基于正交各向异性介质理论的地应力地震预测方法

The in-situ stress seismic prediction method based on the theory of orthorhombic anisotropic media

地应力是评价页岩气储层是否可压裂成网的重要参数.利用地震资料进行地应力参数预测可以根据水平应力差异比(DHSR,Differential Horizontal Stress Ratio)值大小来判断.现阶段计算水平应力差异比主要基于具有对称轴的横向各向同性介质理论,即HTI介质假设,欠缺对页岩中实际大量存在的VTI特征的考虑.本研究同时考虑页岩气地层VTI和HTI特征的作用,利用正交各向异性介质岩石物理关系,推导出水平应力差异比与弹性参数及各向异性参数之间的关系.首先,在分析应力应变本构方程的基础上,对正交各向异性介质(OA)的本构方程进行推导,通过胡克定律一般形式获得正交各向异性介质的应力和应变关系;其次,利用该应力和应变关系推导出最大水平应力、最小水平应力和水平应力差异比与地层弹性参数和各向异性参数的关系并定义了参数正交各向异性水平应力差异比(ODHSR,Orthorhombic Differential Horizontal Stress Ratio);最后,对正交各向异性水平应力差异比ODHSR与具有水平对称轴的横向各向同性介质的DHSR进行了对比,证明了本文的正交各向异性水平应力差异比(ODHSR)计算公式.

Stress is one of the important parameters to evaluate whether the shale gas can be fractured to network or not. DHSR （Differential Horizontal Stress Ratio） is usually utilized for the stress evaluation with seismic data. Currently DHSR is explicated mainly assuming on transverse isotropic media with a horizontal axis of symmetry （HTI media）. However, the actual shale formation owns strong vertical anisotropy. Therefore, based on the theory of orthorhombic anisotropic media, we re-derived the Orthorhombic Differential Horizontal Stress Ratio （Named as ODHSR） in terms of elastic parameters and anisotropic parameters. Firstly, based on the analysis of stress-strain constitutive equation, we derived the constitutive equation of the orthorhombic anisotropic （OA） media and obtained the relationship between the stress and strain of the orthorhombic anisotropic media by the general form of Hooke＇s law. Then, with this relationship, we derived the relational expression of the maximum horizontal stress, minimum horizontal stress and Orthorhombic Differential Horizontal Stress Ratio in terms of elastic parameters and anisotropic parameters. Finally, the novel ODHSR is verified by comparing the curve of ODHSR to DHSR.