Multiscale uncertainty assessment in geostatistical seismic inversion

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).