A fully non-stationary linear coregionalization model for multivariate random fields

A comparison of search strategies to design the cokriging neighborhood for predicting coregionalized variables

“…Cokriging is used in the earth sciences for predicting coregionalized variables at locations where no observation is available. Application fields include mineral resource assessment (Journel and Huijbregts 1978;Pan et al 1993;Gálvez and Emery 2011;Emery 2012;da Silva and Costa 2014;Minnitt and Deutsch 2014;Uygucgil and Konuk 2015;Cornah and Machaka 2015), petroleum reservoir modeling (Xu et al 1992;Hohn 1999;Masihi and Zarei 2010;Schwab et al 2011;Cao et al 2014;Jalalalhosseini et al 2014), groundwater hydrology (Ahmed and de Marsily 1987;D'Agostino et al 1997D'Agostino et al , 1998Kitanidis 1997;Boezio et al 2006;Dalla Libera et al 2017;Olea et al 2018), geochemistry (Wackernagel 1988;Roberts and McKenna 2009;Tolosana-Delgado and van den Boogaart 2013;Lark et al 2014;Pawlowsky-Glahn et al 2015;Fabijańczyk et al 2016;Fouedjio 2018), soil sciences (Yates and Warrick 1987;Stein et al 1988), and environmental sciences (Goovaerts 1997;Bohorquez et al 2017;Borkowski and Kwiatkowska-Malina 2017).…”

Nonstationary cross-covariance functions for multivariate spatio-temporal random fields

“…We now mention several studies that advanced the models available for studying multivariate purely spatial nonstationary behavior. Genton and Kleiber (2015) started the discussion on these models by highlighting the different nonstationary extensions of the LMC such as that of Gelfand et al (2004) and Fouedjio (2018), and the nonstationary multivariate Matérn model of Kleiber and Nychka (2012). These studies are based on similar approaches, i.e., they use multivariate purely spatial stationary models as the building blocks of complicated nonstationary models.…”

“…There are several nonstationary versions of the classical LMC but we select the nonstationary LMC proposed by Fouedjio (2018), as an example, and extend it to space-time using Theorem 1.…”