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Finding corresponding seismic horizons which have been separated by a fault is still performed manually in geological interpretation of seismic images. The difficulties of automating this task are due to the small amount of local information typical for those images, resulting in a high degree of interpretation uncertainty. Our approach is based on a model consisting of geological and geometrical knowledge in order to support the low-level image information. Finding the geologically most probable matches of several horizons across a fault is a combinatorial optimization problem, which cannot be solved exhaustively since the number of combinations increases exponentially with the number of horizons. A genetic algorithm (GA) has been chosen as the most appropriate strategy to solve the optimization problem. Our implementation of a GA is adapted to this particular problem by introducing geological knowledge into the solution process. The results verify the suitability of the method and the appropriateness of the parameters chosen for the horizon correlation problem.