Intensive studies have been conducted on fluid-related seismic dispersion and attenuation in saturated anisotropic media. Most of the studies are concentrated on the transversely isotropy media. However, the fractures distribution in subsurface reservoirs is often complex. When there are multiple fracture sets developing in a porous background, the signatures of seismic dispersion and attenuation remain unclear. In this paper, we propose a method to calculate the frequency-dependent stiffness matrix of a porous medium with multiple fractures sets from a perspective of viscoelasticity. Due to the favorable approximation performance of the generalized standard linear solid model and Chapman model, we use a modified form of generalized standard linear solid model to simulate the frequency-dependent stiffness tensor of porous media with multiple fracture sets. The representation of the stiffness tensor utilizes the modulus defect to denote the effects the fractures including fracture density and geometry. With the procedure of calculating the stiffness tensors at low- and high-frequency limits, we can easily calculate the frequency-dependent stiffness tensor for media with multiple fracture sets with arbitrary orientations and directions. We then analyze the effects of the fracture parameters on the viscoelasticity characteristics taking orthotropic medium as an example. The results can help to understand the viscoelasticity and the mesoscopic seismic attenuation associated with fractures and fluids and can provide a practical rock physics model when dealing with reservoirs with complex fracture patterns.

已经对饱和各向异性介质中与流体有关的地震频散和衰减进行了深入研究。大多数研究集中在横向各向同性介质上。但是，地下储层中的裂缝分布通常很复杂。当在多孔背景中出现多个裂缝集时，地震扩散和衰减的特征仍然不清楚。在本文中，我们提出了一种从粘弹性角度计算具有多个裂缝的多孔介质的频率相关刚度矩阵的方法。由于广义标准线性实体模型和Chapman模型具有良好的近似性能，我们使用广义标准线性实体模型的改进形式来模拟具有多个裂缝集的多孔介质的频率相关刚度张量。刚度张量的表示利用模量缺陷来表示裂缝的影响，包括裂缝密度和几何形状。通过计算低频和高频极限下的刚度张量的过程，我们可以轻松地计算出具有多个方向和方向任意的多个断裂集的介质的频率相关刚度张量。然后，以正交各向异性介质为例，分析断裂参数对粘弹性特性的影响。