Bayesian Prestack Inversion With A Huber-Markov Random-field Constraint

Bayesian prestack seismic inversion methods play a very important role in reservoir prediction.With the deepening of the oil and gas exploration,the technical requirements are also continuously improved.In this paper,based on the previous research results of the Zoeppritz equation,a suitable Zoeppritz approximation is chosen to study the prestack inversion method.The prestack inversion method in this paper is based on convolution model,and it is implemented in a Bayesian framework.Seismic inversion is usually an ill posed problem because of the error caused by the band limited,noise and forward modeling.In order to solve the problem of multiple solutions and improve the stability of the inversion,a regularization constraint is usually added to the inversion process.Tikhonov method can obtain smooth solution and effectively suppress noise,but will make the edges fuzzy;total variation method can protect the edges well,but cannot effectively suppress noise.In order to suppress the noise as well as protecting edges information,the Markov random field is adopted as a constraint and the Huber function is used as a potential function,by setting a reasonable threshold,the constraint effect of Huber penalty function is realized.In the inner part of the layer,the quadratic function is used to achieve smooth result of the noise;in the edge position part of the layer,the absolute value function is used to achieve the purpose of edge protection.Due to the different proportion of the three parameters of the reflection coefficient in Zoeppritz approximate equation,in addition,the same weight regularization respectively makes different effect on the three parameters;it is very difficult for three parameters to play a good role as constraint.In this regard,different weights are given for the three parameters to be used as the regularization parameter.In this paper,the validity of the method is verified by the model test.