互相关与最小二乘加权目标函数全波形反演

摘要

Full waveform inversion(FWI)is a highly non-linear optimization problem.When there is a lack of low-frequency components in the seismic data and the initial velocity is far from the true velocity,it is easily trapped into local minima.The authors propose a new objective function that combines the normalized cross-correlation of modeled and observed data with the least squares criterion.Cross-correlation emphasizes on phase matching and behaves in a more linear way,thus can mitigate the cycle-skipping issue.By setting a weighting factor,the authors use the cross-correlation norm to update the low-wave number components of the velocity model at the early stage of the inversion,while using the least squares criterion to update high-wave number details of the model.Numerical examples show that FWI based on the new objective function converges quickly toward global minima and does not rely on accurate initial velocity model as well as low-frequency information,it can improve the robustness of the inversion and generate more accurate inversion results than the conventional approach.%全波形反演是一个高度非线性的优化问题,当地震数据中缺少低频成分而初始速度与真实速度相差较远时,反演容易陷入局部极小值.笔者提出一种新的目标函数,将模拟地震记录和观测记录的归一化互相关与最小二乘结合.互相关侧重相位匹配,具有更强的线性,能减弱"跳周"现象.通过设置权重因子,在反演前期利用互相关先恢复低波数的背景速度模型,再加入最小二乘约束恢复高波数的模型细节.数值模拟试验结果表明,基于该目标函数的全波形反演不依赖精确的初始模型和低频信息,向全局极小值迅速收敛,能有效改善反演的稳定性,并获得比基于常规目标函数的全波形反演更精确的结果.