify the conditional probability with posterior probability distribution for model parameters through a composite misfit combining the match between observations and simulations and assumptions about the nature of acceptable models. We discuss Monte Carlo techniques and the assessment of model resolution, leading into the formulation of the non-linear inversion process in terms of optimisation of a measure of misfit.