球谐分析

球谐分析，带谐，田谐，瓣谐
球谐函数是拉普拉斯方程的球坐标系形式的解。

球谐函数表示为：
球谐分析（如重力场）是将地球表面观测的某个物理量f(theta,lambda)展开成球谐函数的级数：
其中，theta为余纬，lambda：经度
如重力位可表示为：
带谐系数：coefficient of zonal harmonics
地球引力位的球谐函数展开式中次为零的位系数。

In themathematicalstudy ofrotational symmetry, the zonal spherical harmonics are specialspherical harmonicsthat are invariant under the rotation through a particular fixed axis. （故m=0，不随经度方向变化）
扇谐系数：coefficient of sectorial harmonics
地球引力位的球谐函数展开式中阶与次相同的位系数。

田谐：coefficient of tesseral harmonics
地球引力位的球谐函数展开式中阶与次不同的位系数。

The Laplace spherical harmonics can be visualized by considering their "nodal lines", that is, the set of points on the sphere where.
Nodal lines of are composed of circles: some are latitudes and others are longitudes.
One can determine the number of nodal lines of each type by counting the number of zer os of in the latitudinal and longitudinal directions independently.For the latitudinal di
rection, the associated Legendre polynomials possess ℓ−|m| zeros, whereas for the longitudin al direction, the trigonometric sin and cos functions possess 2|m| zeros.
When the spherical harmonic order m is zero(upper-left in the figure), the spherical harm onic functions do not depend upon longitude, and are referred to as zonal. Such spherical harmonics are a special case ofzonal spherical functions.
When ℓ= |m| (bottom-right in the figure), there are no zero crossings in latitude, and the functions are referred to as sectoral.
For the other cases, the functionscheckerthe sphere, and they are referred to as tesseral. More general spherical harmonics of degree ℓare not necessarily those of the Laplace bas
is, and their nodal sets can be of a fairly general kind.[10]
360阶（EGM96）分辨率为0.5分的来历：纬向180°、360=0.5°。

因此，different spherical harmonic degrees corresponds to different wavelength.
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