Multi-scale uncertainty assessment for geostatistical seismic inversion

Due to the intrinsic nature of seismic inverse problems there is always uncertainty related with the best-fit inverse model. Traditional geostatistical seismic inversion approaches are able to account the uncertainty related with the stochastic simulation algorithms that are used as part of the inverse methodology for the model perturbation. However, they assume stationarity and no uncertainty related with large scale geological parameters represented for example by the spatial continuity pattern and the prior probability distribution of the property to invert as estimated from well-log data. We propose a multi-scale uncertainty assessment for traditional iterative geostatistical seismic methodologies by integrating stochastic adaptive sampling and Bayesian inference to tune the variogram ranges and the prior probability distribution of the property to invert within the inverse workflow. The application of the proposed methodology to a challenging synthetic dataset showed a good convergence of the inverted seismic towards the recorded one while the local and global uncertainty were jointly assessed.