一阶近似瞬时频率时间域声波全波形反演

通过全波形反演（FWI）在理论上可得到较高精度的深层速度模型，而在实际中相关条件却难以完全具备。究其原因主要为：FWI对初始速度模型的依赖性强；深层信号弱，在目标函数中的贡献较小。为此，提出基于一阶近似瞬时频率的时间域声波FWI方法。根据瞬时相位公式推导出一阶近似瞬时频率的目标函数和伴随震源项公式；充分发挥瞬时频率可突出低频信息和深层弱信号的特点，为FWI建立初始速度模型；同时加入梯度衰减因子以进一步提高深层反演效果、防止深浅层间互相干涉。模型和实际资料测试证明了该方法的可行性和有效性。

Full waveform inversion of time-domain acoustic wave based on first-order approximate instantaneous frequency

A deep velocity model with high accuracy can be obtained by full waveform inversion (FWI) in theory.However,it is difficult to find underground conditions in actual exploration.This is because that,on the one hand,full waveform inversion is strongly dependent on the initial velocity model；and on the other hand,deep signals are weak，and their contribution to the objective function is small.This paper proposes time-domain full waveform inversion based on first-order approximate instantaneous frequency.First,according to the instantaneous phase formula， the objective function and the adjoint source term formula of the first-order approximate instantaneous frequency are derived； Then the initial velocity model for full waveform inversion is established by making full use of the advantage of the instantaneous frequency to highlight low frequency information and deep weak signals.Finally,a gradient attenuation factor is added to further improve the effect of deep inversion and prevent the interference between deep and shallow layers.The feasibility and validity of the method have been proved by model and real data.