Binary 4D seismic history matching, a metric study

Abstract

This paper explores 4D seismic history matching and it specifically focuses on the objective function used during the optimisation with seismic data. The objective function is calculated by using binary maps, where one map is obtained from the observed seismic data and the other is from one realisation of the optimisation algorithm from the simulation model. In order to decide which set of parameters is a relevant update for the simulation model, an efficient way is required to measure how similar these two binary images are, during their evaluation within the objective function. Behind this aspect of quantification of the similarities or dissimilarities lies the metric notion, or the art of measuring distances. Four metrics are proposed with this study, the well-known Hamming distance, two widely used metrics, the Hausdorff distance and Mutual Information and a recent metric, called the Current Measure Metric. These metrics will be tested and compared on different case scenarios, designed in accordance to a real field case (gas exsolution) before being used in the second part of the paper. Despite its simplicity, the Hamming distance gives positive results, but the Current Measure Metric appears to be a more efficient choice to cover a wider range of scenarios, these conclusions remain true when tested on synthetic and real dataset in a history matching exercise. Some practical aspects of binary map processes will be examined through the paper, as it is shown that it is more proper to use a derivative free optimisation algorithm and a proper metric should be more inclined to capture global features than local features.