A multiquadric‐biharmonic representation and approximation of disturbing potential

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.