Bayesian approaches to estimating rock physics properties from seismic attributes

Qi Hu, Kristopher A. Innanen

Bayesian rock physics inversion refers to a set of probabilistic methods for the prediction of reservoir properties from elastic attributes, based on different statistical assumptions for the distribution of the model variables and different linear or nonlinear rock physics models. We have examined three Bayesian approaches using the well-log data at the Carbon Management Canada Newell County Facility, assuming Gaussian, Gaussian mixture, and non-parametric distributions of the rock physics variables. The solution is represented by the posterior distribution of the porosity and lithology parameters conditioned on the elastic data. In this application, because the nonlinearity of the rock physics model is not strong and the data are approximately Gaussian distributed, the three results are similar, all capturing the trend of the actual logs. However, the Gaussian mixture model might be a more appropriate solution, owing to its efficiency and its ability to recognize the multimodality of the data. The proposed methods can be combined with elastic inversion to implement a two-step workflow of seismic reservoir characterization at the field if we assume that the rock physics model calibrated at the well location is also valid far away from the well.