复数矢量球函数的理论研究  

STUDY ON THE THEORY OF COMPLEX VECTOR SPHERICAL FUNCTION

作　　者：张捍卫[1] 郑勇[1] 刘长建 

机构地区：[1]郑州测绘学院,大地测量系,450052

出　　处：《地壳形变与地震》2000年第2期1-7,共7页Crustal Deformation and Earthquake

基　　金：国家攀登计划!(970231003);国家自然科学基金!(9773011)

摘　　要：给出了正交归一化的复数矢量球函数的定义和性质。复数矢量球面调和函数是球体位移的研究基础，采用复数矢量球面调和函数可把位移场的球形场和环形场一同表示出来，为地球各种动力学效应的统一研究提供了理论依据。同时还研究了在球坐标系下弹性应变张量与复数矢量球函数的一些关系，为地球弹性动力学方程的解算提供参考。The study of spheroidal potential is based on spherical surface harmonics and the study of spheroidal displacement is based on complex vector spherical harmonic functions. The definition and the characteristics of complex vector spherical harmonic functions based on orthogonal normalization are given in this paper. And the spherical field and the circular field of displacement field are expressed by complex vector spherical harmonic functions, which provide the study of various kinetic effects with theoretical supports. The solution of the Earth elastic dynamical equations can be also referred to some relations of complex vector spherical harmonic functions to the elastic strain tensor in spherical coordinates.

关 键 词：复数矢量球函数 位移场 弹性应变场 地壳变形 

分 类 号：P551[天文地球—构造地质学] P553[天文地球—地质学]