Numerical Methods for Inverse Problems in Three-Dimensional Geophysical Modeling

摘要

Researchers are performing interactive modeling in powerful workstations coupled with supercomputers to construct mathematical models of the Earth interior. The report discusses some of the mathematical and computational issues involved in developing the modeling environment, concentrating on modeling Earth's elastic properties by seismic methods. The work extends forward and inverse modeling techniques to highly complex geological models, called blocky. A volume of Earth is represented by a collection of smooth inhomogeneous rock masses separated by material interfaces, where elastic properties change discontinuously. These interfaces have been modeled by surface patches, that allow the construction of many complex geological unconformities, that hitherto were not easily represented. First to be considered are issues of geometrical and material description, basic for the direct and inverse modeling techniques. Seismic ray tracing is the forward modeling technique, while inverse modeling is divided between static and dynamic modeling. In the static case, a variation of forward modeling is used only once to determine a preliminary model from measured data. This preliminary model is used to initialize an optimization iteration. In this dynamic inversion loop, forward modeling is used at each step, and therefore large computational resources may be required.