Uncertainty in inverted elastic properties resulting from uncertainty in the low-frequency model

Abstract

A Bayesian linearized inversion (BLI) framework is used to analyze how uncertainty in the low-frequency model (LFM) affects the solution in prestack seismic inversion. Two related effects are considered: sensitivity addresses how a change in the LFM changes the inversion solution, whereas uncertainty addresses how uncertainty in the LFM is propagated into the inversion results. The posterior covariance matrix in the BLI equations does not depend on the LFM, and it can be concluded mistakenly that uncertainty in the inversion result is independent of uncertainty in the LFM. Instead, a broader characterization of uncertainty can be made by using a hierarchical BLI framework that includes uncertainties in the LFM. The standard BLI equations are adequate to describe uncertainty in relative rock-property inversion which can be obtained by subtracting the logarithm of the LFM from the logarithm of the inversion solution. Uncertainty in relative rock-property inversion is independent of both the particular LFM used in the solution and the uncertainty associated with the LFM. On the other hand, uncertainty in absolute rock-property inversion is independent of the particular LFM used but does depend on the uncertainty of that LFM. The uncertainty of absolute rock-property inversion is always greater than the uncertainty of the associated relative rock-property inversion.