| 基于截断牛顿法的VTI介质声波多参数全波形反演 |
| |
| 引用本文： | 王义,董良国.基于截断牛顿法的VTI介质声波多参数全波形反演[J].地球物理学报,2015,58(8):2873-2885. |
| |
| 作者姓名： | 王义 董良国 |
| |
| 作者单位： | 同济大学海洋地质国家重点实验室, 上海 200092 |
| |
| 基金项目： | 国家油气重大专项(2011ZX05005-005-007HZ)资助. |
| |
| 摘 要： | 不同类别参数间的相互耦合使多参数地震全波形反演的非线性程度显著增加,地震波速度与各向异性参数取值数量级的巨大差异也会使反演问题的性态变差.合理使用Hessian逆算子可以减弱这两类问题对反演的影响,提高多参数反演的精度,而截断牛顿法是一种可以比较准确地估计Hessian逆算子的优化方法.本文采用截断牛顿法在时间域进行了VTI介质的声波双参数同时反演的研究.不同模型的反演试验表明,在VTI介质声波双参数同时反演中,截断牛顿法比有限内存BFGS(Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS)法能更准确地估计Hessian逆算子,进而较好地平衡两类不同参数的同时更新,得到了比较精确的反演结果.
|
| 关 键 词： | 多参数 全波形反演 各向异性 耦合 Hessian逆算子 截断牛顿法 |
| 收稿时间： | 2014-08-17 |
Multi-Parameter full waveform inversion for acoustic VTI media using the truncated Newton method |
| |
| WANG Yi,DONG Liang-Guo.Multi-Parameter full waveform inversion for acoustic VTI media using the truncated Newton method[J].Chinese Journal of Geophysics,2015,58(8):2873-2885. |
| |
| Authors: | WANG Yi DONG Liang-Guo |
| |
| Institution: | State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China |
| |
| Abstract: | It is important to reconstruct both seismic velocities and anisotropy parameters by anisotropic full waveform inversion(FWI). But the trade-off between different parameter classes increases its nonlinearity severely. The significant difference of magnitude orders between seismic velocities and anisotropy parameters makes the inversion problem poorly conditioned. Judiciously incorporating the inverse Hessian operator within the FWI scheme can help to alleviate the negative impacts of these two problems on FWI. The truncated Newton(TN)method can better estimate the inverse Hessian operator. Therefore, we use the TN method to tackle these two problems and simultaneously reconstruct both seismic velocities and anisotropy parameters for acoustic VTI media.The TN method has two advantages. On one hand, it does not need explicit Hessian matrix, which is prohibitive to build due to high computational cost and large memory requirements. To get the updated direction, the TN method solves Newton equation at each time of iteration with the conjugate gradient method(CG), which only uses Hessian-vector products. We compute these products by the finite difference method. On the other hand, the TN method can adjust flexibly the updated direction when the Hessian matrix is non-positive definite. The CG method at each step of the TN iteration is terminated as soon as a direction of negative curvature is generated. With this strategy the TN method may perform better than Limited-memory Broyden-Fletcher-Goldfarb-Shanno method(L-BFGS)for ill-conditioned problems.We test the inversion capability of the TN method with two numerical experiments. In each experiment, the NMO velocity and anisotropy parameter eta are inverted simultaneously. The L-BFGS method is also tested for comparison. The first experiment is on a simple 2D VTI homogenous model with three different anomalies inside. The inversion is performed in the time domain with a full acquisition system. Inversion results show that the TN method can balance the updates of the two different parameters, and reconstruct more accurate models. In contrast, the L-BFGS method overestimates parameter eta but underestimates NMO velocity. The second experiment is on a more complex 2D model with a surface acquisition system. The two methods perform the same as they do in the first experiment.The reason for their different performances may be found from the Hessian analysis part that we have finished before the two experiments. We design a small size(51 ×51)inclusion model and compute explicitly the Hessian matrix of the background initial model. The analyses show that the Hessian matrix has several negative eigenvalues and a large condition number(ill-conditioned matrix), which may result in the failure of the L-BFGS method. The TN method better overcomes these difficulties. Hence, in the context of simultaneous inversion of two parameters for acoustic VTI media, the TN method can account for more accurate inverse Hessian operator than the L-BFGS method and get more accurate inversion results. It is a promising method for multi-parameter FWI. |
| |
| Keywords: | Multi-Parameter Full waveform inversion Anisotropy Trade-off Inverse Hessian operator Truncated Newton method |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《地球物理学报》浏览原始摘要信息 |
| 点击此处可从《地球物理学报》下载免费的PDF全文 |
|
