Kriging filters, indicator ccdf, kriging efficiency and collocated co-kriging

FilteredKrige: kriging of the error-free signal from data with white measurement error of variance error_variance (gstat's Err component): the error enters only the data covariance, so predictions at data locations smooth. IndicatorCcdf: ordinary kriging of indicators at several thresholds (one model for all is median indicator kriging), clipped and order-corrected by averaging upward and downward passes (GSLIB), with E-type mean and variance (uniform within classes). KrigingEfficiency: \(KE = (BV - KV)/BV\) and the slope of regression \((BV - KV + |\mu|)/(BV - KV + 2|\mu|)\) of ordinary (block) kriging (Krige 1996). CollocatedCokriging: simple co-kriging with the collocated secondary value under Markov model 1 (Xu et al. 1992). Identical to the Python arm morie.fn.krigfilt.

Usage

FilteredKrige(
  z,
  coords,
  new_coords,
  model,
  error_variance,
  X = NULL,
  X0 = NULL,
  beta = NULL
)

IndicatorCcdf(
  z,
  coords,
  new_coords,
  thresholds,
  models,
  zmin = NULL,
  zmax = NULL
)

KrigingEfficiency(z, coords, new_coords, model, block = NULL)

CollocatedCokriging(
  z,
  coords,
  y0,
  new_coords,
  model,
  rho,
  mean_z = 0,
  mean_y = 0,
  var_y = 1
)

Arguments

z: Observations.
coords, new_coords: Data and target coordinates.
model: Covariance model (as KrigingCovariance), or a list of models per threshold for IndicatorCcdf.
error_variance: Measurement-error variance.
X, X0: Trend designs (universal kriging).
beta: Known mean (simple kriging).
thresholds: Increasing thresholds.
models: Indicator covariance model(s).
zmin, zmax: Tail bounds of the ccdf.
block: Block discretisation (as Krige).
y0: Secondary values at the targets.
rho: Correlation of primary and secondary.
mean_z, mean_y, var_y: Means and secondary variance.

Value

List.

References

Cressie, N. (1993). Statistics for Spatial Data, rev. edn. Wiley.

Deutsch, C. V. and Journel, A. G. (1998). GSLIB: Geostatistical Software Library and User's Guide, 2nd edn. Oxford University Press.

Krige, D. G. (1996). A practical analysis of the effects of spatial structure and of data available and accessed, on conditional biases in ordinary kriging. Geostatistics Wollongong '96, 799-810.

Xu, W., Tran, T. T., Srivastava, R. M. and Journel, A. G. (1992). Integrating seismic data in reservoir modeling: the collocated cokriging alternative. SPE 24742.

Examples

m <- list(model = "Exp", psill = 1, range = 2)
P <- rbind(c(0, 0), c(2, 0), c(0, 2))
FilteredKrige(c(1, 3, 2), P, rbind(c(0, 0)), m, 0.2)$prediction
#> [1] 1.252994
KrigingEfficiency(c(1, 3, 2), P, rbind(c(1, 1)), m)$efficiency
#> [1] 0.4372286