When do we need a trend model in kriging?

Geostatistical modelling of a coal seam for resource risk assessment

“…In this situation, Journel and Rossi (1989) have shown that a stationary model within a local search window gives very similar results to those obtained from a nonstationary model in which the drift is explicitly included. The presence of sufficient data, regularly distributed over the area of interest, has the double effect of conditioning and screening.…”

Computer-assisted mapping of paddy-field soils

“…The theory underlying kriging is well-documented in the reports of Journel and Huijbregts (1978) and in Webster's review (Webster 1985). We describe only the essential aspects of kriging used here.…”

An Integrated Approach to Simulate and Validate Orebody Realizations with Complex Trends: A Case Study in Heavy Mineral Sands

“…A reliable variogram can be calculated by selecting data pairs which are unaffected by the trend (Olea 2006). This assumes that the pattern of spatial variation can be derived correctly while excluding certain directions from the analysis (Journel and Rossi 1989;Goovaerts 1997). A more complicated technique consists of filtering out the particular trend model assumed by linear combinations of available data (theory of Intrinsic Random Functions of order k).…”

“…Once obtained, the residuals are used to condition simulations (Rossi and Deutsch 2014). In practice, it is usually not possible to unambiguously identify and separate the smoothly varying trend from the more erratic residuals (Journel and Rossi 1989;Cressie 1991;Zimmerman and Stein 2010). Nevertheless, the inference of the trend model is critical due to its direct influence on the remaining residuals (Leuangthong and Deutsch 2004).…”