Comparison of map metrics as fitness input for assisted seismic history matching

Assisted seismic history matching (ASHM) is an optimisation problem that incorporates 4D seismic data as a constraint upon a reservoir simulation update. The observed and simulated three-dimensional seismic data is typically reduced to a Cartesian map representation and the misfit between the two is calculated using the mean squared error (MSE). The MSE metric is simple to implement and understand, but it is incapable of capturing the nuances and patterns required to match seismic maps effectively. We test alternative measures of the misfit (metrics) that borrow from image processing and meteorological history matching so that more robust misfit information can be used during optimisation. In this two-part study we first test our metrics on realistic but synthetic one-dimensional problems to understand the metric characteristics, and their sensitivity to noise, better. The introduced metrics are then tested in a realistic ASHM optimisation task. We find that two of our proposed alternatives to MSE are more stable and provide superior results when used for ASHM optimisation.