约束走时层析成像
|
摘要
地震层析成像技术是反演地下速度结构的一种重要方法。与医学CT不同，一般地震波射线对目的区覆盖不均匀，所获得的数据不充分。在这种情况下，若初始猜测不准，常规的成像方法，如阻尼最小二乘法、ART法等难以获得理想效果。为此，我们研究了带有约束条件的成像方法。这种方法是通过加入不等式约束条件后再求解最小二乘问题的。文中得出了这种约束条件下的最优化问题的解。处理该问题的方法也适用于其它非线性约束最优化问题。最后的数值结果及解的评价证明了该方法在处理射线数据不足情况下的有效性及优越性，且有一定的抗噪能力。
Seismic tomography is an important technique for estimating subsurface veloci-ty structure. Unlike medical CT, seismic tomography often uses less enough databecause seismic rays fail to uniformly cover the objective area. If a poor initial mod-el is chosen in such case, conventional tomography methods, such as damped leastsquare method, algebraic reconstructioh technique etc. can hardly produce satisfac-tory results. To cope with the problem, we put forward a restrained tomographymethod, which s0lves least square problem after an inequality restriction is given.The solution of optimized problem under the restriction is deduced in the article.The idea of solving this prob1em is also app1icable to solving other non1inear re-strained optimization problems. The final numerical result and the relevant evalua-tion prove this method effective and superior in the case 0f less enough data. Whatis more, the method has certain noise resistance.
Seismic tomography is an important technique for estimating subsurface veloci-ty structure. Unlike medical CT, seismic tomography often uses less enough databecause seismic rays fail to uniformly cover the objective area. If a poor initial mod-el is chosen in such case, conventional tomography methods, such as damped leastsquare method, algebraic reconstructioh technique etc. can hardly produce satisfac-tory results. To cope with the problem, we put forward a restrained tomographymethod, which s0lves least square problem after an inequality restriction is given.The solution of optimized problem under the restriction is deduced in the article.The idea of solving this prob1em is also app1icable to solving other non1inear re-strained optimization problems. The final numerical result and the relevant evalua-tion prove this method effective and superior in the case 0f less enough data. Whatis more, the method has certain noise resistance.
引文
1Aki K, Christoffersen A and Husebye E S. Determination of the three-dimensional seismic structure ofthe lithosphere.J Geophys Res,1977,82(1):277～296
2Guust N0let主编,冯锐、郝锦绮泽.地震层析技术,地质出版社,1991
3Tarantola A著,张先康等泽.反演理论,学术期刊出版社,1989
4陈宝林.最优化理论与算法,清华大学出版社,1989
5Philip M Carrion and hnlzetl de Jesus Carnelro. Generallied approach to llnearlzed Inversion with con-straints.Geophysical Reseach Letters, 1989, 16(9):1039～1042
6Philip Carrion.Dua1 tomography for imaging complex structures.Geophsics,1991,56(9):1395～1404
7Keith A Meyernoltz, Gary L Pavlis and Sally A Szpakowski. Convolutional quelling in seismic tomogfa-Phy.GeoPhysics,1989,54(5):570～580
8John E Peterson, Bjonn N P Paulsson and Thomas V McEvllly. Applications of algebraic reconstructlontechniquestocrossholeseismicdata、. Geophysics, 1985,50(10):1566～1580
9Scales J A. Tomographich inversion via conjugate gradient method.Geophysics, 1987,52(l):179～185
10杨文采编著.地球物理反演和地震层析成像,地质出版社,1989
11 Gersztenkorn A and Scales J A.Smoothing seismic tomograms with alpha-trimmed means.GeophysicalJOurnal,1988,92(1):67~ 72
2Guust N0let主编,冯锐、郝锦绮泽.地震层析技术,地质出版社,1991
3Tarantola A著,张先康等泽.反演理论,学术期刊出版社,1989
4陈宝林.最优化理论与算法,清华大学出版社,1989
5Philip M Carrion and hnlzetl de Jesus Carnelro. Generallied approach to llnearlzed Inversion with con-straints.Geophysical Reseach Letters, 1989, 16(9):1039～1042
6Philip Carrion.Dua1 tomography for imaging complex structures.Geophsics,1991,56(9):1395～1404
7Keith A Meyernoltz, Gary L Pavlis and Sally A Szpakowski. Convolutional quelling in seismic tomogfa-Phy.GeoPhysics,1989,54(5):570～580
8John E Peterson, Bjonn N P Paulsson and Thomas V McEvllly. Applications of algebraic reconstructlontechniquestocrossholeseismicdata、. Geophysics, 1985,50(10):1566～1580
9Scales J A. Tomographich inversion via conjugate gradient method.Geophysics, 1987,52(l):179～185
10杨文采编著.地球物理反演和地震层析成像,地质出版社,1989
11 Gersztenkorn A and Scales J A.Smoothing seismic tomograms with alpha-trimmed means.GeophysicalJOurnal,1988,92(1):67~ 72
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心