Geodetic Applications of Multiquadric Equations.

摘要

It is shown that geodetic applications of multiquadric functions in harmonic form are quite closely related to functional methods associated with point mass anomalies. Multiquadric equations are also used in a least square prediction method which is conceptually different than least squares prediction using covariance functions. In comparative tests the multiquadric method was found to be superior to the covariance method in applications involving topography and gravity anomalies. This is probably true for other phenomena which involve marginally stationary,or nonstationary random processes. The multiquadric method has also been used to develop a formula for estimating the best depth for point mass anomalies as a function of their number and areal extent on a sphere.