基于共轭梯度法的全波形反演

全波形反演是一种全新的地震成像方法，主要利用全波形信息反演地下介质参数，通过非线性优化波场理论值和观测值的残差实现波形反演。基于时间域声波方程，建立了时间域波场残差目标函数，以分层模型为例，分别从波场精度、目标函数收敛性和运行时间3个方面，比较了共轭梯度（Conjugate Gradient，CG）算法和拟牛顿算法（Broyden-Fletcher-Goldfarb-Shanno，BFGS）反演的效果。同时，应用共轭梯度法对正、逆断层模型和Marmousi模型进行了速度结构反演。反演结果表明：共轭梯度法计算效率较高，反演得到的速度模型精度更高，反演效果较好，是一种有效的波形反演方法。

Full waveform inversion based on the conjugate gradient method

Full waveform inversion is a new seismic imaging method, which mainly uses full waveform information to inverse parameters of medium in the subsurface, and realizes waveform inversion by minimizing the residual between observed wavefield and theoretical wavefield using nonlinear optimization methods. The objective function of wavefield residual was established based on time domain acoustic wave equation. To test the capability of conjugate gradient(CG) algorithm and BFGS Quasi-Newton algorithm, waveform inversion was applied to a hierarchical model. The inversion effect was compared from wavefield precision, objective function convergence and running time respectively. The CG method was used to reconstruct velocity model on positive, reverse fault and Marmousi models. The inversion results show that the CG method has higher computation efficiency and inversion precision. The CG method is a promising method for full waveform inversion.