基于高斯混合模型的碳酸盐岩储层物性与孔隙参数地震岩石物理同步反演

Seismic rock-physics simultaneous inversion for petrophysical and pore parameters of carbonate reservoirs with Gaussian mixture model

碳酸盐岩储层是我国油气资源增储上产的重要领域,然而此类储层通常发育复杂的孔隙结构,极易影响物性参数地震预测结果的精度.本文提出一种基于高斯混合模型的物性与孔隙参数地震岩石物理同步反演方法.基于微分有效介质模型和Gassmann方程,推导定量关联孔隙度、流体饱和度及孔隙纵横比与弹性参数的线性正演算子.引入了高斯混合模型表征物性与孔隙参数的联合先验概率分布,进而表征岩相统计差异特征.基于贝叶斯线性反演理论及线性正演算子,构建目标参数后验概率的解析表达式,然后根据测井数据反演井旁孔隙纵横比,以提供可靠的孔隙参数先验约束,并利用迭代贝叶斯反演算法,提高线性正演算子的模拟精度.本方法将孔隙纵横比作为反演目标参数,表征碳酸盐岩孔隙结构的空间变化特征,结合贝叶斯线性反演方法,以提高物性参数地震反演结果的精度与运算效率.数据测试表明,所提出的方法物性参数反演结果对比常规方法精度有明显改善,且在一定程度上,新方法受初始模型和弹性参数的影响较小.三维地震数据的应用验证了本方法的有效性,其孔隙度反演结果能够有效的指示有利储层的空间分布.

Carbonate reservoirs are an important aspect for improving the revealed reserves and productions of oil/gas resources in China. However, such sort of reservoirs usually develops complex pore structures, which may influence the accuracy of seismic prediction for petrophysical parameters. This work proposes a seismic rock-physics simultaneous inversion method for petrophysical and pore parameters with the Gaussian mixture model. Based on the differential effective medium model and the Gassmann equation, a linearized forward operator is derived to quantitatively relate porosity, fluid saturation, and pore aspect ratio to the elastic parameters. To characterize the statistical variations within lithofacies, the Gaussian mixture model is introduced to describe the joint prior probability distribution of petrophysical and pore parameters. The analytical expression for the posterior distribution of the objective parameters is obtained with the linearized model based on the Bayesian inverse theory. Pore aspect ratio is inverted at a well location so as to provide reliable prior constraints of the pore parameter, and an iterative Bayesian inversion algorithm is adopted to improve the forward modeling accuracy. The proposed method treats pore aspect ratio as an objective parameter to account for the spatial variations of pore structures in carbonates, and employs the Bayesian linear inversion to improve the accuracy and efficiency of seismic prediction for petrophysical parameters. Numerical tests indicate that the accuracy of inverted petrophysical parameters by the proposed method is significantly improved, and the method is less affected by the initial models and elastic parameters to some extent, compared to those by the conventional method. The application to the 3D data validates the method, wherein the porosity result well indicates the spatial distribution of potential reservoirs.