Generalized linear AVO inversion with the priori constraint of trivariate cauchy distribution based on Zoeppritz equation
Generalized linear AVO inversion with the priori constraint of trivariate cauchy distribution based on Zoeppritz equation
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发表时间：
2013
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通讯作者：
Zhang Feng;Sinopec Shengli
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作者：
Zhang Feng;Sinopec Shengli
传统的三项AVO反演中，AVO正演建模总是通过Zoeppritz方程的近似来构造。但在临界角和弹性参数变化剧烈的情况下，该近似方法受到限制。考虑到这个问题，我们可以使用精确的 Zoeppritz 方程来构造反演目标函数。由于纵波反射系数与弹性参数之间的关系是非线性的，常用的方法是采用非线性优化算法，但由于计算量大，尚未得到广泛应用。另一种方法是使用广义线性反演，即通过将 P 波反射系数展开为截断泰勒级数，利用线性方程来表达非线性关系。 GLI理论上可以通过多次迭代获得较高的精度。但由于雅可比矩阵的条件数较多，GLI有时会不稳定。贝叶斯反演将模型参数的先验分布与噪声的似然函数结合起来形成模型参数的后验分布，将目标函数的最小化转化为后验概率分布的最大化。由于引入了模型参数的先验信息，可以大大减少不适定问题。本文结合两种方法的思想，利用GLI的思想构建AVO正演模型，提高大入射角地震数据反演的精度，并利用贝叶斯理论引入模型参数先验信息，构建反演目标函数的正则化，减少反演的不适定问题。该算法假设模型参数的先验分布遵循三变量柯西分布。
AVO forward modeling is always constructed by the approximation of Zoeppritz equation in traditional three-term AVO inversion. But the approximation is limited in the case of critical angle and elastic parameters varying severely. Given this problem, we can use the exact Zoeppritz equation to construct the inversion objective function. Because the relationship between P wave reflection coefficient and elastic parameters is nonlinear, the common approach is to use nonlinear optimization algorithm which hasn't been widespread because of the large computation. The alternative is to use generalized linear inversion which uses the linear equation to express the nonlinear relation through the expansion of P wave reflection coefficient into a truncated Taylor series. The GLI can get high accuracy through several iterations in theory. But GLI is unstable sometimes because of the large conditional number of Jacobian matrix. Bayesian inversion combines the prior distribution of model parameters with the likelihood function of the noise to form the posterior distribution of model parameters, which transforms the minimization of objective function into the maximization of the posterior probability distribution. Because of the introduction of the prior information of model parameters, the ill-posed problem can be reduced dramatically. This article combines the ideas of the two methodologies, which uses the idea of GLI to construct AVO forward modeling for improving the accuracy of inverting the large incident angle seismic data and uses Bayesian theory to introduce the model parameters prior information to construct the regularization of inversion objective function for reducing the ill-posed problem of inversion. This algorithm assumes that the prior distribution of the model parameters honors trivariate Cauchy distribution.