Compositing and regularization of drillhole data for geostatistical resource estimation

Compositing and regularization of drillhole data for geostatistical resource estimation by L.W. Palmer1 Affiliation: 1Camborne School of Mines, University of Exeter, Penryn Campus, Cornwall, United Kingdom Correspondence to: L.W. Palmer Email: Dates: Received: 6 Aug. 2018 Revised: 14 Oct. 2023 Accepted: 10 Feb. 2024 Published: June 2024 How to cite: Palmer, L.W. 2024. Compositing and regularization of drillhole data for geostatistical resource estimation. Journal of the Southern African Institute of Mining and Metallurgy, vol. 124, no. 6, pp. 331–338 DOI ID: http://dx.doi.org/10.17159/24119717/258/2024 Abstract Compositing or regularization of drillhole data is common practice in mineral resource estimation and is deemed a necessary step in producing unbiased estimates of mineral resources and reserves. Commonly, data are collected over irregular distances due to the varying relative thicknesses of lithologies drilled or sampling/assaying strategies. This necessitates data transformation to regular lengths of equal size to ensure that all data have the same sample support. However, there have been few detailed publications on the effect of this process on the composited data that are subsequently taken forward for the estimation process. In this paper, three currently available compositing methods are reviewed and the effects of inappropriate compositing methodologies presented. It is shown through a case study that compositing samples to different lengths leads to changes in the average and variance of the grades in the drillcores in the dataset, which will impact the final estimated value. These differences are exacerbated by breaks or gaps in data where, for a variety of reasons, there has been no data collection or data have been lost. The importance of appropriately treating blank and zero data is also presented. Globally, these differences might be minimal, but locally may be substantial, affecting the efficiency of the estimation and subsequent use of the results in, for example, mine planning and reconciliation. Further detailed investigation of compositing practices is required if the full implications of compositing are to be understood and any induced bias effectively defined. Keywords resource estimation, geostatistics, compositing, regularization, drillhole data, bias, uncertainty Introduction Data gathered from drilling are extensively used within the mining industry for the purpose of resource estimation and, ultimately, resource delineation. As part of the standard data-processing procedure for resource estimation (or grade-control purposes), it is common practice to composite or regularize multiple samples together and take the results forward for further analysis (Rossi and Deutsch, 2013). The purpose of compositing is to ensure that all samples have the same weighting, so further analyses are not affected by bias. Compositing is a linear-weighted averaging approach, where the sum of the product of the lengths and the measured variables is divided by the total length of all samples considered in calculating a composite value. Regularization is performed whether solid core, for example, from diamond coring (DC), or chips from rotary air blast (RAB) or reverse circulation (RC) are recovered. Drillholes are commonly non-vertical, to ensure that the best possible intercept with lithologies and/or mineralization is achieved (Biel et al., 2010; Lomberg, 2014; Moorhead et al., 2001). The compositing method may be adjusted to take this into account. Sampling of core or chips for assay is a complex process. The number and nature of samples taken depends on several factors, including the nature of the geology, the drilling method, the location of the deposit, the cost of obtaining reliable assay results, and the degree of compliance of the project with international reporting codes, such as the SAMREC (2016), JORC (2012), and CIM (2010) codes. If the geology is highly complex, then more samples need to be taken spatially to elucidate the geological picture. If the drilling method is more basic (chip recovery) or poorly executed, sample collection will be less efficient. If the project is located in a challenging or remote environment, the cost of sending samples for assaying increases, which makes it likely that fewer samples will be analysed. If the project is to be compliant with JORC or other reporting codes, then more, and higher quality, samples are likely to be taken. To illustrate some of the potential issues that poor treatment of drillhole data can cause, a hypothetical example is presented (Figure 1). Here, drilling was conducted across a zone of interest, the results of which will subsequently be used to best delineate a mineralized zone in a gold deposit. Each sample was analysed for gold and arsenic. These two variables, Au (g/t) and As (%), form the basis of the resource estimation. The Journal of the Southern African Institute of Mining and Metallurgy VOLUME 124 JUNE 2024 331 Experimental Semi-Variogram (%)2 Compositing and regularization of drillhole data for geostatistical resource estimation Distance between samples/Metres Figure 2—Experimental semi-variograms constructed from core regularized to three lengths for a lead/zinc sample (adapted from Clark, 1979) Figure 1—Sampling results (sample length and assay values) for two variables of interest, Au and As, in a hypothetical drillhole Arsenic has no economic value, but could affect downstream processing efficiency and, ultimately, the value of the project. Higher density sampling was conducted across the area of highest gold mineralization. The arithmetic average of the gold assay values data is 1.05 g/t, compared with the length-weighted composite value of 0.80 g/t. This shows that the original arithmetic average considerably over-valued the Au grade for this drillhole. In the biased arithmetic average, all samples are equally weighted, irrespective of the length that the sample assay represents; in calculating the average, the 0.5 m sample at 2 g/t receives the same weighting as the 3 m sample at 0.6 g/t. The arithmetic average ignores representivity of the sample, resulting in this grade difference. A composite sample is a more representative value of the grade, and is obtained by weighting every sample assay according to the length it represents. Considering the As data, we see that the arithmetic average under-estimates the actual As levels by selectively over-sampling specific targets where lower values of As are found: the arithmetic average of the As sample data is 1.36% and the length-weighted average is 1.60%. It is known that the variance of a grade variable decreases as the sample support increases, which is a derivation of Krige’s relationship (Krige, 1951). This is known as the volume-variance relationship, or dispersion variance, and is used in the operation of estimators that make use of the change of support rule, the most common being uniform co (...truncated)