Contouring Very Large Datasets Using Kriging

Geostatistics Applied to Gas Reservoirs

“…Because an estimation performed with n experimental points normally leads to an inversion of at least an (n+ 1) x(n+ 1) matrix, special care must again be taken to create an accurate cartography. 5 Another point is the existence of faults and the estimation of their correct influence on the interpolation. Despite having found a satisfactory solution in the one-ciimensiopal case, 6 this is still a difficult task.…”

“…Universal kriging is the easiest way to obtain the desired permeability map. (5) where m(cpIC sh ) = -560+339 log 100 cp/C sh '…”

Parallel Geostatistics for Sparse and Dense Datasets

“…An alternative approach for selecting the neighbourhood is to select a predetermined number of near observations for each prediction location. As noted by Davis and Culbane [1984], these methods produce spurious behaviour in some of the estimates and hence should be used with caution, this is apparent as observations are added or removed from the moving window. Ad-hoc methods of subsetting the data were formalised by the moving-window approach of Haas [1995], although the local covariance functions fitted within the window may yield incompatible covariances at larger spatial lags.…”

System development and application of Taylor Kriging metamodeling

“…The early application of Kriging was mainly in geological settings (Krige, 1951; David, 1977; Journel and Huijbregis, 1978; Davis, 1986; Soares, 2004). Kriging has used extensively to produce contour maps (Olea, 1974; Davis and David, 1978; Davis and Culhance, 1984; Galli, et al , 1984; Trochu, 1993), to predict the values of soil attributes at unsampled locations (Voltz and Webster, 1990; Webster, 1991; Goovaerts, 1992; Smith et al , 1993; Moyeed et al , 2002; Reisa et al , 2004), and to render predications in hydrology (Delhomme, 1978; Clifton and Neuman, 1982; Orr and Dutton, 1983; Bras and Rodriguez‐Iturbe, 1985; Cheng and Wang, 2002) and in meteorology (De Iacoa et al , 2002). Recently, Kriging has been applied in engineering design (Limaiem and ElMaraghy, 1996; Fregeau et al , 2005; Simpson et al , 2001), in material sciences (Echaabi et al , 1995; Terriault et al , 1997; Kamanayo et al , 2003; Mamat et al , 2004), in biomechanical engineering (Andr et al , 1996; Carrier et al , 2005), in wireless wave propagation (Leflbvre et al , 1996; Doncker et al , 2003; Yu et al , 2006; Khafaji et al , 2009), in economic sensitivity analysis and cost estimation (Rossel et al , 2001; Chaveesuk and Smith, 2005; Baioumy et al , 2008), in simulation interpolation (Sacks et al , 1989; Mitchell and Morris, 1992; Barton, 1994; Koehler and Owen, 1996; Trochu et al , 1999; Régnire and Sharov, 1999; Santner et al , 2003; Kleijnen and van Beers, 2003, 2004, 2005), and in optimization (Jones et al , 1998; Huang et al , 2006a, b; Liu and Smith, 2007).…”