ABSTRACT The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.

中文翻译：

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简化多孔弹性理论中岩石物理参数对地震波衰减和频散的影响

摘要 基于 Hickey 理论，在忽略热机械耦合的影响以及通过波引起的孔隙度和密度波动的基础上，提出了多孔弹性介质的简化宏观方程。具有确定物理参数的宏观方程预测两种类型的压缩波（P波）和两种类型的剪切波（S波）。第一类 P 波和 S 波与 Biot 理论中的快 P 波和 S 波类似，传播速度快，色散和衰减相对较弱，而第二类波由于其明显的色散和衰减而表现为扩散模式。强衰减。由孔隙流体中的体积和剪切粘性损失引起的第二个 S 波比第二个 P 波慢，但在较低频率下有很强的衰减。基于简化的多孔弹性方程，对比Biot理论结果，研究了在饱和盐水砂岩中岩石物理参数（渗透率、孔隙度、耦合密度和流体粘度）对P波和S波速度频散和衰减的影响。结果表明，由于孔隙流体中存在体积和剪切粘性损失，简化理论中P波的色散和衰减比Biot理论强，并且出现在略低的频率上。第一个S波的性质与Biot理论中的S波几乎一致，而Biot理论中未包含的第二个S波由于衰减极强，甚至在其源头周围消失。渗透率和孔隙度对 P 波和 S 波的速度色散和衰减都有明显的影响。较高的磁导率使衰减峰值向较低频率移动。较高的孔隙率对应于较高的色散和衰减。此外，流体和固体之间的惯性耦合导致 P 波和 S 波在较高频率下的速度色散和衰减较弱，而流体粘度在宏观多孔介质中主导色散和衰减。此外，还利用稠油砂研究了高粘性流体对纵横波的弥散和衰减的影响。由于稠油具有相当大的剪切粘度，在稠油砂岩中的弥散和衰减比在盐水饱和砂岩中强。抗震特性受流体粘度的影响很大；因此，粘度应包含在流体特性中，以正确解释固-流体组合行为。