Multivariate geostatistical estimation using minimum spatial cross-correlation factors (Case study: Cubuk Andesite quarry, Ankara, Turkey)

Abstract

The quality properties of andesite (Unit Volume Weight, Uniaxial Compression Strength, Los500, etc.) are required to determine the exploitable blocks and their sequence of extraction. However, the number of samples that can be taken and analyzed is restricted, and thus the quality properties should be estimated at unknown locations. Cokriging has been traditionally used in the estimation of spatially cross-correlated variables. However, it can face unsolvable matrices in its algorithm. An alternative to cokriging is to transform variables into spatially orthogonal factors, and then to apply kriging to them. Independent Component Analysis (ICA) is one of the methods that can be used to generate these factors. However, ICA is applicable to zero lag distance so that using methods with distance parameter in their algorithms would be advantageous. In this work, Minimum Spatial Cross-correlation (MSC) was applied to six mechanical properties of Cubuk andesite quarry located in Ankara, Turkey, in order to transform them into approximately orthogonal factors at several lag distances. The factors were estimated at 1544 (5 m × 5 m) regular grid points using the kriging method, and the results were back-transformed into the original data space. The efficiency of the MSC-kriging was compared with Independent Component kriging (IC-kriging) and cokriging through cross-validation test. All methods were unbiased but the MSC-kriging outperformed the IC-kriging and cokriging because of having the lowest mean errors and the highest correlation coefficients between the estimated and the observed values. The estimation results were used to determine the most profitable blocks and the optimum direction of extraction.