Economic gas production from unconventional shale-gas reservoirs requires hydraulic fracturing to reconnect and open existing fractures which are lower than the actual fracture gradient. Estimating sensitive parameters of fractured sweet spots such as effective stress parameter and fracture properties from azimuthal seismic amplitude data can be useful to optimize the development of shale-gas fractured reservoirs. Based on the anisotropic Gassmann’s equation and the relationship between porosity and effective stress, we propose a simplified expression of the saturated stiffness tensor for a horizontal transverse isotropic (HTI) model formed by a single rotationally symmetric set of vertical fractures. Using the perturbation in the stiffness matrix, we derive a linearized reflection coefficient as a function of effective stress parameter and fracture parameters and corresponding Fourier series expression. The sensitivity analysis of Fourier coefficients (FCs) shows that the zeroth FC is sensitive to effective stress parameter, and the second FC is sensitive to fracture parameters. Thus, we propose to estimate the effective stress parameter and fracture weaknesses using a three-step azimuthal FCs inversion involving 1) estimating the FCs using azimuthal seismic data, 2) estimating the effective stress parameter using the zeroth FC, and 3) estimating the normal and tangential fracture weaknesses using the second FC. A synthetic seismic data example reveals that the effective stress parameter and fracture parameters can be reliably estimated even with moderate noise. Test on a real data set implies that the proposed inversion method can generate meaningful results that are useful for identifying abnormal pressure and fractures in reservoirs.

非常规页岩气储层的经济天然气生产需要水力压裂来重新连接和打开低于实际裂缝梯度的现有裂缝。从方位地震振幅数据估计裂缝甜点的敏感参数，例如有效应力参数和裂缝特性，可用于优化页岩气裂缝性储层的开发。基于各向异性 Gassmann 方程以及孔隙度与有效应力之间的关系，我们提出了由一组旋转对称的垂直裂缝形成的水平横向各向同性 (HTI) 模型的饱和刚度张量的简化表达式。使用刚度矩阵中的扰动，我们推导出线性反射系数作为有效应力参数和断裂参数以及相应的傅立叶级数表达式的函数。傅里叶系数(FCs)的敏感性分析表明，第0个FC对有效应力参数敏感，第2个FC对断裂参数敏感。因此，我们建议使用三步方位角 FC 反演来估计有效应力参数和裂缝弱点，包括 1) 使用方位地震数据估计 FC，2) 使用第零个 FC 估计有效应力参数，以及 3) 估计法向和使用第二个 FC 的切向断裂弱点。合成地震数据示例表明，即使在中等噪声的情况下，也可以可靠地估计有效应力参数和裂缝参数。