Seismic inversion and uncertainty quantification using transdimensional Markov chain Monte Carlo method

Abstract

We applied a transdimensional stochastic inversion algorithm, reversible jump Markov chain Monte Carlo (rjMCMC), to angle-stack seismic inversion for characterization of reservoir acoustic and shear impedance with uncertainty quantification. The rjMCMC is able to infer the number of parameters for the model as well as the parameter values. In our case, the number of parameters depends on the number of model layers for a given data set. We also use this method in uncertainty quantification because a transdimensional sampling helps prevent underparameterization or strong overparameterization. An ensemble of models with proper parameterization can improve parameter estimation and uncertainty quantification. Our new results in uncertainty analysis indicate that (1) the uncertainty in seismic inversion, including uncertainty in earth properties and their locations, is related to the discontinuity of property across an interface, and (2) there is a trade-off between property uncertainty and location uncertainty. A stronger discontinuity will induce more property uncertainty but less location uncertainty at the discontinuity interface. Therefore, we further use the inversion uncertainty as a novel seismic attribute to assist in delineation of subsurface discontinuity interfaces and quantify the magnitude of the discontinuities, which further facilitates quantitative interpretation and stratigraphic interpretation.