一种基于谱共轭梯度法的时间域全波形反演

Full waveform inversion in time domain based on spectral conjugate gradient method

针对全波形反演中常规共轭梯度法收敛速度较慢的问题,提出了一种谱共轭梯度法。全波形反演的本质为最小二乘优化,是利用地震波场的全部信息,根据实际数据与正演模拟得到的数据差值建立目标函数。目标函数值越小,则认为正演模型越接近实际的地下构造。全波形反演目前应用较为广泛的是梯度类局部优化反演方法,主要包括最速下降法、共轭梯度法等。通过引入谱变量对共轭梯度法进行改进,在加快收敛速度的同时使收敛更加稳定。将该法应用于频率域声波全波形反演中,并用简单的Marmousi模型进行测试。结果表明,相对于传统的共轭梯度法,谱共轭梯度法能加快收敛速度,深部反演效果更好。

Aiming at the slow convergence speed of the conventional conjugate gradient method in full waveform inversion,a spectral conjugate gradient method is proposed.The essence of full waveform inversion is least square optimization,which uses all the information of seismic wave field to establish the objective function according to the difference between the actual data and the data obtained by forward simulation.The smaller the value of the objective function,the closer the forward model is to the actual underground structure.At present,the gradient local optimization inversion method is widely used in full waveform inversion,mainly including the steepest descent method,conjugate gradient method and so on.By introducing spectral variables to improve the conjugate gradient method,the convergence speed is accelerated and the convergence is more stable.This method is applied to the full waveform inversion of acoustic wave in frequency domain,and tested with a simple Marmousi model.The results show that compared with the traditional conjugate gradient method,the spectral conjugate gradient method can speed up the convergence speed,and the deep inversion effect is better.