Reconditioning inverse problems using the genetic algorithm and revised parameterization

The better conditioned an inverse problem is, the more independent pieces of information may be transferred from the data to the model solution, and the less independent prior information must be added to resolve trade offs. We present a practical measure of conditioning that may be calculated swiftly even for large inverse problems. By minimizing this measure, a genetic algorithm can be used to find a model parameterization that gives the best conditioned inverse problem. We illustrate the method by finding an optimal, irregular cell parameterization for a cross-borehole tomographic example with a given source-receiver geometry. Using the final parameterization, the inverse problem is almost a factor of three better conditioned than that using an average random parameterization. In addition, this method requires little additional programming when solving a linearized inverse problem. Hence, the improvement in conditioning and corresponding increase in independent information available for the model solution essentially come for free.