Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

Gordon Yu; John Parianos

doi:10.3390/min11050449

Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

Minerals ◽

10.3390/min11050449 ◽

2021 ◽

Vol 11 (5) ◽

pp. 449

Author(s):

Gordon Yu ◽

John Parianos

Keyword(s):

Mineral Resource ◽

Statistical Method ◽

Field Measurements ◽

Rayleigh Distribution ◽

Core Sample ◽

Resource Estimation ◽

Mining Equipment ◽

Polymetallic Nodules ◽

Generalized Rayleigh Distribution ◽

Offshore Mining

An efficient empirical statistical method is developed to improve the process of mineral resource estimation of seabed polymetallic nodules and is applied to analyze the abundance of seabed polymetallic nodules in the Clarion Clipperton Zone (CCZ). The newly proposed method is based on three hypotheses as the foundation for a model of “idealized nodules”, which was validated by analyzing nodule samples collected from the seabed within the Tonga Offshore Mining Limited (TOML) exploration contract. Once validated, the “idealized nodule” model was used to deduce a set of empirical formulae for predicting the nodule resources, in terms of percentage coverage and abundance. The formulae were then applied to analyzing a total of 188 sets of nodule samples collected across the TOML areas, comprising box-core samples and towed camera images as well as other detailed box-core sample measurements from the literature. Numerical results for nodule abundance and coverage predictions were compared with field measurements, and unbiased agreement has been reached. The new method has the potential to achieve more accurate mineral resource estimation with reduced sample numbers and sizes. They may also have application in improving the efficiency of design and configuration of mining equipment.

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Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

10.20944/preprints202103.0639.v1 ◽

2021 ◽

Author(s):

Gordon Yu ◽

John Michael Parianos

Keyword(s):

Mineral Resource ◽

Reasonable Agreement ◽

Field Measurements ◽

Rayleigh Distribution ◽

Core Sample ◽

Resource Estimation ◽

Mining Equipment ◽

Polymetallic Nodules ◽

Generalized Rayleigh Distribution ◽

Offshore Mining

An effective empirical statistical method is developed to improve the process of mineral resource estimation of seabed polymetallic nodules and is applied to analyse the abundance of seabed polymetallic nodules in the Clarion Clipperton Zone (CCZ). The newly proposed method is based on three hypotheses as the foundation for a model of “Idealized Nodules”, which was validated by analysing nodule samples collected from the seabed within the Tonga Offshore Mining Limited (TOML) exploration contract. Once validated, the “Idealized Nodule” model was used to deduce a set of empirical formulae for predicting the nodule resources, in terms of Percentage Coverage and Abundance. The formulae were then applied to analysing a total of 188 sets of nodule samples collected across the TOML areas, comprising box-core samples and towed camera images collected by one of the authors and detailed in [4]. The analysis also relies upon detailed box-core sample measurements from other areas reported by [7]. Numerical results for resource prediction were compared with field measurements, and reasonable agreement has been achieved. The new method has the potential to achieve more accurate mineral resource estimation with reduced sample numbers and sizes. They may also have application in improving the efficiency of design and configuration of mining equipment.

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Polymetallic Nodules Resource Estimation in the Suoi Thau-Sang Than Area, northeastern Vietnam

Inżynieria Mineralna ◽

10.29227/im-2020-02-03 ◽

2020 ◽

Vol 1 (2) ◽

Author(s):

Khuong THE HUNG ◽

Pham NHU SANG ◽

Nguyen PHUONG ◽

Nguyen TIEN DUNG ◽

Bui HOANG BAC ◽

...

Keyword(s):

