Abstract:According to Bayesian inversion theory and with the help of convolution operator and Fatti approximation forward model operator,we utilize Trivariate Cauchy prior distribution to regularize the three term inversion problem based on covariance matrix by well log sampling statistics.The long tail property of the Cauchy distribution preserves weak reflection information and diminishes the statistical correlation between the three parameters,which makes the inverse problem more stable.Through the inversion process,we finally obtain P impedance,S impedance and density.The model test confirms the practicability and advantage of this method.The application of the method on real prestack seismic gathers shows that the inverted elastic parameters are reliable and results are good.