不依赖子波、基于包络的FWI初始模型建立方法研究

地震全波形反演(FWI)从理论走向实际面临着诸多难题,其中之一就是需要一个较高精度的初始模型,另一个难题就是需要一个较为精确的震源子波,初始模型和震源子波的准确程度严重影响着全波形反演的最终结果.为此,本文提出了不依赖子波、基于包络的FWI初始模型建立的方法,建立了相应的目标函数,推导出了反演的梯度,给出了伴随震源的表达式,理论上分析了不依赖子波FWI的可行性.在数值试验中,讨论了参考道的选取方式,通过分析归一化目标函数收敛速率,认为近偏移距参考道优于远偏移距参考道,在地震数据含干扰噪音时,平均道作为参考道要优于最小偏移距参考道.通过包络、包络对数、包络平方三种目标函数反演结果的比较,发现包络对数目标函数对深层的反演效果最好.通过不同子波的试验进一步验证了本方法的正确性.

Source-independent envelope-based FWI to build an initial model

Full waveform inversion (FWI) is facing many difficulties in practice. One of the issues is how to construct a relatively precise initial model. Another one is the treatment of source wavelet. Both seriously affect the final inversion result. To tackle this problem, we propose a source-independent envelope-based FWI approach to build an initial model for the traditional FWI.On one hand, the cross-convolved wavefields, including the convolution of observed wavefields with a reference trace from the modeled wavefields and the convolution of modeled wavefields with a reference trace from the observed wavefields, can eliminate source wavelet effect in the misfit function of waveform inversion.On the other hand, the envelope of wavefields contains abundant low-frequency components, which are crucial for initial model inversion. Therefore, we use the envelope of cross-convolved wavefields to establish misfit functions, the feasibility of which is proved by theoretical analysis. The expressions of the corresponding gradient and adjoint source are derived. Furthermore, we use a Marmousi synthetic data example to test our method.The proposed method is tested by using different reference traces, misfit functions and source wavelets. (1) The normalized misfit of long offset reference trace converges more slowly than that of short-offset reference trace for noise-free data and the average trace as reference trace is better than the minimum-offset reference trace for noisy data. (2) The logarithmic envelope is the best and the squared envelope is the worst misfit function to invert the deep part of the model. The initial model built by our method choosing the logarithmic misfit function and minimum-offset reference trace is much better than that of the traditional envelope-based FWI when the source wavelet is incorrect. (3) Using other kinds of source wavelets, such as 20 Hz Ricker wavelet without low frequency below 5 Hz and 12 Hz Gauss wavelet, both of which are quite different from the true 8 Hz Ricker wavelet, the inversion result of our method can provide a good initial model for the traditional FWI. In addition, the initial model can be used in seismic depth migration, and the imaging result is close to the RTM result with true velocity model and much better than that with gradient initial model.In conclusion, first, we propose a source-independent envelope-based FWI approach to build an initial model for the traditional FWI without any prior information when the source wavelet is unknown and even the data lack low frequency. The initial model built by our method can also be used as the velocity model for pre-stack depth migration. Second, the short-offset reference trace is better than long-offset reference trace for noise-free data and average trace as reference trace is better than the minimum-offset reference trace for noisy data. Third, the logarithmic envelope misfit function is the optimal misfit function. Finally, by changing the source wavelet, it is further proved that our method is source-independent.