Mineral Resource ◽

Calculation Method ◽

Mineral Exploration ◽

Direct Calculation ◽

Resource Estimation ◽

Cutoff Grade ◽

Grade Change ◽

Polymetallic Nodules ◽

The One ◽

Selection Of

1,720 chemical, mineral, and petrography samples in the Suoi Thau-Sang Than area, northeastern Vietnam were collected to investigate polymetallic nodules resource. The similarity-analogy in ore geology, direct calculation method for metallization parameters, and mineral resource estimation based on cutoff grade change methods are employed to estimate polymetallic nodules resource from the Suoi Thau, Sang Than, and Ban Kep areas in northeastern Vietnam. The similarity-analogy in ore geology indicates 1,785,000 tons Cu, 12,005,000 tons Pb+Zn, and 195 kg Au in total. The direct calculation method for metallization parameters shows 2,060,000 tons Cu, 13,648,000 tons Pb+Zn, and 224 kg Au in total. These methods display that the Sang Than area contains mainly polymetallic nodules in the studied area. Following the mineral resource estimation based on cutoff grade changes, estimation results indicate potential Pb-Zn nodules resource in the Ban Kep and Cu nodules resource in the Sang Than, while no potential Au nodules resource in the Suoi Thau and the Sang Than as well as the Ban Kep. The estimation results obtained from mineral resource estimation based on cutoff grade changes are suitable with the results from the traditional geometric block methods. Our study suggests that the Sang Than area can be considered as a potential Cu nodules resource, and the Ban Kep area is potential Pb-Zn nodules resource in northeastern Vietnam for future exploitation, while there is no potential polymetallic nodules resource in the Suoi Thau area. Furthermore, the one resource estimation based on cutoff grade changes method displays an overview of the prospect on polymetallic nodules resources, indicating that this method can serve as a basis for the proposed selection of the prospective areas for effective Cu, Pb-Zn, and Au mineral exploration in the Suoi Thau-Sang Than area, northeastern Vietnam.

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Geostatistical Estimation of Multi-Domain Deposits with Transitional Boundaries: A Sensitivity Study for the Sechahun Iron Mine

Minerals ◽

10.3390/min9020115 ◽

2019 ◽

Vol 9 (2) ◽

pp. 115 ◽

Cited By ~ 3

Author(s):

Sara Kasmaee ◽

Giuseppe Raspa ◽

Chantal de Fouquet ◽

Francesco Tinti ◽

Stefano Bonduà ◽

...

Keyword(s):

Mineral Resource ◽

Sensitivity Study ◽

Accurate Estimate ◽

Resource Estimation ◽

Real Application ◽

Grade Estimation ◽

Boundary Identification ◽

Geostatistical Estimation ◽

Iron Mine ◽

Geological Information

In mineral resource estimation, identification of the geological domains to be used for modeling, and the type of boundaries dividing them, is a major concern. Generally, the variables within a domain are estimated with an assumption of the hard boundaries (sharp contact). However, in many cases, the geologic structures that generate a deposit are transitional (overlapping of several geologic domains). Consequently, boundary identification of the geological domains is essential for an accurate estimate of resources. This paper considers a real application to examine whether the addition of geologic information benefits grade estimation in the presence of transitional boundaries. Results proved that the accuracy of the grade estimation can be improved by adding geological information and there is a significant sensitivity in grade estimation results in the existence of transitional boundaries.

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Review of the Book “Mineral Resource Estimation” by Mario Rossi and Clayton Deutsch, 332p, Published by Springer in Early 2014 (ISBN 978-1-4020-5716-8)

Mathematical Geosciences ◽

10.1007/s11004-014-9547-9 ◽

2014 ◽

Vol 46 (8) ◽

pp. 1029-1034

Author(s):

Michel Dagbert

Keyword(s):

Mineral Resource ◽

Resource Estimation

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On double stage minimax-shrinkage estimator for generalized Rayleigh model

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v5i1.5553 ◽

2016 ◽

Vol 5 (1) ◽

pp. 39 ◽

Cited By ~ 1

Author(s):

Abbas Najim Salman ◽

Maymona Ameen

Keyword(s):

Sample Size ◽

Shape Parameter ◽

Mean Squared Error ◽

Scale Parameter ◽

Rayleigh Distribution ◽

Shrinkage Estimator ◽

Squared Error ◽

Expected Sample Size ◽

Generalized Rayleigh Distribution ◽

The Mean

This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a0) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(×) and suitable region R.Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved for the proposed estimator are derived.Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.

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Mineral resource estimation using a combination of drilling and IP&Rs data using statistical and cokriging methods

Bulletin Of The Mineral Research and Exploration ◽

10.19111/bulletinofmre.502794 ◽

2018 ◽

pp. 1-10

Author(s):

Kamran Mostafaei ◽

Hamidreza Ramazi

Keyword(s):

Mineral Resource ◽

Resource Estimation

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Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

Baghdad Science Journal ◽

10.21123/bsj.11.2.193-201 ◽

2014 ◽

Vol 11 (2) ◽

pp. 193-201

Author(s):

Baghdad Science Journal

Keyword(s):

Current Model ◽

Survival Function ◽

Information Matrix ◽

Interval Estimation ◽

Real Data ◽

Rayleigh Distribution ◽

Point Estimation ◽

Distribution Model ◽

Unknown Parameters ◽

Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

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