Appropriate formulation of the objective function for the history matching of seismic attributes

The purpose of history matching is to find one or several reservoir models which can reproduce as best as possible all the available data. The available data are traditionally some production data, but today seismic data are often integrated in the history matching process. The way of measuring the misfit between real data and simulated responses has a significant impact on the optimization process and hence on the final optimal model obtained. The classical formulation of the misfit is the least square one, which was used with success for production data. This formulation was naturally extended for seismic data. However, it yields an objective function term which is difficult to reduce. Indeed, seismic data are different from production data since they are defined by millions of points and are generally very noisy. When matching seismic data, the goal is then to capture the main features. As a result, computing a point to point error is not adapted and the resulting objective function is not representative of the quality expected for the match. We propose in this paper to define a more appropriate formulation. The idea is to use some image analysis tools to define a formulation focusing on the main features of seismic images. More precisely, it is based on image segmentation and on a modified Hausdorff metric. We illustrate the success of this formulation on a simple history matching case.