HR: 14:25h
AN: NG33B-03 INVITED     [Abstracts]
TI: Invariance, Non-uniqueness, and Symmetry Groups
AU: * Vasco, D W
EM: dwvasco@lbl.gov
AF: Earth Sciences Division, Berkeley Laboratory, Building 90-1116, 1 Cyclotron Road, Berkeley, CA 94720 United States
AB: Non-uniqueness is an important aspect of most geophysical inverse problems. Non-uniqueness is equivalent to the invariance of the constraints with respect to changes in the Earth model. In this talk I will examine approaches to the analysis of invariance and non-uniqueness which are based upon Lie group methods. A key aspect of these methods involves the determination of symmetry groups associated with the constraint equations. In a general sense, a symmetry group of a system of equations is a group which transforms solutions of the system to other solutions. Therefore, the symmetry groups associated with an inverse problem may be used to explore the range of possible solutions. Lie group methods provide an alternative to conventional perturbation approaches. Mathematical methods from the theory of continuous groups may also be used to determine if a nonlinear inverse problem can be transformed into a linear problem. From the analytical form of the equations representing the inverse problem a set of linear partial differential equations, the defining equations, may be derived. The solutions to the defining equations provide the generators from which a transformation group may be constructed.
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting