Geological and geophysical data acquired from naturally fractured hydrocarbon reservoirs usually exhibit the presence of multiple sets of fractures. Two different nonorthorhombic sets of fractures embedded in isotropic background rocks can reveal the anisotropic characteristics of monoclinic symmetry with a horizontal symmetry plane. Here, we focus on the modeling and inversion of the effective elastic properties in fractured reservoirs with monoclinic symmetry induced by a set of horizontal fractures and a set of tilted fractures with rotationally invariant properties embedded in purely isotropic host rock. To facilitate the seismic characterization of fractured reservoirs with monoclinic symmetry, we introduce two sets of fracture weakness parameters to replace the Thomsen-type anisotropic parameters and describe these two nonorthogonal sets of rotationally invariant fractures. With the incident and reflected P wave in such a monoclinic anisotropic medium, we perform the seismic characterization of two nonorthogonal sets of rotationally invariant fractures based on the reflected amplitudes variation with offset and azimuth (AVOAz). Using the linear-slip theory, we first derive the effective elastic stiffness tensor as a function of background isotropic elastic moduli, normal and shear weakness parameters of horizontal and tilted fractures, and the dip angle. We then derive the first-order perturbations in elastic stiffness tensor and formulate the linearized PP-wave reflection coefficient based on the seismic scattering theory. Next, we propose a robust AVOAz inversion approach to characterize these two nonorthogonal fractures with rotationally invariant fractures. Finally, synthetic and real data examples are used to demonstrate that the background elastic moduli and fracture properties can be reasonably estimated using the azimuthal seismic reflected amplitudes. The new formulation and inversion approach may provide us a useful tool to characterize the naturally fractured reservoirs with monoclinic symmetry induced by horizontal and tilted fractures in a more reasonable manner than previous method.

从天然裂缝性油气藏获得的地质和地球物理数据通常表现出多组裂缝的存在。嵌入各向同性背景岩石中的两组不同的非斜方裂缝可以揭示具有水平对称面的单斜对称的各向异性特征。在这里，我们专注于由一组水平裂缝和一组具有旋转不变性质的倾斜裂缝引起的单斜对称裂缝储层的有效弹性性质的建模和反演，这些裂缝具有嵌入在纯各向同性母岩中的旋转不变性质。为了便于对具有单斜对称性的裂缝性储层进行地震表征，我们引入两组断裂弱点参数来代替汤姆森型各向异性参数，并描述这两组非正交旋转不变断裂。利用这种单斜各向异性介质中的入射和反射 P 波，我们基于反射幅度随偏移和方位角 (AVOAz) 的变化对两组非正交旋转不变裂缝进行地震表征。使用线性滑移理论，我们首先导出有效弹性刚度张量作为背景各向同性弹性模量、水平和倾斜裂缝的法向和剪切弱参数以及倾角的函数。然后，我们推导出弹性刚度张量的一阶扰动，并基于地震散射理论制定线性化 PP 波反射系数。下一个，我们提出了一种稳健的 AVOAz 反演方法来表征这两个具有旋转不变骨折的非正交骨折。最后，利用合成数据和真实数据示例证明，利用方位地震反射幅度可以合理地估计背景弹性模量和裂缝特性。新的公式和反演方法可以为我们提供一个有用的工具，以比以前的方法更合理的方式表征水平和倾斜裂缝引起的具有单斜对称性的天然裂缝储层。合成和真实数据示例用于证明使用方位地震反射幅度可以合理估计背景弹性模量和裂缝特性。新的公式和反演方法可以为我们提供一个有用的工具，以比以前的方法更合理的方式表征水平和倾斜裂缝引起的具有单斜对称性的天然裂缝储层。合成和真实数据示例用于证明使用方位地震反射幅度可以合理估计背景弹性模量和裂缝特性。新的公式和反演方法可以为我们提供一个有用的工具，以比以前的方法更合理的方式表征水平和倾斜裂缝引起的具有单斜对称性的天然裂缝储层。