Sedimentary rocks are often heterogeneous porous media inherently containing complex distributions of heterogeneities (e.g., fluid patches and cracks). Understanding and modeling their frequency-dependent elastic and adsorption behaviors is of great interest for subsurface rock characterization from multiscale geophysical measurements. The physical parameter of dynamic volumetric strain (DVS) associated with wave-induced fluid flow is proposed to understand the common physics and connections behind known poroelastic models for modeling dispersion behaviors of heterogeneous rocks. We have derived the theoretical formulations of DVS for patchy saturated rock at the mesoscopic scale and cracked porous rock at microscopic grain scales, essentially embodying the wave-induced fluid-pressure relaxation process. By incorporating DVS into the classic Gassmann equation, a simple but practical “dynamic equivalent” modeling approach, the extended Gassmann equation, is developed to characterize the dispersion and attenuation of complex heterogeneous rocks at nonzero frequencies. Using the extended Gassmann equation, the effect of microscopic or mesoscopic heterogeneities with complex distributions on the wave dispersion and attenuation signatures can be captured. Our theoretical framework provides a simple and straightforward analytical methodology to calculate wave dispersion and attenuation in porous rocks with multiple sets of heterogeneities exhibiting complex characteristics. We also demonstrate that, with the appropriate consideration of multiple crack sets and complex fluid patches distribution, the modeling results can better interpret the experimental data sets of dispersion and attenuation for heterogeneous porous rocks.

中文翻译：

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具有动态体积应变的扩展Gassmann方程：建模非均质多孔岩石的波频散和衰减

沉积岩通常是非均质的多孔介质，其固有地包含非均质的复杂分布（例如，流体斑块和裂缝）。对于多尺度地球物理测量中的地下岩石表征，了解和建模它们的频率相关弹性和吸附行为非常重要。提出了与波浪引起的流体流动相关的动态体积应变（DVS）的物理参数，以了解已知的多孔弹性模型背后的常见物理原理和联系，以建模非均质岩石的扩散行为。我们得出了介观尺度上的片状饱和岩石和微观晶粒尺度上的裂隙多孔岩石的DVS的理论公式，基本上体现了波浪引起的流体压力松弛过程。通过将DVS纳入经典的Gassmann方程，开发了一种简单但实用的“动态等效”建模方法，即扩展的Gassmann方程，以表征非零频率下复杂非均质岩石的色散和衰减。使用扩展的Gassmann方程，可以捕获具有复杂分布的微观或介观异质性对波色散和衰减特征的影响。我们的理论框架提供了一种简单直接的分析方法，可以计算具有多组非均质性且表现出复杂特征的多孔岩石中的波频散和衰减。我们还证明，在适当考虑多个裂纹集和复杂流体斑块分布的情况下，