Low-frequency shadows are frequently interpreted as attenuation phenomena due to partial saturation with free gas. However, several researchers have argued that shadows are not necessarily a simple attenuation phenomenon because low-frequency energy must have been added or amplified by some physical or numerical process. Attenuation alone should attenuate higher frequencies, not boost lower frequencies. The physical or numerical effects explaining this phenomenon are still debatable in the literature. To better understand the elastic wave energy’s spectral changes in partially saturated rock, we have considered the hysteresis of liquid bridges phenomena inside the crack. We determine that liquid bridges’ hysteresis leads to the nonlinear energy exchange between frequencies, explaining the wave energy boost at lower frequencies. We find that the energy exchange between different frequencies depends on the wave amplitude and the seismic wave spectrum. The low-frequency energy boost is stronger for a continuous spectrum of seismic waves, smaller for the discrete spectrum, and zero for the monochromatic spectrum of seismic waves. In addition, we find that at seismic frequencies, the attenuation 1/Q-factor due to the friction of the contact line can be much larger than the attenuation due to viscous fluid flow inside the partially saturated crack. Our model depends on the wave amplitude and weakly depends on the wave frequency. The suggested model can help interpret the low-frequency shadows, bright spots, and attenuation anomalies frequently observed around hydrocarbon fields.

中文翻译：

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液桥滞后现象引起的部分饱和裂纹对地震波能量谱变化的影响

由于游离气体的部分饱和，低频阴影经常被解释为衰减现象。但是，一些研究人员认为，阴影不一定是简单的衰减现象，因为低频能量必须通过某种物理或数值过程来添加或放大。单独的衰减应该衰减较高的频率，而不是增加较低的频率。解释这种现象的物理或数字效应在文献中仍值得商de。为了更好地理解部分饱和岩石中弹性波能量的频谱变化，我们考虑了裂缝内部液桥现象的滞后现象。我们确定液桥的磁滞导致频率之间的非线性能量交换，从而解释了在较低频率下波能的增强。我们发现，不同频率之间的能量交换取决于波幅和地震波谱。低频能量提升对于地震波的连续频谱更强，对于离散频谱较小，对于地震波的单色频谱为零。此外，我们发现在地震频率处，衰减1 /由于接触线的摩擦而产生的Q因子可能比由于部分饱和裂缝内部的粘性流体流动引起的衰减大得多。我们的模型取决于波幅，而弱取决于波频率。建议的模型可以帮助解释在油气田周围经常观察到的低频阴影，亮点和衰减异常。