PROPAGATION OF WELL-LOG DATA IMPUTATION UNCERTAINTIES TOWARDS THE INTERPOLATED 3D-PETROPHYSICAL MAP USING EPISTEMIC KERNELS AND KRIGING

Abstract

In this work, we present a method for propagating the uncertainties related to a well-log data imputation procedure towards the interpolated 3D-Petrophysical map using epistemic kernels and kriging. We introduce the concept of epistemic kernels which bring a convenient way of incorporating the uncertainty related to the lack of knowledge about the true (observed) value of a variable into the covariance and variogram matrices. An advantage of doing that is that we don’t modify the kriging equations to incorporate such uncertainties, all is done by the kernel. We conduct an experimental study to support our claims using well-log data from the New Zealand repository. We showed that those epistemic kernels when used in Ordinary kriging, avoid optimistic estimates of the variances of the predicted 3D-Petrophysical map when a well-data source contains imputed values.