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Least squares prediction of gravity anomalies, geoidal undulations, and deflections of the vertical with multiquadric harmonic functions
Author(s) -
Hardy R. L.,
Göpfert W. M.
Publication year - 1975
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl002i010p00423
Subject(s) - covariance , mathematics , covariance function , mathematical analysis , harmonic function , least squares function approximation , geoid , gravity anomaly , geodesy , geology , geophysics , statistics , measured depth , paleontology , estimator , oil field
Least squares prediction with MQ (multiquadric) functions is conceptually different from least squares prediction using covariance functions. MQ kernels are based on geometric or physical considerations rather than stochastic processes, and were found to be superior to covariance functions in topographic applications. This may be true also for gravity anomalies or other phenomena which result from marginally stationary, or non‐stationary random processes. The MQ harmonic kernel is used to develop a formula for estimating the best depth of point mass anomalies as a function of their number and areal extent on a sphere. Functional relationships between geoidal surface parameters are developed which provide linear equation analogs for the solution of Stokes and Vening Meinesz Integral Formulas as well as for the inversion of these classic problems. These relationships are extended to solutions at exterior equipotential surfaces.