Cokriging for optimal mineral resource estimates in mining operations.

This paper arose from the Citation Course in Geostatistics presented by the second author in Johannesburg, South Africa in August 2011.Cokriging uses a sparsely sampled, but accurate and precise primary dataset, together with a more abundant secondary data-set, for example grades in a polymetallic orebody, containing both error and bias, to provide improved results compared to estimation with the primary data alone, as well as filtering the error and mitigating the effects of conditional bias. The method described here may also be applied in polymetallic orebodies and in other cases where the primary and secondary data could be collocated, and one of the data-sets need not be biased, unreliable, etc. An artificially created reference data-set of 512 lognormally distributed precious metal grades sampled at 25×25 m intervals constitutes the primary data-set. A secondary data-set on a 10×10 m grid comprising 3200 samples drawn from the reference data-set includes 30 per cent error and 1.5 multiplicative bias on each measurement. The primary and secondary non-collocated data-sets are statistically described and compared to the reference data-set. Variograms based on the primary data-set are modelled and used in the kriging of 10×10 m blocks using the 25×25 m and 50×50 m data grids for comparison against the results of the cokriged estimation. A linear model of coregionalization (LMC) is established using the primary and secondary data-sets and cokriging using both data-sets is shown to be a significant improvement over kriging with the primary data-set alone. The effects of the error and bias are filtered and removed during the cokriging estimation procedure. Thus cokriging using the more abundant secondary data, even though it contains error and bias, significantly improves the estimation of recoverable reserves.MvdH2016http://www.saimm.co.za/publications/journal-paper

Use of geostatistical Bayesian updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration

Mineral exploration programmes around the world use data from remote sensing, geophysics, and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and mineral exploration. Since airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions, they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. However, with increasing numbers of variables the inference of the crosscovariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximize information generated from the soil survey, enabling more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland. The geostatistical technique was used to improve the resolution of soil geochemistry, at a density of one sample per 2 km2, by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular enhanced information on the mapped distributions of zinc, copper, and lead. The enhanced delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential for discovering stratabound base metal deposits

Advanced Vadose Zone Simulations Using TOUGH

The vadose zone can be characterized as a complex subsurface system in which intricate physical and biogeochemical processes occur in response to a variety of natural forcings and human activities. This makes it difficult to describe, understand, and predict the behavior of this specific subsurface system. The TOUGH nonisothermal multiphase flow simulators are well-suited to perform advanced vadose zone studies. The conceptual models underlying the TOUGH simulators are capable of representing features specific to the vadose zone, and of addressing a variety of coupled phenomena. Moreover, the simulators are integrated into software tools that enable advanced data analysis, optimization, and system-level modeling. We discuss fundamental and computational challenges in simulating vadose zone processes, review recent advances in modeling such systems, and demonstrate some capabilities of the TOUGH suite of codes using illustrative examples

Utilizing image texture to detect land-cover change in Mediterranean coastal wetlands

Land-use/cover change dynamics were investigated in a Mediterranean coastal wetland. Change Vector Analysis (CVA) without and with image texture derived from the co-occurrence matrix and variogram were evaluated for detecting land-use/cover change. Three Landsat Thematic Mapper (TM) scenes recorded on July 1985, 1993 and 2005 were used, minimizing change detection error caused by seasonal differences. Images were geometrically, atmospherically and radiometrically corrected. CVA without and with texture measures were implemented and assessed using reference images generated by object-based supervised classification. These outputs were used for cross-classification to determine the ‘from–to’ change used to compare between techniques. The Landsat TM image bands together with the variogram yielded the most accurate change detection results, with Kappa statistics of 0.7619 and 0.7637 for the 1985–1993 and 1993–2005 image pairs, respectively

Combining two national‐scale datasets to map soil properties, the case of available magnesium in England and Wales

Given the costs of soil survey it is necessary to make the best use of available datasets, but data that differ with respect to some aspect of the sampling or analytical protocol cannot be combined simply. In this paper we consider a case where two datasets were available on the concentration of plant‐available magnesium in the topsoil. The datasets were the Representative Soil Sampling Scheme (RSSS) and the National Soil Inventory (NSI) of England and Wales. The variable was measured over the same depth interval and with the same laboratory method, but the sample supports were different and so the datasets differ in their variance. We used a multivariate geostatistical model, the linear model of coregionalization (LMCR), to model the joint spatial distribution of the two datasets. The model allowed us to elucidate the effects of the sample support on the two datasets, and to show that there was a strong correlation between the underlying variables. The LMCR allowed us to make spatial predictions of the variable on the RSSS support by cokriging the RSSS data with the NSI data. We used cross‐validation to test the validity of the LMCR and showed how incorporating the NSI data restricted the range of prediction error variances relative to univariate ordinary kriging predictions from the RSSS data alone. The standardized squared prediction errors were computed and the coverage of prediction intervals (i.e. the proportion of sites at which the prediction interval included the observed value of the variable). Both these statistics suggested that the prediction error variances were consistent for the cokriging predictions but not for the ordinary kriging predictions from the simple combination of the RSSS and NSI data, which might be proposed on the basis of their very similar mean values. The LMCR is therefore proposed as a general tool for the combined analysis of different datasets on soil properties