Prestack Bayesian Linearized Inversion with Decorrelated Prior Information

The statistical correlation between the three elastic parameters of the P- and S-wave velocities and density is significant for stabilizing the prestack inversion. In the prestack Bayesian linearized inversion (BLI), the prior correlation of the three elastic parameters is included in a multivariate Gaussian distribution, and is represented by the cross-variograms between the three model parameters. However, the cross-variograms are roughly calibrated from certain sparse existing data (such as well-log data), which may produce statistical error and reduce inversion accuracy. To address this issue, this work proposes a decorrelated Bayesian linearized inversion (DBLI) by integrating the BLI with a decorrelation strategy. The decorrelation utilizes principal component analysis to obtain independent model parameters with zero covariances. Since the cross-variograms of the model parameters are no more than their covariances according to the derivation, the cross-variograms between the three independent model parameters are also zero. Thus, the estimation of the cross-variogram is unnecessary in DBLI, thereby avoiding the statistical error produced in the prior correlation characterization. The contribution of DBLI can be summarized by two main aspects. First, DBLI enables one to avoid the problem of reduced inversion stability and accuracy caused by statistical error, which is verified by tests on both the theoretical model and field data. Second, the derived relationship between the covariance and the cross-variogram is a potential contribution to both the geophysical inversion and geostatistical modeling.