Local relationships between the disturbing density, the disturbing potential and the disturbing gravity of the Earth's gravity field

A function having some properties of a wavelet and being harmonic around a given point in R-3 is defined, and three models showing the local relations hips between the disturbing density, the disturbing potential and the distu rbing gravity are established by using the function as the kernel function of the integrals in the models. The local relationship has two meanings. On e is that we can evaluate with a high accuracy the integrals in the models by using mainly high-accuracy and high-resolution data in a local area. The other is that we can obtain a stable solution with high resolution when we invert the integrals in the models because of the rapid decrease of the ke rnel function of the integrals. As a result, with these models we evaluate one quantity with high resolution, in a band limited by the maximum degree of a set of geopotential coefficients or by the resolution (spacing) of the local data, from another quantity (or quantities) in a local area, and the resulting solution is stable.