基于新的惩罚因子算法的波场重构反演

Time domain wavefield reconstruction inversion based on new penalty scalar algorithm

全波形反演是一种高精度的反演方法,其目标函数是一个强非线性函数,易受局部极值影响,而且反演过程计算量较大.波场重构反演是近几年提出的一种改进的全波形反演理论.该反演方法通过将波动方程作为惩罚项引入到目标函数中,通过拓宽解的寻找空间减弱了局部极小值的影响,而且反演过程不需要计算伴随波场,提高了计算效率.但该反演方法一直缺少准确的惩罚因子算法,直接影响到该方法的准确度.本文将波场重构反演拓展到时间域并利用梯度法进行波场重构.频率域的惩罚因子用来加强波动方程的约束,而时间域惩罚因子表现为调节模拟波场和实际波场的权重因子.为此,我们根据约束优化理论,在波动方程准确以及重构波场与反演参数解耦的假设下,提出以波动方程为目标函数的新的惩罚因子算法.根据波形反演在应用时普遍存在的噪音干扰、子波错误和低频信息缺失的情况下,应用部分Sigsbee2A模型合成数据对本文提出的算法进行实验.数值实验结果表明:基于新的惩罚因子算法,在其他信息不准确的情况下,波场重构反演可以给出高精度的反演结果.

Wavefield reconstruction inversion(WRI)is a novel waveform inversion theory proposed in recent years.The objective function of WRI consists of a misfit term and a penalty term,which measures how accurately the wavefields satisfy wave equation.WRI can update model parameters by reconstructing the wavefield through relaxing wave equation constraint without any adjoint wavefield,which greatly improved the computational efficiency.By expanding the search space,WRI can overcome some of the local minimum problems.As for the penalty scalar used to neutralize the magnitude between synthetic data and observed data,there is still a lack of efficient algorithm.Due to various causes of the differences between observed data and modeling data,a flexible and accurate penalty parameter is significant for the inversion stability.To this end,we extend WRI into the time domain and reconstruct the wavefield with gradient method.Time domain augmented wave equation shows that penalty scalar combines observed wavefield and synthetic wavefield in a limited range instead of penalizing any departure from the wave equation constraint in the frequency domain.Hence,we propose an efficient penalty parameter algorithm based on constraint optimization theory.The calculation of the penalty scalar is essentially trying to rebuild true wavefield by combining synthetic data and observed data.When the observed data contain noises or lack low-frequency information,or the seismic wavelet is inaccurate,WRI can still provide a stable and accurate result by adjust the different weight of synthetic data and observed data.Numerical results show the accuracy of time domain WRI and proposed penalty parameter algorithm.Furthermore,we also test the sensitivity of proposed algorithm for noise interference,wrong wavelet and missing low-frequency information respectively and obtain reliable results.