Modeling Frequency‐Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media
Modeling Frequency‐Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media
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DOI：
10.1029/2019jb017985
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
G. Xing;T. Zhu
中科院分区：
文献类型：
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作者：
G. Xing;T. Zhu
量化地震波在地球内部传播的衰减对于研究地下结构至关重要。以前的研究提出了分数滞弹性波方程来模拟与频率无关的Q地震波传播。这种波动方程涉及分数阶导数，在处理非均匀地球介质时，在精度和效率方面对数值方案提出了计算挑战。为了解决这些挑战，在这里，我们推导出一个新的粘声波方程，其中分数拉普拉斯算子的幂项是空间独立的，因此准确和有效的方法（例如，傅立叶伪谱方法）。我们的推导使所得到的方程，以捕捉振幅和相位签名的滞弹性波传播匹配的复波数为所有的频率感兴趣。我们通过比较新波动方程产生的衰减因子和相速度的频散曲线与它们的理论值以及Pierre Shale现场测量值来验证推导。在此基础上，我们使用合成衰减气烟囱模型来演示衰减对地震波形的影响，然后构造Q补偿逆时偏移来消除这些影响，用于地震图像增强。最后，我们发现，我们的正演模拟结果可以表征的时空衰减效应中揭示的Frio-II CO2注入时移地震监测数据。我们希望这个公式可以用来量化地震数据中的衰减，以推动地震成像和反演的分辨率极限。
Quantifying the attenuation of seismic waves propagating in the Earth interior is critical to study the subsurface structure. Previous studies have proposed fractional anelastic wave equations to model the frequency‐independent Q seismic wave propagation. Such wave equations involve fractional derivatives that pose computational challenges for the numerical schemes in terms of accuracy and efficiency when dealing with heterogeneous Earth media. To tackle these challenges, here we derive a new viscoacoustic wave equation, where the power terms of the fractional Laplacian operators are spatially independent, thus accurate and efficient methods (e.g., the Fourier pseudospectral method) can be adopted. Our derivation enables the resultant equation to capture both amplitude and phase signatures of the anelastic wave propagation by matching the complex wave numbers for all the frequencies of interest. We verify the derivation by comparing the dispersion curves of both the attenuation factor and the phase velocity produced by the new wave equation with their theoretical values as well as the Pierre Shale in situ measurements. Following that, we use a synthetic attenuating gas chimney model to demonstrate the attenuation effects on seismic waveforms and then construct the Q‐compensated reverse time migration to undo these effects for seismic image enhancement. Finally, we find that our forward modeling results can characterize the spatiotemporal attenuation effects revealed in the Frio‐II CO2 injection time‐lapse seismic monitoring data. We expect this proposed equation to be useful to quantify the attenuation in seismic data to push the resolution limits of seismic imaging and inversion.