地震层析成像反演中3种广义解的误差分析与评价

ERROR ANALYSIS AND APPRAISALS FOR THREEGENERAL SOLUTIONS IN SEISMIC TOMOGRAPHY

在地震波速度和地震波 值层析成像中，对于非线性反演问题解的可靠性研究非常重要．为了讨论ＡＲＴ（ＡｌｇｅｂｒａｉｃＲｅｃｏｎｓｔｒｕｃｔｉｏｎ Ｔｅｃｈｎｉｑｕｅ）、ＳＶＤ（Ｓｉｎｇｕｌａｒ ＶａｌｕｅＤｅｃｏｍｐｏｓｉｔｉｏｎ）、ＬＳＱＷ（ＬｅａｓｔＳｕａｒｅ）３种方法的算法稳定性以及反演效果，本研究将这３种算法用于求解非常病态问题和一般稳定问题，根据数值计算结果，分别给出了在非常病态问题和一般稳定问题中３种算法的相对误差及其算法稳定性评价．进而针对３种算法在同一地质模型上的速度成像结果进行了比较，为地震层析成像反演效果分析提供了定量参数．

It is very important to study the solution reliability of nonlinear inversion problemwhen we reconstruct the seismic velocities and Q value images. In order to discussthe algorithms stability and inversion resultS to ART (Algebraic ReconstructionTechnique), SVD (Singular Value Decomposition) and LSQR (Least Square oR), thispaper deals with qiute illconditioned problems by using the three algorithms.According to the numerical computation results, the relative errors and stabilityappraisals for the three methods were given under the above conditions. Further,velocity images tO a geological model were compared based on the three algorithms,which provide a quanhtative paraxneters for the analysis of results of seismictomograph.