Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration. ?? 1995 International Association for Mathematical Geology.