第十四讲地震波层析成像

1、第六章 地震层析成像,Seismic wave is currently the only effective tool that can penetrate the entire earth Structural information of the Earth,From IRIS,Seismic waves,Jeffreys-Bullen 1-D Earth Model,1939: Jeffreys Sabra et al., 2005; Pollitz and Flecher, 2005）,Ambient noise is enriched at short periods. Bette

2、r constraints on crustal and uppermost mantle structure than information from earthquakes. Particularly useful in aseismic areas; e.g., continental interiors. For temporary deployments - do not have to wait for earthquakes to occur. Measurements are repeatable: rigorous uncertainty estimates.,R. Wea

3、ver,Science, 2005,Processing Steps: Remove instrument response, de-mean, de-trend, bandpass filter, time-domain normalization, spectral whitening Cross-correlation: 1 day at a time. Stack over many days. Waveform selection (SNR) for tomography,Mike Ritzwoller et al., 2008,体波走时层析成像,1. 块体模型方法（Aki and

4、Lee, 1976）,该方法是将整个反演模型用多个均匀的六面体表示，而每个六面体中心的速度来表示该六面体的整体速度。,块体=Block,Roecher（1982）提出了模型空间由多个尺度大小不同的六面体来描述，即可变块体方法。该方法在我国首先由刘福田等（1989）运用。,后来者在块体模型中引入了不连续界面（Wintlinger et al., 1998,2004;胥颐等， 2000）,2. 格点模型方法,Thurber（1983）提出了六面体内的速度变化用其八个顶点的速度变化来表示的技术。,之后有人提出利用四个顶点组成的四面体代替六面体（Lin and Roecker, 1997）,在六面体格

5、点模型的基础上，通过引入Snell定律和射线伪弯曲法，Zhao (1992,1994) 利用相关区域的先验信息资料（如莫霍面、康拉德面以及板块边界等）构建较为接近真实的模型结构。,Travel time (or slowness) inversions:,慢度的扰动，作为反演的基本变量,30,Menke, 1989,Least-Squares Solutions,Suppose we have a simple set of linear equations,A X = d,We can define a simple scalar quantity E,Mean square error (

6、or total error),Error function,We want to minimize the total error, to do so, find first derivative of function E and set to 0.,So, do, we should have,This is known as the system of normal equations.,So this involves the inversion of the term ATA, This matrix is often called the inner-product matrix

7、, or Toeplitz matrix. The solution is called the least-squares solution, while X=A-1 d is not a least squares solution.,最小二乘法适合于观测数据个数多于未知数个数。,Left multiply by,Pre-conditioning for ill-conditioned inverse problem (damping, smoothing, regularization. Purpose: Stabilize, enhance smoothness/simplicity)

8、,Lets use the same definition,Define: An objective function J where,where m is the damping or regularization parameter.,I is identity matrix,Minimize the above by,(Damped Least Squares solution),阻尼最小二乘法，适合于观测数据个数少于未知数个数。,Solve for the inverse problem,(1) Standard Least Squares Solution,GTG may be si

9、ngular or ill-conditioned singular value decomposition (SVD),(2) Damped Least Squares Solution,minimize,Ray-based traveltime tomography,minimize,L: Laplacian operator,Solution: m = (GTG+2LTL)-1GTd,3. Smooth model,Combined norm and Laplacian regularization,misfit function,Crust correction,Data misfit

10、,Model roughness,Model norm,在Zhao 等( 1992, 1994) 方法基础上, 双差走时定位( double difference location; Waldhauser and Ellsw orth, 2000; Wolfe, 2002) 方法被引入到地震波层析成像反演中, 即地震波双差走时层析成像方法( Zhang and Thurber, 2003, 2005),基本概念 震相对：如果两个时间到同一个站台有相同震相的走时数据，那么对于这 两个事件来说这两个震相就是一个震相对。 2. 事件对：两个事件有一定数目的震相对，并且震中之间的距离在一定的范围内。,

11、Double difference method,汪锐等，2013,参考模型（Reference model）：计算理论走时。 地震波走时自动拾取：获得观测走时.,Crust correction: using 3-D Crust 2.0 as the reference crust model,Crust 2.0,Input model,1-D crust reference model,3-D crust reference model,检测版试验是为了检查模型的分辨率。,Checkerboard resolution tests,Checkerboard and synthetic re

12、solution tests,地震波走时自动拾取问题,相邻道互相关方法(Gelchinsky，1983) 、能量比较方法 (Coppens，1985) 、改变褶积算子宽度的方法 (Ramananantoandro，1987)，分形理论的Divider 方法和Hurst 方法(Boschetti，1996)。中国科学家提出的基于hausdorff 分维算法的地震波走时全自动拾取方法 (Chang，1999)。,走时是地震层析成像的最基础数据， 这个数据量一般都是很大的， 需要研究走时的自动拾取技术。,A dense path coverage minimizes the amount of a priori information needed,射线覆盖密度,射线覆盖越密，反演结果越好！,P波隐区 104-143度,一次较大的地震激发的地震波，可以在很长的距离上观测到，结果发现在1040突然消失了，到了1430重又出现!也就是说，1040 到1430“销声匿迹”。这是因为地球内存在一个速度很低的“核”，“影区”就是地核的影子。,S波隐区 104-180度,from:,P波隐区：104-143度 S波隐区：104-180度 两侧皆是,Mantle tomography,E.g., Bijwaard, Sp