Inversion of the seismic reflection coefficients are formulated in a Bayesian framework. Measured reflection coefficients and model parameters are assigned statistical distributions based on information known prior to the inversion, and together with the forward model uncertainties can be propagated into the final result. A quadratic approximation to the Zoeppritz equations is used as the forward model and compared with the linear approximation the bias is reduced. The differences when using the quadratic approximations and the exact expressions are minor. Joint inversion using information from both reflected PP-waves and converted PS-waves yield smaller bias compared to using only reflected PP-waves. The solution algorithm is sampling based and because of the nonlinear forward model the Metropolis-Hastings algorithm is used.


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