用球面调和函数拟合地震波Q值空间分布收敛性的研究

本文从球面调和多项式的数学理论方面研究了用球函数拟合地慢地震波Q 值空间分布方法的收敛性的问题。运用一种逼近的球面多项式的误差公式,证明用球谐函数拟合地幔地震波Q 值空间分布的方法是收敛性的;也提出从地震P 波的振幅A 和周期T 拟合、反演地幔范围P 波品质因数空间分布的误差Qer 与P 波(A、T)的观测数目N 的增加,Qer 的减少来予以验证。

On the Convergence of Fitting Seismic-wave's Q-value Distribution by Using of Spherical Harmonic Function

In this paper,the authors discuss the convergence of fitting seismic-wave's Q value distribution in earth-mantle by using of spherical harmonic polynomial function, we define a formula of Q-value's error by an approximate method that using a spherical polynomial function.Finally we present a method which may verify the above conclusion and we wish to establish a relation between the observational number N of amplitude A and its corresponding period T.We have used this relation to inverse the seismic Q-values which will be calculated by the spherical harmonic function fitting method.