The Strict Transformation Formula between the Expansion of Different Tidal Generating Potential

The expansion of tidal generating potential (TGP) is a basic theoretical problem in geodesy and astrometry. It not only improves the reduction accuracy of spatial geodesy, but also plays an important role in geodynamic evolution and crustal deformation monitoring. Since there have been different Laplace expansions in history, there are different tables of tidal wave (harmonic) expansions. These tidal wave expansion tables cannot be directly compared with each other except that the tidal wave frequencies are the same. In this paper, by studying the normalization of Laplace expansions of different tide-generating potential, the internal relations between different tide tables are revealed completely in theory, and a unified transformation formula of arbitrary order is given. It is pointed out that there is a mistake in IERS (International Earth Rotation and Reference Systems Service)(2010) code, that is, the ratio of 3-order 1-degree CT (Cartwright & Tayler) development to HW (Hartmann & Wenzel) development coefficient should be added with a negative sign.