Kimura's Z-Term and the Liquid Core Theory

Abstract

Kimura (1902) pointed out that there might be an unknown cause other than polar motion which would produce an apparent latitude variation, and introduced the Z-term as, Δϕ = Xcos λ + + Ysin λ + Z.The theoretical results by Jeffreys-Vicente (1957) and Molodensky (1961) have shown that the effect of a liquid core of the Earth may increase the coefficients of the semi-annual solar nutation term (2 ⊙) which is involved in the diurnal nutation (the so-called Oppolzer term) by 0″.02. It is reasonable to accept this correction which will appear in the Z-term with an argument of (2 ⊙ −α).From comparison of the observed amplitudes and the phase angles of the annual Z-terms derived from the ILS data, it is concluded that the argument of the principal annual term in Z is (2 ⊙ −α) and not ⊙. The following results were obtained for the annual Z-term for 1955-1966 from the analysis of data by two independent methods (Wako, 1970): 0″.0137 sin (2 ⊙ −α + 2°.2), 0″.0203 sin (2 ⊙ −α + 4°.3).Melchior (1970) proposed another effect of the Earth's liquid core for the annual nutation in obliquity, thus a term such as a sin (⊙ +α + A) would appear in the Z-term and it might cause a part of semi-annual Z-term. For the determination of these corrections, analysis of Kimura's Z-term is the most effective method.