  Gaussian conditional realizations are routinely used for risk assessment and
planning in a variety of Earth sciences applications. Conditional realizations
can be obtained by first creating unconditional realizations that are then
post-conditioned by kriging. Many efficient algorithms are available for the
first step, so the bottleneck resides in the second step. Instead of doing the
conditional simulations with the desired covariance (F approach) or with a
tapered covariance (T approach), we propose to use the taper covariance only in
the conditioning step (Half-Taper or HT approach). This enables to speed up the
computations and to reduce memory requirements for the conditioning step but
also to keep the right short scale variations in the realizations. A criterion
based on mean square error of the simulation is derived to help anticipate the
similarity of HT to F. Moreover, an index is used to predict the sparsity of
the kriging matrix for the conditioning step. Some guides for the choice of the
taper function are discussed. The distributions of a series of 1D, 2D and 3D
scalar response functions are compared for F, T and HT approaches. The
distributions obtained indicate a much better similarity to F with HT than with
T.
