Those of us engaged in exploration geochemistry have undoubtedly faced difficulties in the interpretation of geochemical surveys for resistate minerals. Over the past ten years, nugget effects in elements such as tungsten, tin, and now gold have undoubtedly caused many headaches. The large amount of exploration currently under way for Au makes the nugget effects associated with Au particularly important for the exploration geochemist.
Many geochemists have attempted to reduce nugget effects by taking large samples, taking replicate samples, or analyzing numerous ‘check’ samples to monitor and estimate sample variability. Most of us would agree that there cannot be too much care taken in sampling for gold. Factors such as target type, sample spacing, sample size, sample media, sample preparation/reduction technique, and sample determination procedure must all be considered during interpretation because each of these factors can influence the observed geochemicaf signal.
Recently, much ado has been made about the futility of collecting geochemical samples for Au. (Gy 1982), grain size studies (Clifton et al. 1969) and Poisson statistics (Ingamells 1981, Figure 1) invariably show that a monster (greater than 10kg) sample must be taken in order to faithfully reproduce and “anomolous” gold concentration. Unfortunately, studies of this type consider only the representiveness of the individual sample. They do not consider the spatial relationships of the, hopefully, several samples which are ‘anomalous’.
Attaining reproducible gold results in a given sample is not the ultimate goal of the exploration geochemist. Rather, our goal is to recognize a pattern of element distribution which can be attributed to an economic mineral target or geological feature. This is the crucial point. Since interpretable patterns (anomalies) are, in many cases, composed of groups of samples, the individual sample representiveness need not be at a level where anomaly detection is highly likely. Rather the product of the probability of anomaly detection at an individual sample site times the number of sites which sample anomalous material controls whether a pattern can be recognized. Essentially, there is safety in numbers.
Obviously, a trade-off exists between sample size and sample density. Increasing sample size increases the probability of detecting gold at a specific anomalous sample site. Increasing sample density increases the probability of detecting gold in at least one of several anomalous sample sites. In each case, our goal of anomaly detection can be realized.
To illustrate this point, a computer program was designed to randomly generate a simple geological model consisting of a geochemical anomaly on a mineral claim. The geochemical anomaly forms a linear pattern and is subject to rare grain-sampling difficulties similar to what might be expected from a Au-bearing quartz vein (Figure 2). The length and location of the ‘vein’ was randomly chosen by the computer. Eastward dispersion of the surficiaf materials (soils) overlying the N-S oriented vein has been simulated by the program and this dispersion decays in an exponential form (Bird and Coker 1987; Shilts 1976). Sample sites located on a series of lines perpendicular to the vein orientation are spaced close enough to ensure that several samples will contain truly anomalous concentrations (either from the Au source or its dispersion train). The sizes of the dots on Figure 2a represent the ‘true’ relative concentrations (the groundtruth) of the soils on the mineral claim.
Computer-effected sample collection at each site of the groundtruth was done using Poisson statistics to simulate the sample variance produced by the existence of rare grains (Figure I). Due to sampling or laboratory error, the ‘background’ areas occasionally report detectable Au concentrations.
In each sampling simulation, a different sample size was used to determine the (Poisson) probabilities, at any given concentration, of detecting different numbers of rare grains in the sample. Thus a different expected number of Au grains is contained in each of the sample realizations shown in Figures 2b and 2c. The sampled grid of Figure 2c represents a sample size 4 times larger than the sample size for Figure 2b. Obviously, the reliability of Au detection on an individual sample varies from case to case, but the linear relationship of the pattern of anomalous samples makes detection easier.
Clearly, based on this simple stochastic model, the probability of anomaly detection is some function of sample density and sample size. Both must be considered when designing geochemical surveys for rare resistate minerals.
As a test of your ability to recognize a similar anomaly, Figure 2d contains a realization of an unknown groundtruth, produced using a small sample size. In the next issue of the newsletter, the groundtruth used to generate this realization will be published, along with a similar realization using a larger sample size. It may be interesting to compare your best guess of the location and length of the anomaly on Figure 2d with the groundtruth used to produce the grid. Hopefully, this example allows insight into the control of both sample density and sample size on the reliability of rare resistate mineral analyses and on the probability of anomaly detection.
Clifford R. Stanley
Dept. of Geological Sciences, University of British Columbia
and CyberQuest Exploration Systems
Vancouver, B.C. V6CIJ8
Barry W. Smee
Bird, D.J. and Coker, W.B. (1987)
Quaternary Stratigraphy and Geochemistry at the Owl Creek Gold Mine, Tim- mins, Ontario, Canada.
JGE v.28, p. 267-284.
Clifton, H.E., Hunter, R.E., Swanson, F.J. and Phillips, R.L. (1969)
Sample Size and Meaningful Gold Analysis.
USGSPP 625-C, p. C1-C17.
Gy, P.M. (1982)
Sampling of Particulate Materials. Eisevier,
New York, p. 1431.
Ingamells, CO. (1981)
Evaluation of Skewed Exploration Data – The Nugget Effect.
GCA, v. 45, p. 1209-1216.
Shilts, WW (1976)
Glacial Till and Mineral Exploration, in Legget, R.F. (Ed.),
Glacial Till – An Interdisciplinary Study.
Royal Soc. Can. Sp. Pub., v. 12, p. 205-224.