Uncertainty quantification in forward petro-physical model using Empirical Bayes

In this paper we applied the so-called Empirical Bayes method to quantify the uncertainties of a petro-elastic model. The petro-elastic model presents compressional and shear wave velocity as a function of rock and fluid properties such as porosity, clay content, water saturation, and effective pressure. Due to the micro-scale heterogeneity of rocks it is very difficult to define a single petro-elastic model for a geological basin. As a result any proposed model must quantify its associated uncertainties. The presented results show that the proposed method is able to model measured compressional and shear velocity logs with their associated uncertainties.