Block model in a multi facies context - Application to a porphyry copper deposit

International audienceWhen a mineral deposit is made of geological bodies such as breccias or lenses that concentrate high grades, and when production blocks contain few such bodies, estimating block grades by ordinary kriging may produce unrealistic spatial continuity. To improve the block model, a usual practice consists in (1) estimating spatial proportions of facies (unit), (2) estimating the grades, facies by facies, and (3) combining the results to obtain the block grades. We show that this practice assumes some links between the geological bodies, which will be verified. Then, we try to answer this general question: Given a set of samples where facies and grades are known, what is the best way to build a block model? We propose a methodological work flow which leads to a cokriging system where facies indicators are used, together with their product with the grade, a method that does not require the previous calculation of the facies proportions, at the scale of the blocks, but is implicitly based on them, at the point-support scale. The method is applied to a porphyry copper deposit located in northern Chile. When compared to a usual kriging without any facies consideration, the improvement of the method is slight because the grade follows the contact hierarchy between facies and also an important part of the spatial variability is purely random. When compared to the traditional approach we notice very poor correlation and this makes perhaps questionable some choices made by the geologists

Geostatistical comparison between blast and drill holes in a porphyry copper deposit

International audienceDiamond drill-hole grades are known to be of better quality than those of blast holes; is this true? We present a formal study of a porphyry copper deposit in Chile where the variogram of 3 meter long drill hole samples is compared to 15 meter long blast hole ones and we show that the blast holes can be assumed to regularizing the point information deduced from the drill holes, except for a nugget effect specific to the blast samples. Complementary analyses based on migrated data show that the drill holes also have their own errors

Spatial sampling effect of laboratory practices in a porphyry copper deposit

International audienceSampling protocols usually concern the way some kilograms of material are reduced to some grams with the same properties, but another protocol has to be considered: the choice of the samples to be used for estimating the resources of the deposit or some of its attributes. An important attribute is the metallurgical recovery, calculated with data sampling the deposit, on which laboratory tests are made to reproduce the metallurgical recovery process at a reduced scale. Such tests are very few because they are expensive; hence, the idea to combine them with exploratory data where the sole in situ grade is known using geostatistical techniques. While trying to put into practice this idea in a porphyry copper deposit located in the Chilean Central Andes, we encountered a surprising situation: laboratory tests and exploration measurements are supposed to use the same material but the total grades they measure do not have the same spatial variability. The paper presents the study and the impact of four causes. Spatial restriction: laboratory samples do not cover the same domain as exploration data. Regularization: laboratory and exploration samples do not have the same size. Sampling density: in the rich unit of the studied area, there are about two hundred laboratory samples and four thousand exploration ones. Grade selection: laboratory practice avoids high and low grades. The study shows that the major cause of the observed differences is the grade selection, but also that the number of laboratory tests is certainly too small with regards to the spatial variability of the grades. The consequence is that the sampling protocol for the metallurgical recovery tests shall be reconsidered if one wants to use them jointly with exploratory data

Breccia Pipe Estimation: a new approach using non-stationary covariances

International audienceThe El Teniente mine is famous not only as one of the largest known porphyry-copper ore bodies but also, among geologists, for its typical breccia pipe named “Braden”, an almost vertical poorly mineralized cone, located at the center of the mine and surrounded by early-stage mineralizations. As the edge of the pipe constitutes the limit of the deposit and of the mining operation, estimating it accurately is important. In this paper, we are interested in estimation of the elevation of the pipe surface using a geostatistical approach based on non-stationary covariances. Previous approaches have been applied on this dataset by Séguret and Celhay (2013). The proposed estimation method offers an integrated treatment of all aspects of non-stationarity (mean, variance, spatial continuity) in the modelling process. The proposed method has revealed an increased prediction accuracy when compared to standard stationary method, and demonstrated the ability to extract the underlying non-stationarity from a single realization. A comparison of predictions and prediction standard deviations maps indicates that the proposed non-stationary method captures some varying spatial features (such as locally varying anisotropy) in the data that are not present using the stationary method, the outcome appears more realistic

Geometric modeling of a Breccia pipe - comparing five approaches

International audienceThe El Teniente mine is famous not only as one of the largest known porphyry-copper ore bodies but also, among geologists, for its typical breccia pipe named "Braden", an almost vertical poorly mineralized cone, located at the center of the mine and surrounded by early-stage mineralizations. As the edge of the pipe constitutes the limit of the deposit and of the mining operation, estimating it accurately is important. For the ten thousand samples coded by a pipe indicator, four approaches are proposed: - Two-dimensional: among all the data, only the samples on the surface are used and the elevation of the pipe surface is estimated as a function of the northing and easting coordinates. - Binary: the samples are coded 0 or 1, and the probability of being in the pipe is estimated in three-dimensional space. - Intermediate: in the three-dimensional space, the points on the surface, initially coded 0 or 1, are replaced by 0.5 and the studied variable can then take three values: 0, 0.5 and 1. - Non-stationary: techniques of Intrinsic Random Functions of order k are applied on the previous variable. In this article, the four methods are described. The quality of the results is evaluated by cross validation and compared to the geologist approach. The article concludes with a discussion of the relevance of using stationary techniques in such a fundamentally non-stationary context

