## GSLIB Help Page: COKB3D

Description:

- A cokriging program for a points or blocks on a regular grid.

Parameters:

- datafl: the input data in a simplified Geo-EAS formatted file.
- nvar: the number of variables (primary plus all secondary). For example, nvar=2 if there is only one secondary variable.
- icolx, icoly, icolz and icolvr(): the columns for the x, y and z coordinates, the primary variable to be kriged, and all secondary variables.
- tmin and tmax: all values (for all variables) strictly less than tmin and greater than or equal to tmax are ignored.
- coloc: set to 1 if performing co-located cokriging with a gridded secondary variable, otherwise set to 0.
- secfl: if co-located cokriging, the file with the gridded secondary variable.
- icolsec: if co-located cokriging, the column number for the secondary variable in secfl
- idbg: an integer debugging level between 0 and 3. The higher the debugging level the more output. Normally level 0 or 1 should be chosen.
- dbgfl: the debugging output is written to this file.
- outfl: the output grid is written to this file. The output file will contain both the kriging estimate and the kriging variance for all points/blocks. The output grid cycles fastest on x then y then z
- nx, xmn, xsiz: definition of the grid system (x axis).
- ny, ymn, ysiz: definition of the grid system (y axis).
- nz, zmn, zsiz: definition of the grid system (z axis).
- nxdis, nydis and nzdis: the number of discretization points for a block. If nxdis, nydis and nzdis are set to 1 then point cokriging is performed.
- ndmin, ndmaxp and ndmaxs: the minimum and maximum number of primary data, and the maximum number of secondary data (regardless of which secondary variable) to use for kriging a block.
- search radii for primary data
- search radii for secondary data (same for all types)
- the angles defining the common orientation of the search ellipsoids for primary and secondary data
- ktype: the kriging type must be specified: 0 = simple cokriging, 1 = standardized ordinary cokriging with re-centered variables and a single unbiasedness constraint; 2 = traditional ordinary cokriging.
- mean(): the mean of the primary and all secondary variables are required input if either simple cokriging or standardized ordinary cokriging are used. The program calculates the data residuals from these means.

The direct and cross variograms may be specified in any order; they are specified according to the variable number Variable ``1'' is the primary (regardless of its column ordering in the input data files) and the secondary variables are numbered from ``2'' depending on their ordered specification in icolvr() It is unnecessary to specify the j to i cross variogram if the i to j cross variogram has been specified; the cross variogram is expected to be symmetric (as from theory). For each i to j variogram the following are required:

- nst and c0: the number of variogram structures and the isotropic nugget constant. The nugget constant does not count as a structure.
- For each of the nst nested structures one must define it the type of structure (the power model is not allowed); cc the c parameter; ang1,ang2,ang3 the angles defining the geometric anisotropy; aa_hmax, the maximum horizontal range; aa_hmin, the minimum horizontal range; and aa_vert, the vertical range.

Application notes:

- The construction of the cokriging matrix requires the linear model of coregionalization. The input variogram parameters are checked for positive definiteness. The power model is not allowed.
- A specific search is done for secondary data (same for all secondary) allowing the option of collocated cokriging.
- A cokriging program for scattered points and cross validation is not provided; programs `cokb3d` and `kt3d` could be combined for this purpose.