基于截断牛顿法的频率域全波形反演方法

摘要

The full waveform inversion method can be regarded as a large nonlinear minimization problem.In this method,Hessian operator exerts significant influence on the inversion result.Nevertheless,traditional optimization methods can only express the Hessian operator approximately,which will lead to low inversion accuracy,slow convergence speed,and the result that the parameter cannot be focused,especially for deep inversion region target with poor illumination.In contrast,the truncated Newton method,a new optimization method,can obtain the information of Hessian operator more accurately by the computation of the product of Hessian matrix and a known vector,and thus can solve the problem mentioned above.Therefore,this paper achieves full waveform inversion in the frequency domain based on truncated Newton method.And the model test shows that the truncated Newton method has more precise inversion results and improves the efficiency of inversion,especially for deep area with insufficient illumination compared with the limited memory BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS) method.%全波形反演方法可以视为大型非线性最小化问题.其中Hessian算子对反演结果有着重要的影响,传统的优化方法只能近似地表示Hessian算子,反演精度较低,收敛速度较慢,且对于反演目标照明不足的深部区域,往往出现参数无法聚焦的情况.而一种新的优化方法截断牛顿法,通过计算Hessian矩阵与已知向量乘积的形式,能够获得更精确的Hessian算子信息,从而解决以上问题.本文基于截断牛顿法在频率域实现全波形反演,通过模型试算表明,截断牛顿法相对于有限内存BFGS(Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS)法,能够得到更精确的反演结果,同时能提高收敛速度,尤其对于照明不足的深部区域,截断牛顿法有更明显的优势.