摘要
全波形反演能够利用地震波场信息进行高分辨率地下介质速度建模,具有精确刻画模型细节特征的潜力.传统的全波形反演以L2范数作为目标函数,逐样本比较观测地震数据和合成地震数据之间差异,利用伴随状态法求解梯度.由于全波形反演是高度非线性的,当初始模型不准确时,反演结果容易陷入局部极小值.本文提出使用具有全局比较能力的图空间最优输运Sinkhorn距离作为目标函数.图空间Sinkhorn距离对信号时移和振幅变化具有较好的凸性,能够解决反演过程中的周期跳变问题.利用理论指导的数据科学算法将全波形反演问题转化为深度学习优化问题,偏微分方程约束用于优化波动方程中表征介质地球物理性质的模型参数.反演过程中采用自动微分计算梯度,并利用Adam优化算法对模型进行更新.模型测试结果表明本文方法能够取得较好的反演结果,并且具有较强的噪声鲁棒性,对于震源子波和初始模型的依赖性较低.
Full waveform inversion(FWI)is able to model the velocity of high-resolution subsurface medium by using the seismic wavefield information,and has the potential to accurately describe the detailed characteristics of the model.The conventional FWI takes the L2 norm as the objective function to compare the differences between observed and synthetic seismic data and uses the adjoint state method to solve the gradient.FWI is highly nonlinear and tends to fall into local minimum when the initial model is inaccurate.This paper proposes the optimal transport Sinkhorn distance with global comparison capability as the objective function.The graph space Sinkhorn distance has desirable convexity to time shift and amplitude change,which can effectively address cycle-skipping and improve the inversion result.By using the theory-guided data science algorithm,the FWI can be transformed into the deep learning optimization problem.The partial differential equation constraint is used to optimize the model parameters in the wave equation to characterize the geophysical properties of the medium.The inversion gradient is calculated by automatic differentiation,and the model is updated by Adam optimization algorithm.The model test results show that the method can obtain good inversion results and has strong noise robustness,less dependence on the seismic wavelet and the initial model.
作者
唐杰
孟涛
刘英昌
孙成禹
TANG Jie;MENG Tao;LIU YingChang;SUN ChengYu(School of Geosciences,China University of Petroleum(East China),Qingdao Shandong 266580,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2022年第7期2704-2718,共15页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(41504097,42174140)资助.
关键词
全波形反演
最优输运
图空间变换
Sinkhorn距离
自动微分
Full waveform inversion
Optimal transport
Graph space transform
Sinkhorn distance
Automatic differentiation
