天顶距微分公式用于重力、倾斜和应变固体潮资料的拟合检验

THE ZENITH DISTANCE FORMULAS OF THE FIRST ORDER DIFFERENTIAL QUOTIENT FOR THE THEORETIC VALUE OF THE EARTH TIDES APPLIED TO THE FITTESTING OF THE GRAVITY,TILTER AND LINE STRAIN EARTH TIDES

本文提出了固体潮理论值一阶微商值(G′=dG/dt)的新的计算方法——天顶距微分法。文中系统地给出了(重力、倾斜、线应变)固体潮之G′的实用计算公式。作者将这套公式用于拟合检验(NAKAI法),并与分波法(用分波法计算G和G′)和差分法(用天顶距公式计算G,用差分法计算G′)进行了对比计算,文中给出了部分对比计算结果。计算过程和计算结果表明:对于重力,微分法的计算时间仅是分波法(取484个分波)计算时间的1/15左右,对于倾斜和应变,仅为分波法计算时间的1/25左右,微分法也只是差分法计算时间的60％左右。各种方法的计算结果基本一致,但差分法计算中△t的取值须介于1-100秒之间。

In this paper, the zenith distance formulas of the first order differential quotient of earth tides to time is given. In the method of the fit-testing for the observation data of the earth tides (Nakai, 1975), it is nessessary to compute the theoretic values of the earth tides(G)as well as its first order differential quotient(G') Usually G and G'are computed by the method of harmonic development waves or by the method of the first order difference.In the former, it isnessessary to compute so many sinusoidal values and cosine values thatmueh time will he occupied in the fit-testing.In the later, it is nessessary to compute twice theoretic values(G(t),G(t+Δt)), therefore the computing accuracy is not higher and the computing speed is slow.In order to economize the computational time and to raise the computational accuracy, the author gives the zenith distance formulas of the first order differential quotient for the earth tides to time(including gravity tides,tilter tides and line strain tides).In fit-testing,if the theoretic values of the earth tides and its first orde differential quotient were computed by the method of zenith distance formalas,the computational time will only be one fifteenth of the method of harmonic developmement waves(for 484 waves),and will be 60 percent of the method of the first order difference.