非对称地震矩张量时间域反演:理论与方法

A time-domain inversion for the asymmetric seismic moment tensor:Theory and method

本文在对称地震矩张量反演的基础上,进一步研究了非对称地震矩张量时间域反演的理论与方法,结果表明:非对称地震矩张量反演与对称地震矩张量反演类似,只需将对称地震矩张量反演方法略加改动,即增加3个待解参数,便可实现非对称地震矩张量反演.为了判断非对称地震矩张量反演相对于对称地震矩张量反演是否存在过度拟合,运用了AIC准则(赤池信息准则).为了定量地描述地震矩张量之间的差异,引入了地震矩张量的矢量表示法.通过分析格林函数与地震矩张量各分量之间的关系,得出:在非对称地震矩张量反演时,若仅用垂直向地动位移数据,将无法区分M_(xy)与Myx这两个分量,需要同时运用垂直向与水平向地动位移数据进行联合反演才能区分M_(xy)与Myx;若采用不同的速度结构模型或不同的格林函数计算方法,则需重新评估地震矩张量各分量的分辨度问题.为检验非对称地震矩张量反演方法的可行性,利用合成地震图进行了一系列数值试验.数值试验结果表明,在非对称地震矩张量反演中,有必要引入S波进行P波与S波联合反演以提高反演的准确性和判定断层面的能力.

In this paper the theory and method of time-domain inversion for the asymmetric seismic moment tensor are studied based on the symmetric seismic moment tensor inversion. It is shown that the asymmetric seismic moment tensor inversion is analogous to the symmetric one, and that only a minor modification on the method of symmetric seismic moment tensor inversion, i.e., increasing three unknown parameters is required to realize the asymmetric seismic moment tensor inversion. The Akaike Information Criterion （AIC） is introduced to judge whether the asymmetric seismic moment tensor inversion is over fitting as compared with the symmetric seismic moment tensor inversion. In analyzing the asymmetric seismic moment tensor the vector representation of the moment tensor is introduced to describe the difference between seismic moment tensors quantitatively. By analyzing the relation between Green＇s function and each of moment tensor＇s components, it is found that, in asymmetric seismic moment tensor inversion, the components M^y and My could not be distinguish- ed if only vertical displacement data were used in inversion. The vertical and horizontal displacement data should be used jointly in inversion to distinguish M^y from Ms. It is also found that if a different velocity structure model or a different method for calculating the Green＇s function was adopted for the inver- sion, the resolutions between any seismic moment tensor components need to be re-analyzed. A series of numerical tests were performed to test the feasibility of the present inversion method by using synthetic data. It is shown that the present inversion method is feasible and that it is necessary to use jointly both the P and S wave data to invert for the asymmetric seismic moment tensor.