Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petroelastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The spatial uncertainty of the inferred petroelastic properties is represented with the updated a posteriori variance from an ensemble of the simulated realizations. Within this setting, petroelastic realizations are generated assuming stationary and known large-scale geologic parameters (metaparameters), such as the spatial correlation model and the global a priori distribution of the properties of interest, for the entire inversion domain. This assumption leads to underestimation of the uncertainty associated with the inverted models. We have developed a practical framework to quantify uncertainty of the large-scale geologic parameters in geostatistical seismic inversion. The framework couples geostatistical seismic inversion with a stochastic adaptive sampling and Bayesian inference of the metaparameters to provide a more accurate and realistic prediction of uncertainty not restricted by heavy assumptions on large-scale geologic parameters. The proposed framework is illustrated with synthetic and real case studies. The results indicate the ability to retrieve more reliable acoustic impedance models with a more adequate uncertainty spread when compared with conventional geostatistical seismic inversion techniques. The proposed approach accounts for geologic uncertainty at the large scale (metaparameters) and the local scale (trace-by-trace inversion).

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