A Pragmatic Investigation of the Objective Function for Subsurface Data Assimilation Problem

One of the main mechanisms of an optimization problem is the effectiveness and relevance of the objective function. In the context of an optimization problem in the subsurface domain, called seismic history matching, this study proposes to investigate further aspects of assimilating data. We focus on two main characteristics of the objective function: the influence and the sensitivity to the amount of data used in the seismic history matching. We select four metrics to analyse the similarity/dissimilarity measurement used in the matching. The optimization method used to perform the seismic history matching is an auto-adaptive differential evolution algorithm. This study has been carried out on three real datasets. Based on the results and analysis of the seismic history matching experiments, we are able to draw some practical suggestions on what kind of objective function should be established. Despite its simplicity, the Least Square metric performs as well as any other metric. Using all the possible data is safer but it is not compulsory to obtain good history matching results, in some cases using less data leads to the same answer. Using different metrics or more data does not change the computing time.