利用低阶卫星重力位系数研究下地幔横向密度异常分布
DISTRIBUTION OF LATERAL DENSITY ANOMALIES IN THE LOWER MANTLE OBTAINED THROUGH LOW ORDER GEOPOTENTIAL COEFFICIENTS
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摘要: 本文试图采用卫星重力资料和一种新的反演方法来研究地幔的横向密度异常分布.先将密度异常△（r,,（?））在一个三维正交函数系下进行展开,其展开系数待定.然后,根据密度异常与重力扰动位之间的关系建立观测方程组,其中未知向量由密度异常展开系数组成,重力扰动观测向量由 GEM10B 重力模型中的位系数计算而得,并通过适当选取重力位系数的阶数,对观测向量进行滤波.最后,就下地幔（670km——CM 界面）作了实际计算.计算中,重力扰动位阶数取为2——11阶,密度异常展开式的截断阶数取为 K=4和 L=6,求解观测方程组时采用阻尼最小二乘法.结果表明:密度扰动值在670km 不连续面及核幔界面处达到极大值,且在环太平洋地区存在一高密度带,太平洋中部对应于一低密度区,这些特征与 Dziewonski 得到的下地幔三维波速异常分布特征相一致.但是,在南极地区、大西洋及印度洋部分地区,所得的密度异常分布与三维波速异常分布呈负相关,文章就其原因作了初步分析.Abstract: In this paper, we attempt to use satellite gravity data and a new inversion method to study the lateral density anomalies distribution in the mantle.First, the density difference p(r, , (?)) is expanded in terms of a three-dimensional orthogonal function system, the coefficients of the expansion are to be determined. From the relationship between density anomalies and disturbing geopotential, then, a set of observation equations is established, in which the unknown vector contains the coefficients of density anomaly expansion, and the observational vector is obtained by computing geopotential perturbations using the potential coefficients of GEM10B. By suitably selecting the harmonic orders of geopotential, a filtering process is conducted for the observational values. Finally, the lateral density variations in the lower mantle (670 km to the core-mentle boundary) are investigated. In this case, the orders of disturbing geopotential are selected as l = 2-11, the truncated orders of density anomaly expansion are taken as L = 6 and K - 4, and the damping least squares method is used to solve the observation equations.The resulting model shows the high level of density perturbations at the 670 km discontinuity and core-mantle boundary, a high-density zone circumscribing the Pacific and a lower-density region under the center of the Pacific. These features are in agreement with the features of three-dimensional seismic velocity variation obtained by Dziewonski (1984). In the Antarctic region and some parts of the Atlantic and Indian Oceans, however, the resulting density anomalies are negatively correlated with the seismic velocity anomalies. The cause resulting in these phenomena is preliminarily analysed in this paper.
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[12] H,tKrr, B. H., Clayton, R. Richards, M. A., l.omer,R. P,Dziewonski, A. M,1985. Lower ,uantlr lrererogeneity. dynamic topography and geoid, N.rzure, 313, 511——545.[1] Dzicwonski, A. M., 1984. Mapping the lower mantle: Determination of lateral heterogeneity in P velocity up to degree and order 6. J. Grapl:ys. Rrs. 80. 87, 5929——5952.
[2] Woodhousc, J. H.&Dziewonski, A. M., 1984, Mapping the upper mantle:Three——dimensional modeling of earth structure by inversion of seismic wavefurttts. J. Craphys. Rr. 89, 87, 5953——59$6.
[3] Lerch, F. J., 1983. Status of the geopotential, Ret——Crnph,s. Space Phys,21, 3, 560——565.
[4] Khan, M. A,1983. Accuracy of the earth's gravity field models. Phys. Earth Planet. Inter., 31, 231——240
[5] 李瑞浩,I988.重力学引论.地震出版社,北京.
[6] Loch, F. J., Putney, B. H., Wagner, C. A., Klosko, S. M., 1981. Goddard Earth Models for ceanographic Applications (GEM lOB and 10C). Marine Geodesy, S, 2, 145——187.
[7] 曾融生,1984.固体地球物理学导论,172——173.科学出版社,北京.
[8] 王石任,1987重力异常源深度分布的探讨.地震学报,9,增刊,371——381,
[9] 陈运泰、黄立人、林邦慧、刘妙龙、王新华,1979.用大地测量资料反演的1976年唐山地震的位错模式,地球物理学报,22,201——217,
[10] Stacey, F. D.著,中国科学技术大学地球物理教研室译,1981地球物理学,340——345地震出版社,北京.
[11] Mckcnzic, D. P., Roberts, J. M,Weiss, N. O., 1974. Convection in the earth's mantle: Towards a nume——rical simulation, J. Fluid Mech., 62, part, 3, 465——538.
[12] H,tKrr, B. H., Clayton, R. Richards, M. A., l.omer,R. P,Dziewonski, A. M,1985. Lower ,uantlr lrererogeneity. dynamic topography and geoid, N.rzure, 313, 511——545. -
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