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A Bayesian approach to nonlinear inverse problems is considered where theunknown quantity (input) is a random spatial field. The forward model iscomplex and non-linear, therefore computationally expensive. An emulator-basedmethodology is developed, where the Bayesian multivariate adaptive regressionsplines (BMARS) are used to model the function that maps the inputs to theoutputs. Discrete cosine transformation (DCT) is used for dimension reductionof the input spatial field. The posterior sampling is carried out usingtrans-dimensional Markov Chain Monte Carlo (MCMC) methods. Numerical resultsare presented by analyzing simulated as well as real data on hydrocarbonreservoir characterization.

Spline-Based Bayesian Emulators for Large Scale Spatial Inverse Problems