A geophysical inverse problem entails inferring properties of the Earth's interior from data gathered at the surface or from boreholes. There are several impediments to obtaining reliable inferences based upon external measurements. A major problem is the non-uniqueness inherent in almost all inverse problems. Also, the uncertainties associated with a set of estimates are critical for evaluating the reliability of any proposed Earth structure. A primary goal of this work is to use the power of today's supercomputers to study the non-uniqueness and uncertainty associated with the inverse problem.
Inverse problems divide naturally into linear and nonlinear problems.
However, the linear systems may be extremely large and ill-conditioned. For nonlinear problems, estimating non-uniqueness and uncertainty is a topic of research. Because most approaches are computationally intensive, use of parallel computers appears promising. A Lanczos technique is used to solve the linear inverse problem and compute estimates of non-uniqueness and uncertainty. An iterative conjugate gradient method is used to find a solution that is compatible with the observations.