The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. The models considered here include explicit pore geometry information in determining the poroelastic parameters. They are extensions of the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models to the whole frequency range, based on the Zener model. Knowing the degree of stiffness dispersion between the low- and high-frequency limits, we fit experimental data in the whole frequency range and obtain the average crack aspect ratio and soft porosity as a function of effective pressure. Then, we compute the dispersion and quality factor of the bulk, shear and Young moduli, and the P- and S-wave seismic velocities and quality factors as a function of frequency. However, when measuring axial or volumetric motions along a cylindrical sample, there is fluid flow at the ends of the sample in the experiments considered here. This generates dispersion and attenuation due to axial flow of the pore fluid, which does not occur for a plane wave in unbounded media. This phenomenon is called “drained/undrained transition" Pimienta et al. (J Geophys Res Solid Earth; https://doi.org/10.1002/2017JB014645 , 2017). Actually, it is an axial version of the Biot–Gardner (BG) effect, and implies an “artificial" (mesoscopic) attenuation peak (and dispersion) due to the generation of slow (diffusion) Biot modes at the cylinder boundary, inducing a global flow at the scale of the sample. The classical BG effect is due to fluid flow along the radial direction, on the basis of open-pore conditions at the sides of the sample. In this case, the sides are sealed. To use the EIAS and CPEM models, the BG effect has to be removed to obtain the intrinsic Q of the rock. The models are applied here for measurements on sandstone. The axial BG effect is more evident if the intrinsic attenuation is weak or absent. An example is Lavoux limestone, which has a bimodal porosity distribution, with an equal proportion of intragranular microporosity and intergranular macroporosity (round pores). In this case, the attenuation and dispersion are related to the BG effect, since no squirt flow is detected due to the absence of cracks. We verified that the bulk and Young moduli obtained from the axial and hydrostatic oscillations are consistent with each other, and that the theoretical description of the axial BG effect shows some discrepancies with the data.

中文翻译：

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岩石非弹性、孔隙几何形状和 Biot-Gardner 效应

多孔岩石的弹性特性取决于孔隙特征，特别是孔隙纵横比和孔隙率（与软孔隙度有关）。在高频下，整个孔隙空间没有流体压力交流，岩石变得比低频下更硬，在低频下，孔隙压力完全平衡。此处考虑的模型包括用于确定多孔弹性参数的显式孔隙几何信息。它们是基于齐纳模型的 EIAS（等效夹杂平均应力）和 CPEM（裂纹和孔隙有效介质）模型在整个频率范围内的扩展。知道低频和高频限制之间的刚度分散程度，我们在整个频率范围内拟合实验数据，并获得作为有效压力函数的平均裂纹纵横比和软孔隙率。然后，我们计算体积、剪切和杨氏模量的色散和品质因子，以及作为频率函数的 P 波和 S 波地震速度和品质因子。然而，当测量沿圆柱形样品的轴向或体积运动时，在此处考虑的实验中，样品末端存在流体流动。由于孔隙流体的轴向流动，这会产生弥散和衰减，这对于无界介质中的平面波不会发生。这种现象称为“排水/不排水过渡” Pimienta 等人（J Geophys Res Solid Earth; https://doi.org/10.1002/2017JB014645 , 2017）。实际上，它是 Biot-Gardner (BG ） 影响，衰减和扩散与 BG 效应有关，因为由于没有裂缝，所以没有检测到喷射流。我们验证了从轴向和流体静力振荡获得的体积和杨氏模量彼此一致，并且轴向 BG 效应的理论描述与数据存在一些差异。