Spherical Geodetic Transformations. Volume 1. Spectral Theory and Optimal Template Design
Abstract
A general theory and method is developed by which more accurate and efficient summation approximations can be derived fro any of the integral transformations of geodesy. The theory and method are applied to the well-known Stokes' and Vening-Meinesz' Integrals and improved summations are determined which have lower rms discretization errors than the approximations presently in use, even though only rudimentary optimization algorithms are employed. Thus the validity of the theory and the feasibility of the method are numerically demonstrated. The theory is based upon spherical spectral analysis. The integral transformations of geodesy are revealed as two dimensional spherical convolutions, and their discrete summation approximations are interpreted as spherical digital filters with a number of adjustable parameters determined by the underlying template. The spherical transfer functions of the integral transformation and of their discrete summation approximations are derived and shown to be close but not exactly equal to each other. An analytic expression for the partial derivative of the discrete summation transfer function with respect to its parameters is derived and used in a Gauss-Newton optimization process.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1978
- Accession Number
- ADA202487
Entities
People
- William M. Robertson
Organizations
- Charles Stark Draper Laboratory