摘要
The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational reso
时间域多尺度全波形反演通过利用地震数据中的不同频率成分进行顺序反演,减小了非线性反演中局部极值问题的影响。拟牛顿法不需要直接求解Hessian逆矩阵,能够降低反演所需的计算量和存储量。二者结合可以提升反演精度与效率。但时间域多尺度全波形反演中的拟牛顿方法仍然无法完全解决反演算法陷入局部极小的问题。本文通过模型数据试验分析得到拟牛顿Davidon-Fletcher-Powell(DFP)和Broyden-Fletcher-Goldfarb-Shanno(BFGS)法易陷入局部极小的原因为:由于地震波传播过程中振幅会随几何扩散而减小,导致速度模型的梯度集中在浅部,深部的速度得不到修正,使反演陷入局部极小。针对这一问题,本文引入虚源预条件来去除几何扩散的影响,让深部和浅部的模型速度同时得到充分修正,使反演能够更稳定地向全局最小收敛。在使用虚源预条件后,拟牛顿法容易陷入局部极小的问题虽然得到了改善,但仍存在迭代一定次数后搜索方向不正确,目标函数不再下降等问题。因此,本文进一步对基于虚源预条件拟牛顿法的时间域多尺度全波形反演进行了流程上的改进,通过加入近似Hessian逆矩阵的重置这一环节,保证了拟牛顿法搜索方向的正确性。数值试验表明,改进后的拟牛顿法可以得到更准确的反演结果,且与梯度法相比,其收敛速度更快,更节约计算成本。
基金
supported by the Open Foundation of Engineering Research Center of Nuclear Technology Application,Ministry of Education(No.HJSJYB2017-7)
the Science and Technology Research project of the Jiangxi Provincial Education Department(No.GJJ170481)
the National Natural Science Foundation of China(No.41874126)。
