Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits

Maleki, Mohammad; Emery, Xavier; Mery, Nadia

doi:10.3390/min7120241

Cited by 15 publications

(7 citation statements)

References 33 publications

(32 reference statements)

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“…It is also worth mentioning that anisotropy was examined through the original dataset (not transformed), and it was seen that the existence of anisotropy in the region was improbable. For fitting of theoretical variograms over experimental variograms, the linear model of co-regionalization [45] with semi-automatic technique is chosen, in which the semi-definiteness condition [36,46] is respected through the process of fitting. In this model, direct and cross-covariances are defined as the sum of basic covariances.…”

Section: Variogram Inferencementioning

confidence: 99%

Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships

Battalgazy

Madani

2019

Minerals

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Modeling multivariate variables with complexity in a cross-correlation structure is always applicable to mineral resource evaluation and exploration in multi-element deposits. However, the geostatistical algorithm for such modeling is usually challenging. In this respect, projection pursuit multivariate transform (PPMT), which can successfully handle the complexity of interest in bivariate relationships, may be particularly useful. This work presents an algorithm for combining projection pursuit multivariate transform (PPMT) with a conventional (co)-simulation technique where spatial dependency among variables can be defined by a linear model of co-regionalization (LMC). This algorithm is examined by one real case study in a limestone deposit in the south of Kazakhstan, in which four chemical compounds (CaO, Al2O3, Fe2O3, and SiO2) with complexity in bivariate relationships are analyzed and 100 realizations are produced for each variable. To show the effectiveness of the proposed algorithm, the outputs (realizations) are statistically examined and the results show that this methodology is legitimate for reproduction of original mean, variance, and complex cross-correlation among the variables and can be employed for further processes. Then, the applicability of the concept is demonstrated on a workflow to classify this limestone deposit as measured, indicated, or inferred based on Joint Ore Reserves Committee (JORC) code. The categorization is carried out based on two zone definitions, geological, and mining units.

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Section: Variogram Inferencementioning

confidence: 99%

Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships

Battalgazy

Madani

2019

Minerals

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“…To do so, experimental variogram (ℎ) computes the average dissimilarity between data separated by vector ℎ. It is calculated as half the average squared difference between the components of every data pair [10,35]:…”

Section: Modeling Spatial Continuity: Variogram Analysismentioning

confidence: 99%

“…Spatial continuity of geological properties including geomechanical parameters can be a measure of changes in variance versus distance. To do so, experimental variogram γ(h) computes the average dissimilarity between data separated by vector h. It is calculated as half the average squared difference between the components of every data pair [10,35]:…”

Section: Modeling Spatial Continuity: Variogram Analysismentioning

confidence: 99%

Spatial Mapping of the Rock Quality Designation Using Multi-Gaussian Kriging Method

2018

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The rock quality designation is an important input for the analysis and design of rock structures as reliable spatial modeling of the rock quality designation (RQD) can assist in designing and planning mines more efficiently. The aim of this paper is to model the spatial distribution of the RQD using the multi-Gaussian kriging approach as an alternative to the non-linear geostatistical technique which has shown some limitations. To this end, 470 RQD datasets were collected from 9 boreholes pertaining to the Gazestan ore deposit in Iran. The datasets were declustered then transformed into Gaussian distribution. To ensure the model spatial continuity, variogram analysis was first performed. The elevation 150 m with a grid of 5 m × 5 m × 5 m was selected to illustrate the methodology. Surface maps showing the RQD classes (very poor, poor, fair, good, and very good) with their associated probability were established. A cross-validation method was used to check the obtained model. The validation results indicated good prediction of the local variability. In addition, the associated uncertainty was quantified on the basis of the conditional distributions and the accuracy plot agreed with the overall results. It is concluded that the proposed model could be used to produce a reliable RQD map.

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“…Lithotypes are classified into different categories based on interclass dependencies. However, the following two issues, among others, occur during lithotype modeling in an ore deposit 3 . The first one is defining domain layout to minimize misclassifications.…”

Section: Introductionmentioning

confidence: 99%

A v-transformed copula-based simulation model for lithological classification in an Indian copper deposit

Dinda

Samanta

Chakravarty

2022

Sci Rep

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Copula functions are widely used for modeling multivariate dependence. Since the multivariate data may not necessarily be linear and Gaussian, the copula model is very often brought into the picture for modeling such multivariate phenomena. The lithological classification in spatial domain is a class of problems dealing with categorical variables. A generalized class of copula model is effective for such classification tasks. In this paper, a non-Gaussian copula (v-transformed copula) model has been used for lithotype classification of an Indian copper deposit. Coupling of Markov chain Monte Carlo (MCMC) simulation and copula discriminant function is performed for this purpose. Specifically, four lithotypes, e.g., granite, quartz, basic, and aplite are simulated in the case study deposit. The efficacy of v-transformed copula discriminant function-based simulation is compared with those of Gaussian copula, t copula, and sequential indicator simulations. Finally, the classification accuracy of all the approaches is examined with ground-truth lithological classes obtained from blast hole information. The results show that the v-transformed copula simulation has a relatively higher classification accuracy (76%) than those of Gaussian copula (70%), t copula (69%), and sequential indicator (70%) simulations.

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Indicator Variograms as an Aid for Geological Interpretation and Modeling of Ore Deposits

Cited by 15 publications

References 33 publications

Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships

Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships

Spatial Mapping of the Rock Quality Designation Using Multi-Gaussian Kriging Method

A v-transformed copula-based simulation model for lithological classification in an Indian copper deposit

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