# A Geostatistical Simulation of a Mineral Deposit using Uncertain Experimental Data

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## Abstract

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## 1. Introduction

## 2. Methodology

- Experimental local probability distribution functions: the local probability distribution functions were built from 15 soft data samples that were the nearest to the location of the uncertain measurement; and
- Parametric local probability distribution functions: the local probability distribution functions were built using Gaussian distributions with the means and standard deviations inferred from the 15 samples closest to the uncertain location.

- Direct sequential simulation only using the hard data to simulate the mineral deposit;
- Direct sequential collocated co-simulation using the accurate and precise experimental data as the hard data and the uncertain experimental data as the secondary data to simulate the mineral deposit;
- Direct sequential simulation with local probability distribution functions using the accurate and precise experimental data as the hard data and the uncertain experimental data to build experimental local probability distribution functions; and
- Direct sequential simulation with local probability distribution functions using the accurate and precise experimental data as the hard data and the uncertain experimental data to build parametric local probability distribution functions.

## 3. Application

#### 3.1. Dataset Description

#### 3.2. Results

_{Ref_Blocks}represents the true block values.

## 4. Conclusions and Recommendations

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Exhaustive Walker Lake dataset [17] and the experimental data locations used in this work (red filled circles: samples without measurement errors; white filled circles: samples with measurement errors).

**Figure 2.**Schematic representation of the modifications performed to the original exhaustive dataset. Two types of data were considered: samples without and with measurement errors.

**Figure 4.**E-type of the 100 simulations generated for each simulation strategy used: (

**a**) direct sequential simulation with only hard data, (

**b**) direct sequential collocated co-simulation, (

**c**) direct sequential simulation with experimental point distributions, and (

**d**) direct sequential simulation with parameterized point distributions.

**Figure 5.**Variance of the 100 simulations for each simulation strategy used: (

**a**) direct sequential simulation with only hard data, (

**b**) direct sequential collocated co-simulation, (

**c**) direct sequential simulation with experimental point distributions, and (

**d**) direct sequential simulation with parameterized point distributions.

**Figure 6.**Map of the absolute relative errors for each simulation strategy used: (

**a**) direct sequential simulation with only hard data, (

**b**) direct sequential collocated co-simulation, (

**c**) direct sequential simulation with experimental point distributions, and (

**d**) Direct sequential simulation with local distribution functions.

**Figure 7.**Histogram of the absolute error for each simulation strategy used: (

**a**) direct sequential simulation with only hard data, (

**b**) direct sequential collocated co-simulation, (

**c**) direct sequential simulation with experimental point distributions, and (

**d**) direct sequential simulation with parameterized point distributions.

**Figure 8.**Proportions of the classified mineral resources as a function of the calculated error by using different strategies: (

**a**) direct sequential simulation with only hard data, (

**b**) direct sequential collocated co-simulation, (

**c**) direct sequential simulation with experimental point distributions, and (

**d**) direct sequential simulation with parameterized point distributions.

**Table 1.**Main statistics of the original reference dataset and the uncertainty dataset used in this work.

Data | No. of Samples | Mean | Standard Deviation | CV | Minimum | Maximum |
---|---|---|---|---|---|---|

V_Ref_points | 78,000 | 2.78 | 2.50 | 0.90 | 0.00 | 16.31 |

V_Ref_blocks | 3120 | 2.78 | 2.49 | 0.89 | 0.00 | 15.68 |

V_20 × 20 | 195 | 2.73 | 2.43 | 0.89 | 0.00 | 10.13 |

V_5 × 5_+25% | 2925 | 3.44 | 3.12 | 0.90 | 0.00 | 18.30 |

**Table 2.**Proportions of the accurately classified mineral resources as a function of calculated relative error.

Classification of Resource | Blocks with Accuracy Error less than |
---|---|

Measured | 0–30% |

Indicated | 31–50% |

Inferred | >51% |

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## Share and Cite

**MDPI and ACS Style**

Narciso, J.; Araújo, C.P.; Azevedo, L.; Nunes, R.; Costa, J.F.; Soares, A.
A Geostatistical Simulation of a Mineral Deposit using Uncertain Experimental Data. *Minerals* **2019**, *9*, 247.
https://doi.org/10.3390/min9040247

**AMA Style**

Narciso J, Araújo CP, Azevedo L, Nunes R, Costa JF, Soares A.
A Geostatistical Simulation of a Mineral Deposit using Uncertain Experimental Data. *Minerals*. 2019; 9(4):247.
https://doi.org/10.3390/min9040247

**Chicago/Turabian Style**

Narciso, João, Cristina Paixão Araújo, Leonardo Azevedo, Ruben Nunes, João Filipe Costa, and Amílcar Soares.
2019. "A Geostatistical Simulation of a Mineral Deposit using Uncertain Experimental Data" *Minerals* 9, no. 4: 247.
https://doi.org/10.3390/min9040247