由地震背景噪声提取介质衰减:衰减介质中的空间相干表示

On the spatial correlation of seismic noise in an attenuating medium

传统基于地震背景噪声互相关的层析成像技术,主要利用了互相关函数的相位信息,即利用走时来反演地球介质的速度和各向异性特征.最近,开始有研究人员利用互相关函数的振幅信息提取介质的衰减.主要是将二维弹性情形下,互相关函数正比于第一类零阶贝塞尔函数J_0(k_0r)这一结论,通过引入指数衰减系数,直接推广到衰减介质情形,令衰减介质中背景噪声互相关函数类比于J_0(k_0r)·e^(-α(ω)r),以此来反演介质的衰减系数α.然而,在衰减介质中,互相关受源的方位平均的影响,这种简单的推广,可能无法提取可靠的衰减系数.本文基于平面波的叠加模型,研究不同的互相关定义和坐标选择下,衰减介质中两点间互相关函数的理论表达式.结果表明,在平面波叠加模型下,互相关函数的表达形式随着坐标原点的选择,并因而随着源分布的变化而变化,对不同的归一化因子,表达式也不尽相同.利用J_0(k_0r)·e^(-α(ω)r)的形式拟合背景噪声的观测数据得到的衰减比实际值偏小.

Traditionally,the tomography based on the correlation of seismic noise primarily uses the phase information of ambient noise correlation function（NCF）to extract the seismic velocity and anisotropy of the Earth with travel time measurement by performing inversion.Researchers recently utilize the amplitude of NCF to extract the Earth′s attenuation.In theory,NCF is proportional to the first kind of zero-order Bessel function in a 2-D elastic case,which is directly extended to the dissipative media by introducing an exponential attenuation coefficient.The attenuation of the structure is then obtained by comparing the observed data from NCF to the Bessel function multiplied by a decaying exponential term.The NCF,however,is affected by azimuth averaging of ambient noise sources distributed in attenuated media.This empirical and simple extension cannot be used to extract a reliable decay coefficient.In this paper,we study the theoretical expressions of NCF in the frequency domain between two stations under different coordinate systems and accordingly different source distributions which are composed ofsuperposition of plane waves.We show that the coherency expressions in dissipative media vary with coordinate systems.The expressions are different for different normalized factors.The attenuation coefficient obtained by fitting the coherency J0（k0r）·e^-α（ω）r ith the observed data is smaller than the real one.