基于方位各向异性的裂缝密度反演方法及应用

裂缝预测是页岩气甜点预测的重要内容.页岩气储层高角度裂缝发育，具有明显的HTI介质各向异性特征，基于各向异性参数与裂缝密度的相关性，提出了一种裂缝密度反演的新方法.首先推导了一种能反映裂缝密度的方位AVO近似公式及其方位弹性阻抗方程（EVAAz方程）；然后应用贝叶斯理论，形成了组稀疏方位弹性阻抗反演目标泛函，在此基础上通过阻尼最小二乘算法求解弹性矩阵，稳健得到了剪切模量、法向弱度与切向弱度；最后应用裂缝弱度与裂缝密度的关系，实现了裂缝密度的定量预测.经实际数据试验，预测结果与页岩压裂参数吻合度高，证实该方法是有效的.

Fracture density inversion based on azimuthal anisotropy and its application

The fracture prediction is an important area in petroleum geophysics. The shale gas reservoir with the vertical fractures can be equivalent to the transverse isotropy with the horizontal symmetry (HTI). In this paper, a new method of fracture density prediction was proposed based on the relationship between the fracture weakness parameters and the fracture density. Firstly, a new azimuthal AVO approximation equation and an azimuthal elastic impedance equation, which reflect the fracture density, were established. Then, an objective function for group-based sparse azimuth elastic impedance inversion was established with the Bayesian theory. On this basis, the stiffness matrix was solved by the damping least square method, and the shear modulus, normal and tangential weakness parameters were obtained. Finally, the relation between the fracture weakness parameters and the fracture density was used to predict the fracture density quantitatively. The reliability of fracture density estimation method was verified using the model and field tests.