摘要
有别于传统基于梯度信息的反演方法在正则化约束中用总梯度逼近海塞逆矩阵的技术,本文将正则化约束问题的数据拟合项和模型光滑项分开考虑,只利用数据拟合函数的梯度信息对数据拟合项的海塞矩阵进行逼近,通过求解类高斯牛顿下降方向方程得到不依赖前几次迭代正则化因子的更精确下降方向,在求解当前迭代下降方向的过程中,通过保证右端项中两个向量的二范数在同一数量级的原则,实现了正则化因子的自动更新.对理论模型的试算表明这种自适应正则化反演方案可以在拟牛顿反演框架下基本达到OCCAM的算法稳定性,反演结果对初始模型依赖性较小,同时又无需在一次迭代中多次搜索最佳正则化因子.本文还基于此算法讨论了大地电磁各参数对于反演结果的影响,由于本文的反演结果能得到充分的正则化约束,因而在此框架下讨论阻抗和倾子在反演中的作用相对更为客观.
In a traditional inversion method based on gradient information,the regularization constraint uses the total gradient to approximate the Hessian inverse matrix.This work proposes a new approach different from this method,in which the data misfit and the model roughness items of the regularization constrained problem are considered separately,and only the gradient information of data fitting function is employed to approximate the Hessian matrix.Then by solving the Gaussian-Newton descent direction equation,a more accurate descent direction is determined without relying on the previous iterations of regularization factors.Consequently an adapting regularization parameter can be obtained aiming at maintaining the same numeric levels for normal numbers of both averaged data misfit gradient and model roughness gradient.A synthetic dataset with a very sparse sites and frequencies is calculated by this approach,yielding very stable and reliable results with different initial model settings.These indicate that our method is as stabilized as OCCAM,little relying on initial models.Meanwhile,since only the data misfit and its gradient need to be computed once almost in every iteration.Based on thisalgorithm,this paper also discusses the influence of the magnetotelluric parameters on the inversion results.As the inversion results in this paper can get sufficient regularization constraints,the role of impedance and tipper in the inversion is relatively more objective.
作者
邓琰
汤吉
阮帅
DENG Yan;TANG Ji;RUAN Shuai(State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing 100029, China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2019年第9期3601-3614,共14页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(41674081,41704078)资助
关键词
自适应
正则化因子
有限内存
拟牛顿
大地电磁反演
Adaptive
Regularization parameter
Limit memory
Quasi-Newton
Magnetotelluric inversion
