RECONDITIONING INVERSE PROBLEMS USING THE GENETIC ALGORITHM AND REVISED PARAMETERIZATION

The better conditioned an inverse problem is, the more independent pie ces of information may be transferred from the data to the model solut ion, and the less independent prior information must he added to resol ve 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 paramete rization that gives the best conditioned inverse problem. We illustrat e the method by finding an optimal, irregular cell parameterization fo r a cross-borehole tomographic example with a given source-receiver ge ometry. Using the final parameterization, the inverse problem is almos t a factor of three better conditioned than that using an average rand om parameterization. In addition, this method requires little addition al programming when solving a linearized inverse problem. Hence, the i mprovement in conditioning and corresponding increase in independent i nformation available for the model solution essentially come for free.