One of the major criticisms addressed to mainstream stochastic depth conversion models (based on kriging) is that they do not  properly handle non-linearity and non-stationarity of given spatial variables (attribute or property). In most cases, a depth trend is derived from deterministic geophysical processing/modelling steps; based on the depth trend, simple kriging is applied as an interpolator to adjust depth residuals to the well data (such residuals being considered as stationary).

These mainstream stochastic depth conversion models are basically about adding ‘stochastic’ stationary residuals on the top of a deterministic ‘base case’ model.  In most cases, this approach induces wrong/ biased trend estimations and non-realistic uncertainty evaluations. It’s the wrong way to go and this course will run you through a consistent approach to stochastic depth conversion.