Analyse krigeante spatio-temporelle appliquée à des données aéromagnétiques

Application du krigeage trigonométrique a des données magnétiques mesurées par un avio

Geostatistical Evaluation of Rock-Quality Designation and its link with Linear Fracture Frequency

International audienceRock Quality Designation (RQD) is an important attribute used in geotechnics for quantifying the rock quality. It measures the borehole core recovery percentage incorporating only pieces of solid core that are longer than 100 mm measured along the centerline of the core. The presentation examines the behavior of this attribute in a Chilean porphyry copper deposit by analyzing more than 60,000 1.5-meter long samples.The drill holes have different directions and the nature of RQD requires accounting for the sample direction if the fracture network is anisotropic, a concept different from the geostatistical anisotropy which measures the variability along a direction set by two samples. A directional analysis is conducted and shows different variograms associated with different sample direction classes. This leads to different maps, calling into question the usual practices which do not account for the sample direction.The second part of the presentation concerns the link with the linear Fracture Frequency (FF), another important attribute which measures the number of discontinuities per meter. Under the assumption that the discontinuities along a line follow a Poisson process, Priest &Hudson established in 1976 a formula which expresses RQD as a function of FF. This formula is compared to E[RQF|FF], the mathematical expectation of RQD given FF, deduced from the data. The result of the comparison depends on whether FF is or is not corrected by the sinus of the angle between the sample direction and the fracture, as recommended by Terzaghi in 1965. When applied to FF, this correction breaks a natural correlation with RQD which appears when no correlation is applied. In the latter case, the Priest & Hudson formula is acceptable, in the first case it is not. So there is a dilemma: on the one hand, Terzaghi looks necessary to correctly calculate FF, on the other, the correction systematically increases FF and reduces the relative influence of RQD when both attributes are incorporated into an overall rating like the Rock Mass Rating (RMR), for example.A discussion follows, pointing out that RQD is subject to the same directional bias as FF and should be corrected in the same way by a sinus of the angle between the sample and the fracture, but such a correction is difficult, if not impossible; tests are presented. Finally, a correction of RQD is proposed, based on the Priest & Hudson formula

Mapping roadside nitrogen dioxide concentrations using non-stationary kriging

Report of a studyAtmospheric nitrogen dioxide (N02) concentrations around a major road in Alsace (France) are estimated on a fine grid using measurements given by passive samplers and a geostatistical approach. Data are referenced to a local coordinate system where (x, y) are respectively the distance from and along the road. They show a strong non-stationarity which does not allow ordinary kriging to be used in the estimation. Therefore a trend is modelled by a combination of exponential and polynomial functions. Experimental residuals are then computed as the differences between measurements and the trend. The idea is to interpolate the residuals at the nodes of the grid, applying kriging methods, and to add them to the trend estimate. Since their variance is not stationary either, an intermediary step is required. lt consists in modelling the standard deviation of the residuals as a function of the drift and normalizing the residuals by this model. This defines a new regionalized variable which can be estimated in the framework of stationary geostatistics. Two possible kriging systems are tested, depending on the fitted variogram model: in the first one, a pure nugget effect (white noise) is used, in which case the best linear estimator of N02 concentration is the trend model; in the second one, a structured exponential variogram is adjusted. This case study shows that non-stationarity may not only characterize the raw variable but can also affect the variance of a phenomenon. lt illustrates the interest of modelling it so as to improve the experimental variogram, fit an acceptable variogram model and compute the variance of the estimation error even if the estimator is reduced to a simple regression function

Cokriging Partial Grades - Application to Block Modeling of Copper Deposits

International audienceThis work concerns mineral deposits made of geological bodies such as breccias or lenses that contain several categories of grades with different characteristics in terms of distribution and variogram. When production blocks contain few such bodies, estimating block grades by ordinary kriging may produce unrealistic spatial continuity. We propose a method based on the indicators of objects (units or facies) together with their products with the grade. This is illustrated by an application to a porphyry copper deposit

GEOSTATISTICAL ANALYSIS OF VALIDATION DATA OF AN AIR POLLUTION SIMULATOR

International audienceChemistry-transport models for air quality forecasting are affected by the uncertainty on the input data (emissions of pollutants and meteorological conditions), the approximations in the modelling of the physicochemical reactions, and numerical approximations (space and time discretization). The validation of the accuracy of these simulators can be done by comparing predictions with actual measurements. This exercise has been carried out for a model for daily forecasting at the scale of Europe, with reference to daily measurements at about one hundred stations over one year. A thorough variographic analysis shows that the error field cannot be characterized independently of the predicted and observed fields. Indeed the forecasts usually display space and time variations similar to those of the measurement data, up to a multiplicative factor, but are often poorly correlated with the reality. These results can be used to define priorities in the improvement of the chemistrytransport model. The presentation is focused on sulphates and nitrogen dioxide