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