SUMMARY Most researches on the Biot-squirt (BISQ) model are limited to the poroelastic transverse isotropic (TI) media. Actually, the poro-viscoelasticity and the orthorhombic anisotropy are closer to the realistic properties of many reservoir media. Therefore, we expand the BISQ model theory to the poro-viscoelastic orthorhombic media and develop the corresponding constitutive relation and 3-D wave equations in the time domain. Here, the generalized Zener linear body model is introduced to describe the relaxation effect of the solid skeleton, and the pore fluid is assumed to be saturated. The expressions of the complex and phase velocities for two quasi-compressional waves qP fast (qP1) and qP slow (qP2), and two quasi-shear waves qS1 and qS2 are obtained from the homogeneous plane-wave analysis, respectively. While introducing the viscoelasticity to our model, the attenuation value predicted by the conventional quality factor is not accurate, and the group velocity representing the position of the wave front in the poroelastic model becomes meaningless. So we derive the novel quality factor and the energy velocity expression by invoking the energy balance equation and the Poynting theorem. Two examples are implemented. First, the 3-D multicomponent wavefield is simulated. The snapshots show the orthorhombic anisotropy and viscoelastic effects lead to significant changes in the wavefield. The comparison to the synthetic seismogram in the poroelastic model indicates that the relaxed skeleton can describe the strong attenuation of seismic waves in the seismic exploration band. Secondly, the variations in the velocities and the quality factor curves with propagation direction, frequency and porosity are analysed. Both examples present the characteristics of wave propagation in the poro-viscoelastic orthorhombic media and validate the correctness of the proposed theory and equations.

中文翻译：

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多孔粘弹性正交两相介质中的波传播：平面波理论和波场模拟

总结 大多数关于 Biot-squirt (BISQ) 模型的研究仅限于多孔弹性横向各向同性 (TI) 介质。实际上，孔隙粘弹性和正交各向异性更接近许多储层介质的实际性质。因此，我们将 BISQ 模型理论扩展到多孔粘弹性正交介质，并在时域中开发了相应的本构关系和 3-D 波动方程。这里引入广义齐纳线体模型来描述固体骨架的弛豫效应，假设孔隙流体是饱和的。通过均质平面波分析，分别得到了两个准压缩波qP快（qP1）和qP慢（qP2）和两个准剪切波qS1和qS2的复数和相速表达式。在将粘弹性引入我们的模型时，常规品质因数预测的衰减值并不准确，代表波前位置的群速度在多孔弹性模型中变得毫无意义。因此我们通过调用能量平衡方程和坡印廷定理推导出了新的品质因数和能量速度表达式。实现了两个示例。首先，模拟 3-D 多分量波场。快照显示正交各向异性和粘弹性效应导致波场发生显着变化。与多孔弹性模型中合成地震图的对比表明，松弛骨架可以描述地震勘探波段中地震波的强烈衰减。其次，分析了速度和品质因数曲线随传播方向、频率和孔隙率的变化。这两个例子都展示了波在多孔粘弹性正交介质中的传播特性，并验证了所提出的理论和方程的正确性。