地震层析成像反演中解的定量评价及其应用
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摘要
对地震层析成像非线性问题线性化处理之后，各种反演算法归纳成为对不适定方 程的求解．地震层析成像反演算法的解的物理意义是给出地质结构，因此对于解的可靠性及 分辨率研究非常重要．然而许多反演算法不能给出解的评价方法，因而对解的可信度产生怀 疑．本研究根据解估计的分辨率矩阵的原理，提出ＬＳＱＲ（Ｌｅａｓｔ Ｓｑｕａｒｅ ＱＲ）算法解协方差矩 阵的评价算法，用相关分析可以为那些在求解过程中得不到分辨率矩阵的反演方法提供解的 定量评价．并用本文提出的解的定量评价方法试评了一个实际地壳模型的地震层析成像的 速度重建结果．
After converting nonlinear equations to linear equations for seismic tomography, inversion methods can be reduced to solve ill-posed equations. The physical meaning of inversion solutions is an unknown subsurface geological structure. Therefore, it is very important to study the reliability and resolution of a solution. Many inversion methods cannot give a criterion for assessing the solution, so the reliability of the solution is suspected. Based upon the resolution of solution an assessment criterion of covariance matrix of solution is Put forward for LSQR algorithm. Correlation analysis can provide a quantitative assessment to the inversion methods that cannot obtain resolution matrix. This assessment method is used to a velocity construction images for a real crust model.
After converting nonlinear equations to linear equations for seismic tomography, inversion methods can be reduced to solve ill-posed equations. The physical meaning of inversion solutions is an unknown subsurface geological structure. Therefore, it is very important to study the reliability and resolution of a solution. Many inversion methods cannot give a criterion for assessing the solution, so the reliability of the solution is suspected. Based upon the resolution of solution an assessment criterion of covariance matrix of solution is Put forward for LSQR algorithm. Correlation analysis can provide a quantitative assessment to the inversion methods that cannot obtain resolution matrix. This assessment method is used to a velocity construction images for a real crust model.
引文
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[ 2 ] Golub G H. Reinsch C. Singular values decomposition and least Squares solution. Numer. Math, 1970,14(3): 403-420.
[ 3 ] Liu F. On the Tomographic inverse method used in velocity image reconstruction. Chinese J. Geophysics,1986, 32(1):62-80.
[ 4 ] Paige C C. Saunders M A. LSQK Sparse linear equations and least square problems. AMC Transactions.Math. 1982, 8(1): 195-209.
[ 5 ] Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential andintegral operators. J. Res. N. B. S., 1950, 45(2):255-282.
[ 6 ] Backus G, Gilbert F, The resolving power of gross earth data, Geophys. J K astr. Soc., 1968, 16(1);169-205.
[ 7 ] Anderson A ac Kak A C Simultaneous algebraic Reconstruction. Ultrasonic Imaging, 1984, 6(1):81-94.
[ 8 ]常旭,刘伊克地震层析成像反演中三种广义解的误差分析与评价地球物理学报, 1999,43(5) 217-225.CHANG Xu, LIU Yi-Ke. Error analysis and appraisals for three general solution in seismic tomography,Chinese J Geophys.(in Chinese), 1999, 43(5):217-225.
[ 9 ]杨文采,杜剑渊.层析成像新方法及其在工程检测上的应用地球物理学报, 1994, 37(2):239-244.YANG Wen-Cat, DU Jian-Yuan. A new algorithm of seismic tomography with application to engineeringdetections. Chinese J, Geophys: (in Chinese), 1994, 37(2):239-244.[10] Guust Nolet. Seismic Tomography. Reidel Publishing Company, 1987.
[ 2 ] Golub G H. Reinsch C. Singular values decomposition and least Squares solution. Numer. Math, 1970,14(3): 403-420.
[ 3 ] Liu F. On the Tomographic inverse method used in velocity image reconstruction. Chinese J. Geophysics,1986, 32(1):62-80.
[ 4 ] Paige C C. Saunders M A. LSQK Sparse linear equations and least square problems. AMC Transactions.Math. 1982, 8(1): 195-209.
[ 5 ] Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential andintegral operators. J. Res. N. B. S., 1950, 45(2):255-282.
[ 6 ] Backus G, Gilbert F, The resolving power of gross earth data, Geophys. J K astr. Soc., 1968, 16(1);169-205.
[ 7 ] Anderson A ac Kak A C Simultaneous algebraic Reconstruction. Ultrasonic Imaging, 1984, 6(1):81-94.
[ 8 ]常旭,刘伊克地震层析成像反演中三种广义解的误差分析与评价地球物理学报, 1999,43(5) 217-225.CHANG Xu, LIU Yi-Ke. Error analysis and appraisals for three general solution in seismic tomography,Chinese J Geophys.(in Chinese), 1999, 43(5):217-225.
[ 9 ]杨文采,杜剑渊.层析成像新方法及其在工程检测上的应用地球物理学报, 1994, 37(2):239-244.YANG Wen-Cat, DU Jian-Yuan. A new algorithm of seismic tomography with application to engineeringdetections. Chinese J, Geophys: (in Chinese), 1994, 37(2):239-244.[10] Guust Nolet. Seismic Tomography. Reidel Publishing Company, 1987.
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