A multiquadric‐biharmonic representation and approximation of disturbing potential
作者:
Rolland L. Hardy,
Stuart A. Nelson,
期刊:
Geophysical Research Letters
(WILEY Available online 1986)
卷期:
Volume 13,
issue 1
页码: 18-21
ISSN:0094-8276
年代: 1986
DOI:10.1029/GL013i001p00018
数据来源: WILEY
摘要:
Properties of the potential are considered for applications in gravity, geomagnetic, and thermal field studies. It is found that classical theory is somewhat limited because of the common difficulty in evaluating potential within a material body containing the sources. The theory of a new type of representation of disturbing potential, a biharmonic form, is given which eliminates this difficulty. It is shown that multiquadric equations provide us with a physically valid numerical approximation of the formal integral representation. Error bounds are derived. The results of tests with real gravity anomalies are given, which compare classical methods with the new biharmonic form. In summary, the new approach eliminates the classical singularities associated with collocation of points of measurement (or prediction) and the sources of disturbing potential. It also improves computational efficiency.
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