An intrinsic model of coregionalization that solves variance inflation in collocated cokriging

Abstract

Sequential Gaussian simulation (SGS) is a widely used geostatistical simulation approach for continuous variables. A variant of SGS that employs collocated cokriging under a Markov model is commonly applied to integrate seismic data and to cosimulate multiple variables. This approach is popular because it is simple; the correlation coefficient between the primary variable being modeled and secondary data is the sole additional statistic required to integrate the secondary data. Collocated cokriging, however, has a longstanding problem with variance inflation that leads to a systematic bias in the mean and variance of the simulated realizations. An alternative approach is presented here that is equally simple, with no additional parameters needed. An intrinsic model of coregionalization is adopted for cokriging using secondary data at the location being considered and at the locations of the primary data. The resulting technique can be referred to as intrinsic collocated cokriging (ICCK). The resulting estimates are checked carefully and no variance inflation is observed. This implementation should systematically replace all versions of the Markov model and collocated cokriging.