HR:     13:45h
AN:     U12C-02
TI:     Imaging Deformation Sources with Geodetic Data
AU:     *Cervelli, P 
EM:     cervelli@pangea.stanford.edu
AF:     Department of Geophysics,
        Stanford University Stanford, CA 94305-2215  United States
AU:     Murray, M 
EM:     mmurray@pangea.stanford.edu
AF:     Department of Geophysics,
        Stanford University Stanford, CA 94305-2215  United States
AU:     Segall, P 
EM:     segall@pangea.stanford.edu
AF:     Department of Geophysics,
        Stanford University Stanford, CA 94305-2215  United States

AB:     The recent availability of large geodetic data sets from both INSAR and continuous GPS has 
        inspired a significant increase in deformation source modeling.  Two main problems complicate 
        these modeling efforts.  First, geodetic data, such as surface displacements or range changes, 
        relate non-linearly to source geometry.  This makes finding the model that minimizes the 
        difference between observation and prediction a difficult mathematical optimization problem, 
        ill-suited for traditional, derivative-based solutions.  Second, the non-linear relationship 
        between data and model, combined with a poorly known noise distribution, prevents easy 
        evaluation of confidence intervals for the estimated model parameters. Without such 
        knowledge, it is difficult to assess both the scientific and practical significance of a modeling 
        result.
        
        We have applied Monte Carlo optimization techniques, including simulated annealing and 
        random cost to the geodetic inversion problem.  These algorithms contain an element of 
        randomness, which permits them to escape the local minima in misfit space that commonly trap 
        and defeat derivative-based algorithms.  In spite of the randomness, the algorithms remain 
        highly efficient, quickly converging to the global minimum.
        
        To estimate confidence intervals, we have applied the bootstrap method of Efron, which 
        proceeds as follows: the original data set is resampled with replacement to form a new data set,
         which is then used to find a new model.  A large number of resamplings yield empirical 
        confidence intervals. Two main factors complicate the application of the bootstrap method to 
        geodetic data.  First, geodetic data can be significantly correlated with one another, a fact that 
        must be accounted for during a bootstrap resample.  Second, because each resampling entails
         a new optimization problem, the efficient and effective inversion methods outlined above 
        become a necessity.
        
        The geodetic inversion software that we have developed has been successfully used to model 
        many styles deformation in areas throughout the world, including the Izu peninsula of Japan, 
        Kilauea volcano, the Mendocino triple junction, and in the Galapagos Islands.
DE:     1243  Space geodetic surveys
SC:     U
MN:     1998 Fall Meeting