Resource Geology

Domaining and Stationarity

Simply put, get it right! If I had to pick a single item for Resource Geologists to spend the most time on and will make the greatest difference in a model, it's data domaining. This comes in a variety of ways such as a robust geological model, a strong understanding of data statistics (EDA), the art of lumping & breaking, and sound geologic understanding of your deposit or area.  I'm digging out an old article on this post that makes a quick read but hopefully stresses the importance that if you don't get your domains right, no amount of fancy, mind-numbing mathematics can make your model better.

Top Cutting or Capping

“To cap, or not to cap, that is the question: Whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune, or to take Arms against a Sea of trouble”. High-grade samples are of course what we want in mining but when they’re outliers they become problematic. Therefore, Capping or Top Cutting of extreme outlier data is commonly used in resource estimation to generate a realistic estimate by not overstating the “true” underlying mean grade, variance and CV or simply blowing unsupported high-grade into all blocks in the zip code and thus overstating a resource. Here are few points when considering capping: 1) check to see if the data is real or an error, 2) check stats before and after capping to assess the impact to the mean, 3) view them spatially, are they clustered in one area or scattered about the ore body? 4) calculate the extreme outlier upper threshold = (Q3 + 3*(interquartile range),  and 5) perhaps run two estimates, with capping and without, to truly understand their impact on the final estimate and grade-tonne curve. There are many ways of dealing with extreme outliers. When you do cap, ensure you perform capping on composited samples to ensure consistent volume of samples. 

(Top cutting evaluation of raw gold grades

Kriging Neighbourhood Analysis

On the subject of Qualitative Kriging Neighbourhood Analysis (QKNA) and conditional bias. At a high level, this is essentially a method of testing several search neighborhood parameters to find an acceptable compromise in the proper selection of data.  Multiple neighborhoods are reviewed against estimation outputs such as slope of regression, sum of negative weights, weight of the mean, and kriging efficiency to "optimize" the search to reduce conditional bias. A detailed description is best presented by John Vann, Jackson, and Bertoli (2003).  On the flip side, Ed Isaaks and others have shown how KNA can increase estimation error in predicted grade-tonnes. Boyle (2010) demonstrated that KNA overstates benefits of one search over another and domaining and sampling accuracy are far more important.

Nugget

The nugget is a measure of the intrinsic variability of a grade variable + sampling error. Determining  the proportion of nugget effect is critical when you model spatial continuity. In mining, most grade variables have at least some nugget value. The relative nugget effect (proportion of nugget to sill) is the same in all directions and usually best to determine from downhole variograms simply because samples are so close to each other.  The nugget has significant impact on kriging estimates. The kriged estimate determines the grade distribution or histogram. The grade distribution determines total grade-tonnes at cut-offs. So yeah, it's important. The image below shows the same data set estimated with a high relative nugget effect and one with a low nugget. Both have the same mean but the shaded area under the curve represents over or under-estimated tonnages due to changes in the nugget. A low nugget will result in a smoother distribution.  Long story short - pay attention to nugget values and understand how the final nugget value can impact variograms, grade distribution, and final grade-tonne curves.