Strategies for integrating uncertainty in iterative geostatistical seismic inversion

Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic properties, overlooking alternative sources of uncertainty such as those associated with poor well-log data, upscaling, and noise within the seismic data. We have expressed uncertain well-log samples, due to bad logging reads and upscaling, in terms of local probability distribution functions (PDFs). Local PDFs are used as conditioning data to a stochastic sequential simulation algorithm, included as the model perturbation within the inversion. The problem of noisy seismic and narrow exploration of the model parameter space, particularly in the early steps of the inversion, is tackled by the introduction of a cap on local correlation coefficients (CCs) responsible for the generation of the new set of models during the next iteration. We evaluate a single geostatistical framework with application to a real case study. When compared against a conventional iterative geostatistical seismic inversion, the integration of additional sources of uncertainty increases the match between real and inverted seismic traces and the variability within the ensemble of models inverted at the last iteration. The selection of the local PDFs plays a central role in the reliability of the inverted elastic models. Avoiding high local CCs at early stages of the inversion increases convergence in terms of global correlation between synthetic and real seismic reflection data at the end of the inversion.