Half-tapering strategy for conditional simulation with large datasets

TL;DR

This paper introduces a half-tapering strategy for Gaussian conditional simulations that improves computational efficiency and accuracy in Earth sciences applications by applying taper covariance only during the conditioning step.

Contribution

The paper proposes a novel half-tapering approach that enhances speed and reduces memory in conditional simulations while maintaining realistic small-scale variations.

Findings

HT approach closely matches F in distributional properties

HT reduces computational time and memory usage

Guidelines for choosing taper functions are provided

Abstract

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.