A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation
Abstract
This problem is defined in general by the Laplacian and at least two different boundary conditions holding on a spherical boundary, or overlapping parts of it. The least-squares collocation method is applied to estimate spherical harmonic coefficients for the disturbing potential. An algorithm was developed and the method was tested using simulated gravity anomaly and undulation signals. Point as well as mean boundary values were used, both with and without random noise added. The OSU86F spherical harmonic coefficient set was used to generate the simulated data and the required covariances. By computing statistics of the input field recovery, the applicability of the method is judged. Several problems were encountered while applying least-squares collocation to this problem. A theoretical singularity of the covariance matrix, caused by truncation in the summation of the covariance function at a finite degree, is found to be eliminated numerically when summing to degree 180. Instability and singularity due to the data distribution are treated successfully by applying Tikhonov regularization. Inversion of a large covariance matrix resulting from global data coverage limits the feasibility of the solution. To make the computation manageable, the block-Toeplitz pattern of the auto-covariance matrices is exploited in forming and inverting them. A partitioned inversion procedure assists the assimilation of the influence of overlapping datasets into the inverse of the covariance matrix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1989
- Accession Number
- ADA211785
Entities
People
- Lucia Tsaoussi
Organizations
- Ohio State University