Computation of the Hessian for least-squares solutions of inverse problems of reflection seismology

The authors show that the Hessian of the least-squares cost functional arising in the data-fitting approach to inverse problems in reflection seismology may be computed by a minor extension of the adjoint state technique. They examine the implementation of such a calculation using finite differences for a model problem. They give numerical evidence which shows that the Hessian may be computed with considerable accuracy by this technique, and that it may differ considerably from the Gauss-Newton approximation, while costing approximately 50% more computational effort.