用小波变换方法反演接收函数

提出了一种用小波变换方法反演接收函数的新方法. 通过对接收函数作离散小波变换，将接收函数展开到不同分辨尺度，从一给定的初始模型出发，分别在不同分辨尺度上用广义线性反演方法，对展开后的接收函数进行反演. 并将低阶接收函数的反演结果作为高阶接收函数的初始模型，在大尺度空间找到包含全局极小值的一个邻域，并逐步缩小该邻域.渐进地获取介质结构的跳变信息，从而保证反演结果稳定地收敛到全局极小点，降低接收函数波形反演对初始模型的依赖，尽可能克服波形反演的非唯一性，得到比较可靠的高分辨率的地壳上地幔速度结构． 

INVERSION OF RECEIVER FUNCTION BY WAVELET TRANSFORMATION

A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver function is expanded to different scales with different resolution by wavelet transformation. After an initial model being taken, a generalized least square inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low scale receiver function as the initial model for high scale. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradually focus at the global minimum with the introducing of high scale information of receiver function. With the gradual addition of high wave number to smooth background velocity structure, wavelet transformation can keep the inversion result converge to the global minimum, reduce to certain extend the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least square inversion, and obtain reliable crustal and upper mantle velocity with high resolution.