Estimation of Variogram Parameters with Seismic Forward Modelling

Variogram modelling is a useful method to characterise spatial uncertainty of geological formations. For underground radioactive waste repositories, the spatial definition of the formation containing the repository is critical, as several geometric requirements need to be met to achieve safety standards. We propose to characterise the geometrical uncertainties of the formation containing the repository through the definition of a variogram range, sill and nugget from 2D seismic data. Starting from an initial model of acoustic impedance, we perturb it by adding a Gaussian field to it that is generated by sampling from range, sill and nugget distributions; and compute its corresponding seismic forward simulation to later measure the misfit with respect to the 2D seismic data. By converting the misfit to a probability value that represent the feasibility or likelihood of that realization, and by analysing the time shifts between the same-coordinate seismic traces of the seismic forward simulation and seismic data, we obtain distributions of the variogram parameters that can later be used to characterise the uncertainty in other points of the formation containing the repository, in 3D, where seismic data or other sources of information are not available.