Parameter estimation in a Markov mesh model by reversible jump MCMC simulation

Abstract

We have a model for simulating facies values in a rock. We can use the model to find facies structures in a 2-dimensional area, which we can use to find properties of a rock in a petroleum reservoir. The model is a Markov mesh model, with a conditional probability distribution for the facies values, with a set of parameters. By using a training image with known facies values, we can simulate the parameters in the model, and then simulate facies values for a new area. In this text, we simulate the parameters by using a Reversible jump Markov chain Monte Carlo algorithm. This lets us simulate not only the values of the parameters, but also which parameters that should be present in the model. We use the Metropolis-Hastings algorithm in the simulations. We use the model with the simulated parameters to make new images with the Markov mesh model. The images should have similar visual appearance as the training image. We are able to make images with some similar qualities as the training image, even though we are not convinced that the parameter values converge.