基于YPD-Zoeppritz方程的杨氏模量和泊松比直接反演方法

Direct inversion of Young's modulus and Poisson's ratio based on the YPD-Zoeppritz equation

为解决非常规油气勘探中"甜点"的有效识别问题,开展了杨氏模量和泊松比直接反演方法研究。针对Zoeppritz近似方程精度有限的问题,对精确Zoeppritz方程进行重新推导,建立了以杨氏模量、泊松比和密度的自然对数为未知参数的YPD-Zoeppritz方程;在此基础上,结合广义线性反演和贝叶斯理论,引入一阶差分矩阵和三变量柯西分布,构建更为合理的反射系数稀疏约束项,提高了广义线性反演的适定性;引入低频软约束项进一步稳定反演结果的低频成分,提高了反演剖面的横向连续性。模型数据和实际数据试算结果表明,该方法反演精度较高,而且能够逐步压缩子波旁瓣,使反演结果呈现明显的"块化"效果,降低了子波旁瓣对反演结果的影响。基于YPD-Zoeppritz方程的杨氏模量和泊松比直接反演方法适定性强,具有较好的稳定性。

To effectively identify the dessert areas in unconventional oil and gas exploration,a direct inversion method of Young’s modulus and Poisson’s ratio was developed.First,by re-deriving the exact Zoeppritz equation,the YPD-Zoeppritz equation with the natural logarithm of Young’s modulus,Poisson’s ratio,and density as unknown parameters was established.Next,based on generalized linear inversion and Bayesian theory,the first-order differential matrix and the three-variable Cauchy distribution were used to construct a more reasonable sparse constraint term of reflection coefficient,to improve the fitness of generalized linear inversion.Moreover,the low-frequency soft constraint term was introduced for stable inversion of the low-frequency component,to improve the lateral continuity of inversion profile.Testing on both model data and field data indicated that the inversion method could reduce the influence of wavelet side lobes on the inversion results by gradually compressing the wavelet side lobes,thus making the inversion results show an obvious "blocking" effect.The proposed direct inversion method is well-posed and stable.