Multi-Scale Uncertainty Assessment for Geostatistical Seismic Inversion

Seismic inverse problems are by nature ill-posed, nonlinear and with non-unique solutions. Due to these reasons the best-fit inverse model, retrieved from any seismic inversion methodology, is always contaminated with uncertainty that needs to be taken into account when interpreting the inverse solution (Tarantola, 2005). Conventional iterative geostatistical seismic inversion approaches are able to account the small-scale spatial uncertainty of the property to invert by using stochastic simulation algorithms as part of the model parameter space perturbation technique. However, these stochastic sequential simulation algorithms assume stationarity along the entire inversion grid, and therefore do not account for uncertainty in the large-scale geological parameters, e.g. 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 large-scale geological parameters as described by variogram ranges and the prior probability distribution of the property to invert within the inverse workflow. We show here the application of the proposed multi-scale methodology to a challenging synthetic highly non-stationary dataset. The results show a good convergence of the inverted seismic towards the recorded one while the local and global uncertainties are jointly assessed.