Universal kriging of functional data: trace-variography vs cross-variography? Application to forecasting in unconventional shales

53/2015

Universal kriging of functional data: trace-variography vs cross-variography? Application to forecasting in unconventional shales

Monday 19th October 2015

Menafoglio, A; Grujic, O.; Caers, J.

In this paper we investigate the practical and methodological use of universal kriging of functional data to predict unconventional shale production in undrilled locations from known production data. In universal kriging of functional data, two approaches are considered: 1) estimation by means of cokriging of functional components (Universal Cokriging, UCok), requiring cross-variography and 2) estimation by means of trace-variography (Universal Trace-Kriging, UTrK), which avoids cross-variogram modeling. While theoretically, under known variogram structures, such approaches may be quite equivalent, the practical application yields marked differences. We investigate these difference by means of a real field application in the Barnett shale play and by a Monte Carlo study inspired from such real field application. We find that, for the studied cases, in terms of sum of squared errors (SSE), UTrK outperforms UCok. We speculate that the main reason lies in the robustness of estimating experimental trace-variography over the cross-variography and the possible loss of information induced by the functional decomposition required for cokriging.