Kriging, indicators, and nonlinear geostatistics
J Rivoirard, X Freulon, C Demange, A Lécureuil
Historically, linear and lognormal krigings were first created to estimate
the in situ mineral resources of blocks. Nonlinear geostatistics and
indicator kriging were subsequently developed to evaluate also the
portion recovered when applying a cut-off on selective mining units
(SMUs) within blocks. In practice these methods are generally based
either on the Gaussian model with a transformation generalizing the
lognormal case or on the indicators above cut-offs. Very often the
indicator approach is simplified by kriging separately each indicator,
and when starting from a continuous variable, a practical advantage of
the discretization into classes lies in the easy treatment of a zero effect
and of the high values. However, a number of so-called isofactorial
models have also been developed for a discrete or continuous variable,
where the full cokriging of indicators (i.e. disjunctive kriging) simplifies
to the separate kriging of factors. Moreover, these models are equipped
with a change of support, allowing a consistent estimation of
recoverable resources on SMUs.
Min-Max Autocorrelation Factors (MAF) analysis of the indicators
offers a new approach for indicator modelling. In particular the first
factor, the one with the highest spatial continuity, can help in choosing
the type of model. For example a monotonic experimental first factor can
be used directly as the basis of a discrete diffusion model, unless a
continuous diffusion model such as the Gaussian model can be used on
the original variable. This approach is illustrated on a uranium deposit
mined selectively: estimates of recoverable resources by discrete
disjunctive kriging and uniform conditioning in a Gaussian model are
compared locally to short-term estimates based on two areas densely
drilled.
Keywords: disjunctive kriging, indicator kriging, Min-Max Autocorrelation Factors,
recoverable resources, discrete diffusion model.