Generalized linear AVO inversion with the priori constraint of trivariate cauchy distribution based on Zoeppritz equation

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.