用球谐函数拟合地幔Q值三维分布的收敛性问题

On the Convergence of Fitting Seismic body-wave's Q-value 3-dimensional Distribution by Using of Spherical Harmonic Function

本文针对用球谐函数拟合地幔范围，地震体波品质因数Ｑ值三维空间分布是否存在拟合收敛性的问题，从数学理论方面进行了推算研究。分析了球谐函数与勒让得多项式收敛的条件，提出了相应的定理，当Ｑ值随深度分布的连续性甚好时，当多项式的项数多到一定的程度，则可证明这种拟和是趋于收敛的．

In this paper, the authors discuss the convergence offitting seismic body-wave Q-value'S 3D distribution in earth-mantle by using of spherical harmonic function. We analyse the condition of convergence of Q-distribution: if the continuity of Q-distribution with depth is more smoothly and the term of Legendre function arrives a fixed number then this fitting may arrive conversence.