基于贝叶斯理论的AVO三参数波形反演

Three-parameter AVO waveform inversion based on Bayesian theorem

在实际的AVO反演问题中,叠前数据体中的噪声或其他因素严重影响了AVO反演问题的适定性,而采用先验地质信息作为AVO反演问题的约束条件是解决AVO反演问题不适定的一种可行方法.文中的似然函数采用了ιp范数的解,并用Cauchy分布表示先验模型参数的分布.以此为基础,在反演中建立了测井数据的参数协方差矩阵对反演过程进行约束,并采用了共轭梯度算法实现多参数非线性的反演过程.同时,为了提高反演精度,避免动校正拉伸及依赖于炮检距的调谐效应对参数估计的影响,反演采用动校前地震数据进行参数估计.从应用效果分析来看,即使叠前道集的信噪比不高,反演的结果也能较好地与实际情况相匹配,为识别储层流体性质提供了新的手段.

In the actual AVO inversion, the noise and other factors heavily influence the well-posed property of the inversion problem. So AVO inversion constrained by a priori geological information is a practical method to the solution of ill-posed inversion problem. In this paper the solution for the l^p norm is used to describe the likelihood function. The probability of the prior model parameter is independently Cauchy distribution. Based on these theories the impedance reflectivity attribute parameter covariance matrix from well log is established to constrain inversion, and the conjugate gradient algorithm is used to implement multi-parameter non-linear inversion. In order to improve the inversion accuracy and avoid NMO stretch and offset dependent tuning which influences the estimation of the attribute parameters, the attribution parameter inversion is based on synthetic gather before NMO. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved compared to the actual values, even if the signal/noise ratio is not higher. Therefore it can provide a new tool for identifying fluid content in reservoir pores.