Improving stochastic inversion methods in history matching using proxy models

Assisted history methods have been developed to automatically search the parameter space to find optimal models. Stochastic approaches increase the breadth of the search but can be very costly. Proxy models improve convergence by producing parameter sensitivities. Better distributions may be used in stochastic generation of new models. In this paper we present modifications to the neighbourhood and a genetic algorithm. Quadratic proxy models are derived for the misfit surface so that the search process can be made more efficient. We test the approaches on several analytical test functions. We also apply them to the Schiehallion field from the west of Shetland in seismic history matching. A quadratic regression equation was derived from a representative sample of models and used to generate gradients of the misfit with respect to the parameters. These are used to direct the choice of new models during a random search increasing the chance of finding new models. The proxy based method improves convergence by a factor of three generally. Complex surfaces see a lesser improvement though and the regression equation can be updated as better models are found to maintain the benefits.