区域面波群速度反演的球谐函数法

REGIONAL SURFACE-WAVE GROUP VELOCITY INVERSION BY SPHERICAL HARMONIC FUNCTION METHOD

一个定义在球面局部区域的复杂的面波速度函数如果直接利用球谐函数拟合可能需要展开到很高阶的球谐系数．通过保角变换，把一个球面局部区域扩展到球面上更大的区域上，变换过程中面波速度保持不变，在变换后的球面域上用球谐函数来拟合速度函数，达到降低球谐系数阶数的目的，使面波群速度的反演变成了球谐系数的线性化反演.通过球谐系数分析，可得到反演的分辨率.该方法不仅适用于面波群速度反演，同样适用于各种球面区域场的分析.

If one complex surface- wave velocity function defined on a regional area is imitated directly by spherical harmonic functions, maybe very high coefficients are needed. By conformal mapping, a regional area of a global surface can be extended to a more larger area. Surface-wave velocities keep unchanged in conformal mapping.Velocities can be imitated by spherical harmonic functions on the larger region. This is able to reduce coefficients. The inversion of surface-wave group velocities turns into the linear inversion of spherical harmonic coefficients. By analyzing the coefficients, we can obtain the resolution. This method is not only applicable to the surface-wave group velocity inversion, but also to a wide variety of analysis of regional fields.