Abstract Most mining decisions are based on models estimated/simulated given the information obtained from samples. During the exploration stage, samples are commonly taken using diamond drill holes which are accurate and precise. These samples are considered hard data. In the production stage, new samples are added. These last are cheaper and more abundant than the drill hole samples, but imprecise and are here named as soft data. Usually hard and soft data are not sampled at the same locations, they form a heterotopic dataset. This article proposes a framework for geostatistical simulation with completely heterotopic soft data. The simulation proceeds in two steps. First, the variable of interest at the locations where soft data are available is simulated. The local conditional distributions built at these locations consider both hard and soft data and are obtained using simple cokriging with the intrinsic coregionalization model. Second, the variable of interest in the entire simulation grid using the original and previously simulated values at soft data locations is simulated. The results show that the information from soft data improved both the accuracy and precision of the simulated models. The proposed framework is illustrated by a case study with data obtained from an underground copper mine.

Abstract Short-term mining planning typically relies on samples obtained from channels or less-accurate sampling methods. The results may include larger sampling errors than those derived from diamond drill hole core samples. The aim of this paper is to evaluate the impact of the sampling error on grade estimation and propose a method of correcting the imprecision and bias in the soft data. In addition, this paper evaluates the benefits of using soft data in mining planning. These concepts are illustrated via a gold mine case study, where two different data types are presented. The study used Au grades collected via diamond drilling (hard data) and channels (soft data). Four methodologies were considered for estimation of the Au grades of each block to be mined: ordinary kriging with hard and soft data pooled without considering differences in data quality; ordinary kriging with only hard data; standardized ordinary kriging with pooled hard and soft data; and standardized, ordinary cokriging. The results show that even biased samples collected using poor sampling protocols improve the estimates more than a limited number of precise and unbiased samples. A welldesigned estimation method corrects the biases embedded in the samples, mitigating their propagation to the block model.

Abstract Some mineral deposits show mineralization along layers. These layers may pass through several subsequent geological events such as folding and/or severe erosional processes. Grades within these deposits tend to be correlated along orientations where the mineralization was originally deposited or along the same geological period (stratigraphic level). Consequently, some locations close to each other in terms of geographical coordinates can show uncorrelated grades. Spatial continuity analysis can also be affected by error inflicted by combining samples from different stratigraphic levels. This article uses the coordinate transformation (unfolding) to align the grades measured along the same stratigraphic level. The modification in coordinates improved the spatial continuity modeling and the grade estimates at non-sampled locations. The results showed that the mean of the relative error between the estimated value and the real value of the samples using unfolding is -0.10%. However, when using the original coordinates, the mean of the relative error is -0.65%. Furthermore, the correlation between the real and estimated value using crossvalidation is greater using stratigraphic coordinates. A complete case study in a manganese deposit illustrates the methodology.

O planejamento da lavra de um depósito mineral envolve o conhecimento de um ou mais atributos desse depósito. Esse conhecimento é obtido através de amostras do atributo em certos locais do depósito. Contudo a coleta de amostras pode envolver elevados custos, o que restringe o número de amostras e os locais onde valores do atributo são conhecidos. Assim, a estimativa de valores, em locais não amostrados, se torna necessária. A idéia de estimar valores em grids tridimensionais, utilizando amostras em coordenadas cartesianas e algoritmos da geoestatística pode levar a estimativas equivocadas em certas situações. Comumente, esse tipo de coordenadas não é compatível com a aplicação da geoestatística, visto que esse tipo de coordenadas pode prejudicar a determinação da continuidade dos valores amostrais e essa continuidade é a base dos algoritmos geoestatísticos. Assim, a questão da transformação de coordenadas cartesianas para coordenadas que permitam uma melhor determinação da continuidade dos valores amostrais é abordada nesse artigo. Para exemplificar a metodologia, uma transformação de coordenadas em um caso real de estimativas do atributo vagarosidade de onda acústica é apresentado.

Mining planning requires the knowledge of one or more of the deposit's attributes. This knowledge is obtained through attribute samples taken at certain locations. However, the sampling can be extremely costly which restricts the number of samples and locales where attribute values are known. Thus, the estimation of values, in unsampled locales, becomes necessary. The idea of value estimation in three-dimensional grids, using samples in Cartesian coordinates and geostatistical algorithms is the subject which has been approached. Nevertheless, commonly, this type of coordinates is not compatible to geostatistical application, since, this type of coordinates might damage the determination of the sample value's continuity and this continuity is the base of geostatistical algorithms. So, the question of Cartesian coordinate's transformation to coordinates that allow better sample-value continuity determination is approached in this paper. To demonstrate a coordinate's transformation, a real case of sonic wave slowness estimates is presented.