A Top-Cut Model for Deposits with Heavy-Tailed Grade Distribution

Rivoirard, Jacques; Demange, Claude; Freulon, Xavier; Lécureuil, Aurélie; Bellot, Nicolas

doi:10.1007/s11004-012-9401-x

Cited by 17 publications

(17 citation statements)

References 9 publications

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“…Variograms and crossvariograms of indicators were used to estimate transition probabilities, which allowed to define hotspots in relative terms as the areas within which higher values occurred unpredictably. This definition is close in concept to the topcut model of Rivoirard et al (2013). The geostatistical definition of hotspots and their mapping over time using co-kriging allowed to show convincing results on the anchovy in the Bay of Biscay.…”

Section: Discussionmentioning

confidence: 62%

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A Geostatistical Definition of Hotspots for Fish Spatial Distributions

et al. 2015

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Section: Discussionmentioning

confidence: 62%

“…Higher values are spatially uncorrelated with the geometry of A i and cannot be predicted within A i . The cutoff z i plays the role of the topcut in the model proposed by Rivoirard et al (2013). In practice, z i can be estimated using the following procedure.…”

Section: A Geostatistical Definition Of Biological Hotspotsmentioning

confidence: 99%

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

et al. 2015

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“…First, possible outliers and duplicated data were recognized. The presence of outliers in the dataset makes the inference of statistical parameters problematic and nonrepresentative [37,38]. These aberrant values intentionally influence the variance and result in sharp fluctuations in variogram analysis [39].…”

Section: Exploratory Data Analysis In Limestone Depositmentioning

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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“…Spatial data of natural resources or pollutants often show a small percentage of very high concentration values. This makes the inference of second-order statistics non-robust and in particular the variogram (Rivoirard et al 2013). In fisheries survey data, high-density values often result from the fish aggregative and schooling behaviour (Fréon and Misund 1999).…”

Section: Introductionmentioning

confidence: 99%

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

et al. 2018

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Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min-max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

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A Top-Cut Model for Deposits with Heavy-Tailed Grade Distribution

Cited by 17 publications

References 9 publications

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

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

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

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