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. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 10⁶ Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements.

中文翻译：

---

喷流地震扩散模型：比较

多孔岩石的非弹性性质取决于孔隙特征，特别是取决于孔隙长宽比和孔隙分数（与软孔隙度有关）。在高频下，整个孔隙空间之间没有流体压力连通，岩石变得比在低频下（孔隙压力完全平衡）的坚硬。这会导致低频和高频模量之间的显着差异，这被称为地震频散，通常通过喷流机理来解释。在本文中，我们考虑并对比了三种喷流扩散模型：修正的Mavko-Jizba模型（适用于具有任意形状的孔隙和裂纹的多孔介质），以及另外两种基于球形和椭圆形理想几何形状的模型：EIAS（等效夹杂物平均应力）和CPEM（裂纹和孔隙有效介质）模型。我们首先执行分析比较，然后计算几个数值示例以证明模型之间的相似性和差异。分析比较表明，当刚性孔为球形且裂纹密度较小时，这三个模型的理论预测非常接近。但是，当硬质孔是长径比小于1（例如在0.2和1之间）的球体时，基于内含物的模型的预测在岩石样品的超声测量频率下无效。相反，改进的Mavko-Jizba模型的预测在大约10的超声频率下有效 我们首先执行分析比较，然后计算几个数值示例以证明模型之间的相似性和差异。分析比较表明，当刚性孔为球形且裂纹密度较小时，这三个模型的理论预测非常接近。但是，当硬质孔是长径比小于1（例如在0.2和1之间）的球体时，基于内含物的模型的预测在岩石样品的超声测量频率下无效。相反，修改后的Mavko–Jizba模型的预测在大约10的超声频率下有效 我们首先执行分析比较，然后计算几个数值示例以证明模型之间的相似性和差异。分析比较表明，当刚性孔为球形且裂纹密度较小时，这三个模型的理论预测非常接近。但是，当硬质孔是长径比小于1（例如在0.2和1之间）的球体时，基于内含物的模型的预测在岩石样品的超声测量频率下无效。相反，修改后的Mavko–Jizba模型的预测在大约10的超声频率下有效 这三个模型的理论预测非常接近。但是，当硬质孔是长径比小于1（例如在0.2和1之间）的球体时，基于内含物的模型的预测在岩石样品的超声测量频率下无效。相反，修改后的Mavko–Jizba模型的预测在大约10的超声频率下有效 这三个模型的理论预测非常接近。但是，当硬质孔是长径比小于1（例如在0.2和1之间）的球体时，基于内含物的模型的预测在岩石样品的超声测量频率下无效。相反，修改后的Mavko–Jizba模型的预测在大约10的超声频率下有效⁶ Hz，这是实验室对核心样品进行测量的典型频率。我们还介绍了基于Zener的体积和剪切分散指数，它们与高频和低频刚度模量之间的差异成比例，并且是非弹性程度的度量，通过Kramers的观点与质量因子密切相关–克罗尼格关系。结果表明，当裂纹密度较高时，这三种模型产生的模量色散相似，差异很小。可以将指数与裂缝密度的关系视为模板，以从低频和高频速度测量获得裂缝特性。