We have developed a workflow for computing the seismic-wave moduli dispersion and attenuation due to squirt flow in a numerical model derived from a micro X-ray computed tomography image of cracked (through thermal treatment) Carrara marble sample. To generate the numerical model, the image is processed, segmented, and meshed. The finite-element method is adopted to solve the linearized, quasistatic Navier-Stokes equations describing laminar flow of a compressible viscous fluid inside the cracks coupled with the quasistatic Lamé-Navier equations for the solid phase. We compute the effective P- and S-wave moduli in the three Cartesian directions for a model in dry conditions (saturated with air) and for a smaller model fully saturated with glycerin and having either drained or undrained boundary conditions. For the model saturated with glycerin, the results indicate significant and frequency-dependent P- and S-wave attenuation and the corresponding dispersion caused by squirt flow. Squirt flow occurs in response to fluid pressure gradients induced in the cracks by the imposed deformations. Our digital rock-physics workflow can be used to interpret laboratory measurements of attenuation using images of the rock sample.

中文翻译：

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数字岩石物理应用于喷射流

我们开发了一个工作流程，用于计算由于喷流引起的地震波模量色散和衰减，数值模型源自裂纹（通过热处理）卡拉拉大理石样品的微 X 射线计算机断层扫描图像。为了生成数值模型，对图像进行处理、分割和网格划分。采用有限元方法求解描述裂缝内可压缩粘性流体层流的线性准静态 Navier-Stokes 方程以及固相的准静态 Lamé-Navier 方程。我们计算了干燥条件下模型（空气饱和）和甘油完全饱和且具有排水或不排水边界条件的较小模型在三个笛卡尔方向上的有效 P 波和 S 波模量。对于甘油饱和的模型，结果表明喷流引起的显着的和频率相关的 P 波和 S 波衰减以及相应的色散。喷射流响应于由强加变形在裂缝中引起的流体压力梯度而发生。我们的数字岩石物理学工作流程可用于使用岩石样品的图像来解释衰减的实验室测量值。