A Comparative Study Between the Direct and Indirect Methods in Geostatistical Simulation

Ore grades are analyzed separately for different granulometric fractions for many mineralization types, such as iron and bauxite ores. The result is that the samples have very different masses, so the grades are non-additive. The mass of each sample is usually recorded as recovery, which is the mass retained at a specific sieve aperture divided by the total ore mass. The classical geostatistical approach to estimating non-additive variables, known as the indirect approach, involves using accumulation (grade × recovery). In this approach, the grade estimates are obtained by dividing the accumulation estimates by the recovery estimates. The application of the indirect approach to obtain estimates is well discussed in the literature. However, its application in geostatistical simulation still needs to be investigated. This paper investigates how the indirect approach affects geostatistical simulation. The simulations obtained by the indirect approach are compared against those obtained by the direct approach, which consists of simulating the grades directly. These techniques are applied in a case study with data from a real bauxite deposit. The reproduction of basic statistics (histogram and variogram) of the variable of interest was assessed for both methods. We also conducted a cross validation experiment. The results showed that the direct approach outperformed the indirect one. The direct approach generates realizations with better histogram reproduction and higher local accuracy and precision. Specifically, the mean squared error obtained by the direct approach was roughly 2% lower than that obtained by the indirect one.