基于小波域最小平方滤波的多尺度自适应全波形反演

Multi-scales adaptive full waveform inversion based on the wavelet domain least square filter

常规的全波形反演对初始模型和低频数据的依赖性较强,反演精确度经常会受到"跳周"现象的严重影响。将小波域最小平方滤波引入到全波形反演中,并利用小波变换的多尺度特性,有效地提高了反演过程的稳定性,减小反演受到"跳周"现象影响的可能性。小波域最小平方滤波具有更高的精度和更好的性能,利用该算法调整模拟波场的相位,从而改善模拟波场和观测波场之间的相位差异,并由此构造一个新的目标函数。同时利用小波变换的多尺度特性将地震数据分解为不同频带数据,实现多尺度反演。数值模拟实验结果表明,基于小波域最小平方滤波的多尺度自适应全波形反演,对初始模型和低频数据的依赖程度降低,较常规全波形反演具有更好的稳定性,受到"跳周"现象影响的可能性大大降低。

Conventional full waveform inversion（FWI）has a strong dependence on the initial model and low frequency data,it is often suffers from cycle skipping when this two conditions are not met.In order to solve the problem,we introduced the wavelet domain least square filter to FWI,and took advantage of the multiscale characteristic of the wavelet transform.It can effectively avoid the influence of cycle skipping in the inversion procedure,and improves the stability of FWI.Wavelet domain least square filter has the higher accuracy than the time domain,with this can narrow the phase difference between the predicted data and observed data,and construct a new objective function,to make the inversion procedure steadily converge to the global minimum.Meanwhile,with the multi-scales characteristic of wavelet transform,the data can be divided into different frequency bands,and implement the multi-scales inversion.The result of numerical simulation experiment demonstrates that multi-scales adaptive FWI based on the wavelet transform is much less dependent on initial model and low-frequency data.The method can be immune to cycle skipping,and more robust than conventional FWI.