  A Bayesian approach to nonlinear inverse problems is considered where the
unknown quantity (input) is a random spatial field. The forward model is
complex and non-linear, therefore computationally expensive. An emulator-based
methodology is developed, where the Bayesian multivariate adaptive regression
splines (BMARS) are used to model the function that maps the inputs to the
outputs. Discrete cosine transformation (DCT) is used for dimension reduction
of the input spatial field. The posterior sampling is carried out using
trans-dimensional Markov Chain Monte Carlo (MCMC) methods. Numerical results
are presented by analyzing simulated as well as real data on hydrocarbon
reservoir characterization.
