GEM10B地球模型全球自由空气重力异常场及勒让德函数计算的研究

本文给出了GEM 10 B地球重力模型2-36阶、2-12阶以及13-36阶等三幅全球自由空气重力异常图.在2-12阶和2-36阶重力图中,全球重力异常呈现出双层环状结构特征.内环是环绕太平洋地区的正异常带,外环是紧密包围着环太平洋正异常带的巨大负异常带.在13-36阶重力图中,全球大洋海岭地区几乎全部呈低幅值（0-10mGal）正异常. 本文分析了利用递推公式计算勒让德函数的稳定性问题,给出一组适合计算机运用的完全正规化缔合勒让德函数计算公式.采用该组公式计算（双精度运算）的完全正规化缔合勒让德函数值在θ≥1°,L≤300阶时,其ε_L误差小于10^-13. 为了解决对高阶勒让德函数值计算精度的估计问题,本文提出以完全正规化缔合勒让德函数的σ_l=1性质为基础的σ_L函数精度判定法.该方法简便易行.

FREE AIR GRAVITY ANOMALY OF GEM 1 B MODEL AND A STUDY OF COMPUTING LEGENDRE FUNCTION

Three frele-air gravity anomaly computed from the GEM-10B gravity model are given in this paper. Fig. 1 is the complete （2≤n≤36） field; Fig. 2 is the Lower-Degree （2≤n≤12） field; and Fig. 3 is the Higher-Degree （13≤n≤36） field. It shows that the double-ring feature is the most basic gravity feature in the complete and Lower-Degree fields. The inner ring is positive anomaly and surrounds the Pacific; the outer ring is negative and surrounds the inner ring closely. It is positive anomaly with low amplitude （0-10 mgal） over the regions of ocea nridge （Fig. 3）. The stability of recurrence formulas for computing Legendre function was analysed and this stability formulas, when employed for θ≥1°and n≤300, give εL<10^-13.For estimating the precision of computing value of normolized Legendre function, the precision criterion based on σ_l=1 was given in this paper.