Incorporating lithological well-logging as uncertain data in probabilistic inverse problems

Boreholes provide a solid foundation for building models of the subsurface. They provide direct measurements or observations of vital subsurface model parameters unrivaled in both detail and resolution compared to any other existing techniques. However, lithology and facies descriptions from boreholes are often used as the ground truth and are treated as “hard data” without any associated uncertainty in inversions or geostatistical simulation. But uncertainty does indeed exist related to e.g. uncertainties on the layer boundaries from drilling techniques, fixed interval sampling or gradual transitioning of layers, and uncertainty in the lithological characterization i.e. the description procedure, mixing of the sample during drilling and possible misinterpretations.

It is therefore essential to treat borehole information as uncertain information and to find an approach to describe the uncertainty of lithological logs. For doing this we identify two main obstacles when treating lithological borehole descriptions as uncertain information; 1) the lithological information including uncertainty needs to be quantified at the borehole location, 2) the quantified information needs to be used fairly in the applied probabilistic modelling technique, such as geostatistical simulation and probabilistic inversion.

In this work we present different approaches to describe the uncertainty of categorical data from boreholes. We apply and sample from different geological prior models of varying complexity to identify strengths and weaknesses of the methods applied. While a “best” solution appear to be problem dependent, we demonstrate how different choices of quantifying borehole information affect the posterior distribution for inversion problems using both synthetic and real-world data.