HR: 1340h
AN: NG23D-0115    [Abstracts]
TI: Application of Nonlinear Filters to Geophysical Inverse Problems
AU: * Ganse, A A
EM: aganse@apl.washington.edu
AF: Applied Physics Laboratory, University of Washington 1013 NE 40th Street, Seattle, WA 98105 United States
AU: * Ganse, A A
EM: aganse@apl.washington.edu
AF: Department of Earth and Space Sciences, University of Washington Box 351310, Seattle, WA 98195 United States
AU: Odom, R I
EM: odom@apl.washington.edu
AF: Applied Physics Laboratory, University of Washington 1013 NE 40th Street, Seattle, WA 98105 United States
AU: Odom, R I
EM: odom@apl.washington.edu
AF: Department of Earth and Space Sciences, University of Washington Box 351310, Seattle, WA 98195 United States
AB: The goal of solving geophysical inverse problems isn't just to find a model fitting the data. We can always fit a (N-1)th order polynomial to N data points, but it doesn't tell us much about the solution's uniqueness, or limits placed on resolution in the presence of noise. The real goal is to develop more information than just a model that fits the data. For truly linear problems, the statistics are Gaussian, constraints on the model information and uniqueness are characterized by the the null space of the operator which maps the model to the data, and the resolution matrices have well defined meanings. However, many inverse problems of interest in geophysics are nonlinear. Global solution methods such as simulated annealing or genetic algorithms tell us nothing about the statistics and little about the uniqueness of our model solution. Monte Carlo analyses are exhaustive and do provide information about uniqueness and a posteriori statistics but are numerically intensive. As an alternative we have examined a nonlinear filter that is an extension of the Kalman and Extended Kalman filters. We address the question: Can geophysically interesting problems be recast as nonlinear filtering problems, and if so what can they tell us about the evolution of the statistics, uniqueness, and model resolution?
DE: 3260 Inverse theory
DE: 3275 Uncertainty quantification (1873)
DE: 4259 Ocean acoustics
DE: 7260 Theory
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005