Fractures are ubiquitous in rock and therefore considerably affect the overall mechanical properties of rock. In this study, effective medium theory is used to analyze the reflection characteristics of elastic waves in thin-beds containing aligned fractures. First, elastic parameters are obtained for a single thin bed containing discrete vertical fractures. Then, an exact solution is derived for the reflection coefficient of elastic waves in horizontally transverse isotropic (HTI) thin-beds using the propagation matrix method. Next, the effects of the fracture density and fillings on the reflection pattern are analyzed. Thin-beds without fractures are equivalent to a vertically transverse isotropic (VTI) medium in the long-wavelength limit. The introduction of vertical fractures makes thin-beds equivalent to a single thin bed in an orthorhombic anisotropic (ORT) medium (where the thickness of ORT thin bed is the total thickness of the original thin-beds). The ORT model of fractured thin-beds is presented by the equivalent medium theory. The results obtained using the HTI thin-beds and ORT models are compared, and the influences of the ORT model accuracy and formation parameters (such as thickness-to-wavelength ratio of a single thin bed, total thickness of thin-beds, etc.) on the ORT approximation results are analyzed. The response characteristics of elastic waves in complex thin-beds with fractures determined in this study can give an important guidance to real applications in geophysics and rock mechanics.

裂缝在岩石中普遍存在，因此对岩石的整体力学性能影响很大。本研究利用有效介质理论分析弹性波在含排列裂缝的薄层中的反射特性。首先，获得包含离散垂直裂缝的单个薄层的弹性参数。然后，使用传播矩阵法推导了水平横向各向同性 (HTI) 薄层中弹性波的反射系数的精确解。接下来，分析裂缝密度和充填对反射模式的影响。没有裂缝的薄层在长波极限下相当于垂直横向各向同性 (VTI) 介质。垂直裂缝的引入使得薄层相当于正交各向异性（ORT）介质中的单个薄层（其中 ORT 薄层的厚度是原始薄层的总厚度）。利用等效介质理论提出了裂隙薄层的ORT模型。对比了HTI薄层模型和ORT模型得到的结果，比较了ORT模型精度和地层参数（如单个薄层厚波比、薄层总厚度等）的影响。 ) 对 ORT 近似结果进行了分析。本研究确定的含裂缝复杂薄层中的弹性波响应特征对地球物理学和岩石力学的实际应用具有重要指导作用。