FWI Without Low Frequency Data - Beat Tone Inversion
FWI Without Low Frequency Data - Beat Tone Inversion
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DOI：
10.1190/segam2014-0978.1
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发表时间：
2014-08
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影响因子：
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通讯作者：
Wenyi Hu
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文献类型：
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作者：
Wenyi Hu
受干扰拍音（音乐家常用来进行调音检查的一种现象）的启发，我们开发了一种称为拍子反演的新型全波形反演（FWI）方法，无需低频地震数据即可建立可靠的速度模型。在这种新方法中，通过利用在地下传播的频率略有不同的两个记录的地震波，我们能够从高频地震数据中提取非常低的波数（大尺度结构）分量。传统的FWI算法只能通过低频地震数据反演来获得此类长波长信息。我们为这种新方法设计并研究了两种算法，一种是所谓的幅频微分（AFD）节拍反演，另一种是相位频率微分（PFD）节拍反演。 AFD 算法适用于具有精确振幅测量的传输地震数据。 PFD 是一种更稳健的算法，适用于传输数据和反射数据反演，并且可用于复杂的速度模型构建应用。数学分析和数值实验验证了这种新的FWI算法克服了FWI长期以来存在的难题——跳周期问题。 PFD差拍反演算法的另一个独特且重要的特征是它不需要精确的源估计并且对幅度测量误差不敏感。数值算例表明，对于高频地震数据，拍频反演方法可以生成非常平滑的速度模型，并正确恢复大尺度结构信息。另一方面，如果我们使用传统的FWI算法反演相同频率的地震数据，则会观察到许多由于周期跳跃而产生的伪影，并且反演陷入局部极小值。
Inspired by interference beat tone, a phenomenon commonly used by musicians for tuning check, we developed a novel full waveform inversion (FWI) method called beat inversion for reliable velocity model building without low frequency seismic data. In this new method, by utilizing two recorded seismic waves with slightly different frequencies propagating through subsurface, we are able to extract very low wavenumber (large scale structure) components from high frequency seismic data. With the conventional FWI algorithms, this type of long wavelength information can only be obtained by inverting low frequency seismic data. We designed and investigated two algorithms for this new method, one is the so-called amplitude-frequency differentiation (AFD) beat inversion, and the other is the phase-frequency differentiation (PFD) beat inversion. The AFD algorithm works for transmission seismic data with accurate amplitude measurement. The PFD is a more robust algorithm applicable for both transmission data and reflection data inversion and can be used for complex velocity model building applications. The mathematical analysis and the numerical experiment validate that this new FWI algorithm overcomes the long existing difficulty in FWI – the cycle-skipping issue. Another unique and important feature of the PFD beat inversion algorithm is that it does not require accurate source estimation and it is insensitive to amplitude measurement error. The numerical example shows that, with high frequency seismic data, the beat inversion method produces very smooth velocity model with large scale structural information properly recovered. On the other hand, if we invert the same frequency seismic data using the conventional FWI algorithm, many artifacts arising from cycle-skipping are observed and the inversion is trapped in local minima.