基于贝叶斯理论的叠前多波联合反演弹性模量方法

AVO反演可以获得地层岩性和流体信息，而叠前反演问题都是高维的和非适定的，因此获得可靠稳定的解对叠前反演至关重要. 本文给出了一种基于贝叶斯理论的纵波和转换波联合反演密度比和模量比的方法. 鉴于剪切模量比、体积模量比可以更好地指示油气，基于岩石物理中速度比与模量比之间的关系，将此关系式代入Zoeppritz方程的近似形式Aki-Richards公式中，得到与模量比有关的反射系数近似公式. 联合纵波和转换波，利用最小二乘准则构建目标函数，最终反演出密度比、剪切模量比、体积模量比三个参数. 在反演过程中引入贝叶斯理论，假定先验信息服从高斯分布，待求参数服从改进的Cauchy分布，并去除待求参数之间的相关性. 利用模型数据和实际数据对本文方法进行测试，并与常规的单独利用纵波数据来反演方法进行比较，结果表明联合反演稳定性更好、精度更高、抗噪音能力更强，验证了本文方法的可行性和有效性.

Prestack multiwave joint inversion for elastic moduli based on Bayesian theory

Through amplitude versus offset (AVO) inversion, we can obtain parameters which can be used to describe the properties of subsurface fluid and lithology. However, prestack inversion problems are multidimensional and ill posed. So it is necessary to obtain reliable and stable inversion results. In this article, we develop a new method which combines PP wave and PS wave to invert for three parameters including the density contrast, P- and S-wave moduli contrast. Because the moduli contrast is more sensitive to the fluid, we use the relationship between velocity contrast and moduli contrast from rock physics, and substitute the velocity contrast with muduli contrast in Aki-Richards approximation equation. Then we can derive AVO approximations in terms of these moduli. Combining PP wave and PS wave, we construct an objective function to invert density contrast, P- and S-wave moduli contrast. First, this method is based on Bayesian parameter estimation theory, Gaussian distribution is used for likelihood function and modified Cauchy distribution is used for prior distribution. Second, covariance matrix is adopted to describe the degree of correlation between the parameters. Tests on synthetic data and real data show that all parameters are well retrieved. Compared with the conventional inversion method only using PP wave, the joint inversion method is more stable, accurate, and antinoise, which demonstrates its reliability and effectiveness.