A method of improving a geologic model of a subsurface region. One or more sets of parameter values are selected. Each parameter represents a geologic property. A cost and a gradient of the cost are obtained for each set. A geometric approximation of a parameter space defined by one or more formations is constructed. A response surface model is generated expressing the cost and gradient associated with each formation. When a finishing condition is not satisfied, at least one additional set is selected based at least in part on the response surface model associated with previously selected sets. Parts of the method are repeated using successively selected additional sets to update the approximation and the response surface model until the finishing condition is satisfied. Sets having a predetermined level of cost to a geologic model of the subsurface region and/or their associated predicted outcomes are outputted to update the geologic model.