第十四講地震波層析成像課堂

1、1,第六章,地震層析成像,2,Seismic wave is currently the only effective,tool that can penetrate the entire earth,F,r,o,m,I,R,I,S,Seismic waves,3,Jeffreys-Bullen,1-D Earth Model,1939,Jeffreys Sabra et al,2005; Pollitz and Flecher, 2005,Ambient noise is enriched at short periods,Better constraints on crustal and

2、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,25,R. Weaver,Science, 2005,26,Processing

3、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,time (s,16.3 Month Stack,Station Y12C,Station 109C,Mike Ritzwoller et al., 2008,27,體波走時(shí)層

4、析成像,1,塊體模型方法,Aki and Lee, 1976,該方法是將整個(gè)反演模型用多個(gè)均勻的六面體表示，而每個(gè)六面,體中心的速度來表示該六面體的整體速度,塊體,Block,Roecher,1982,提出了模型空間由多個(gè)尺度大小不同的六面體來描述,即可變塊體方法。該方法在我國首先由劉福田等,1989,運(yùn)用,后來者在塊體模型中引入了不連續(xù)界面,Wintlinger et al., 1998,2004,胥頤等,2000,28,2,格點(diǎn)模型方法,Thurber,1983,提出了六面體內(nèi)的速度變化用其八個(gè)頂點(diǎn)的速度變,化來表示的技術(shù),之后有人提出利用四個(gè)頂點(diǎn)組成的四面體代替六面體,Lin and,R

5、oecker, 1997,在六面體格點(diǎn)模型的基礎(chǔ)上，通過引入,Snell,定律和,射線偽彎曲法,Zhao,1992,1994,利用相關(guān)區(qū)域的先驗(yàn)信息資料（如莫霍面、康拉德面以及板,塊邊界等）構(gòu)建較為接近真實(shí)的模型結(jié)構(gòu),29,Travel time (or slowness) inversions,0,1,t,ds,v,2,0,0,1,1,v,t,v,d,s,d,s,v,v,v,v,v,慢度的擾動(dòng)，作為反演的基本變量,30,31,Menke, 1989,32,33,Least-Squares Solutions,Suppose we have a simple set of linear equ

6、ations,T,T,E,A,X,dA,X,d,AX,d,2,A X = d,We can define a simple scalar quantity E,Mean square error (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,E,X,0,we should have,T,2,0,A,A,X,d,A,T,AX,A,T,d,This is known as the

7、 system of normal equations,X,A,T,A,1,A,T,d,So this involves the inversion of the term,A,T,A,This matrix is often called the,inner-product matrix, or Toeplitz matrix,The solution is called the least,squares solution,while,X=A,1,d,is,not,a least squares solution,最小二乘法適合于觀測數(shù)據(jù)個(gè)數(shù)多于未知數(shù)個(gè)數(shù),34,Left multiply

8、 by,A,T,A,I,1,Pre-conditioning for ill-conditioned inverse problem (damping, smoothing,regularization,Purpose: Stabilize, enhance smoothness/simplicity,Lets use the same definition,E,T,AX,d,2,Define: An,objective function,J,where,J,E,X,2,where,m,is the damping or regularization parameter,J,X,E,X,X,2

9、,X,T,2,2,A,A,X,d,I,X,I,is identity matrix,Minimize the above by,J,X,0,A,T,A,I,X,A,T,d,X,A,T,A,I,1,A,T,d,Damped Least Squares solution,阻尼最小二乘法，適合于觀測數(shù)據(jù)個(gè)數(shù)少于未知數(shù)個(gè)數(shù),35,Solve for the inverse problem,1) Standard Least,Squares Solution,G,T,G may be,singular or ill-conditioned,singular value decomposition (SV

10、D,2) Damped Least,Squares Solution,minimize,Ray-based traveltime tomography,T,2,1,T,mG,G,I,G,d,36,minimize,L: Laplacian operator,Smooth model,Solution: m = (G,T,G,2,L,T,L,1,G,T,d,3. Smooth model,37,Combined norm and Laplacian regularization,misfit function,Crust,correction,Data misfit,Model,roughnes

11、s,Model,norm,38,在,Zhao,等,1992, 1994,方法基礎(chǔ)上,雙差走時(shí)定位,double difference location,Waldhauser and Ellsw orth, 2000; Wolfe, 2002,方法被引入到地震波層析成像反演,中,即,地震波雙差走時(shí)層析成像方法,Zhang and Thurber, 2003, 2005,基本概念,1,震相對：如果兩個(gè)時(shí)間到同一個(gè)站臺有相同震相的走時(shí)數(shù)據(jù)，那么對于這,兩個(gè)事件來說這兩個(gè)震相就是一個(gè)震相對,2,事件對：兩個(gè)事件有一定數(shù)目的震相對，并且震中之間的距離在一定的范圍內(nèi),Double difference m

12、ethod,ca,j,k,i,k,obs,j,k,i,k,ij,k,t,t,t,t,dr,Difference in,observed,arrival time for,stations i and j,Difference in,calculated,arrival time,for stations i,and j,Double,difference for,event k,aim to,minimize this,residual,39,汪銳等,2013,40,參考模型,Reference model,：計(jì)算理論走時(shí),地震波走時(shí)自動(dòng)拾?。韩@得觀測走時(shí),41,Crust correctio

13、n: 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,42,檢測版試驗(yàn)是為了檢查模型的分辨率,Checkerboard resolution tests,43,Checkerboard and synthetic resolution tests,44,地震波走時(shí)自動(dòng)拾取問題,相鄰道互相關(guān)方法,Gelchinsky,1983,能量比較方法,Coppens,1985,改變褶積算子寬度的方法,Raman

14、anantoandro,1987,分形,理論的,Divider,方法和,Hurst,方法,Boschetti,1996,中國科學(xué)家提出,的基于,hausdorff,分維算法的地震波走時(shí)全自動(dòng)拾取方法,Chang,1999,走時(shí)是地震層析成像的最基礎(chǔ)數(shù)據(jù),這個(gè)數(shù)據(jù)量一般都是很大的,需要研究走時(shí)的自動(dòng)拾取技術(shù),45,A dense path coverage minimizes the,amount of a priori information needed,射線覆蓋密度,射線覆蓋越密，反演結(jié)果越好,46,P,波隱區(qū),104-143,度,一次較大的地震激發(fā)的地震波，可以,在很長的距離上觀測到，結(jié)果發(fā)現(xiàn)在,104,0,突然消失了，到了,143,0,重又出現(xiàn),也就是說,104,0,到,143,0,銷聲匿跡,這是因?yàn)榈厍騼?nèi)存在一個(gè)速度很低的,核”，“影區(qū)”就是地核的影子,47,S,波隱區(qū),104-180,度,48,from: http:/www.cyberphysics.co.uk/topics/earth/geophysics/Seismic Waves Reading.htm,P,波隱區(qū),104-143,度,S,波隱區(qū),104-180,度,兩側(cè)皆是,49,50,51,52,Mantle tomograp