Application of Three-Dimensional Direct Least Square Method for Ellipsoid Anisotropy Fitting Model of Highly Irregular Drill Hole Patterns

Round 1

Reviewer 1 Report

Following are my comments:

·        Is raw data used for making variograms or the composited data used for making variograms.

·        On page 3 Line 100, the authors have mentioned the variogram models used for the study. What were the lag distance, lag Azimuth tolerance, and bandwidth used to create the input variograms?

·        On page 4,

o   why was the variogram with the dip of 90 degrees not used to see the downhole impact on the variogram?

o   How does changing, adding, or deleting a variogram model from the inputs change the ellipse?

·        On page 5 Line 115, the authors talk about the 3D direct least square method. This is a good place to talk a little bit about the method.

·        Section 3.2 is confusing. On line 216 the authors say “Only eight from 16 data points were beyond the ellipsoid” i.e. 50% of the data is beyond the ellipsoid. Anisotropy within the model shows the trend of the mineralization and the ranges in each direction show the impact of a sample while performing resource estimation.

o   What does the fitting error mean and how is that calculated?

o   Show variogram parameters along with the data points in Table 2.

·        On page 9 Figure 7, an omnidirectional variogram was compared. How is the variogram along the Major, Semi-major and Minor axis for the fitted ellipse?

·        On page 10, add the color scale to Figure 8.

o   What are the block size, number of blocks, and the estimation parameters used for resource estimation?

·        The authors say a new approach for three-dimensional model fitting of the ellipsoid is presented. How was the method different than what is presented in Rahmadiantri et.al. (2017) and how it was improved? It is not mentioned in the manuscript.

·        Authors should discuss and elaborate on the results.

 

·        Authors should elaborate on the conclusion, implications, and future research directions. 

Author Response

We thank you very much for the constructive comments and suggestions to improve our manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Brief report on the paper applsci-1807074 by Muchtadi-Alamsyah et al.

The detailed report can be found in the attached PDF file. I recommend to accept the manuscript.

The issues of geostatistical analysis applied to geological modelling was concerned in this paper with a special focus on using ellipsoid anisotropy
The research presents novel approach using 3D direct least square method for ellipsoid anisotropy applied for highly irregular drill hole patterns.
The manuscript meets general criteria of the significance in geological data analysis and applied sciences.
The structure of the article conforms to an acceptable format of standard sections: Introduction, Methodology, Results, Discussion, Conclusion, References.
The Introduction section presents a background, defines research goals and provides a clear statement of research problem.
Literature regarding the relevant topics is reviewed and appropriately referenced. The weakness in former works are described; the existing gaps are identified.
The Materials and Methods are descriptive. Modifications of the existing methods are mentioned briefly.
The Results are presented with clarity and include description, graphical illustrations, tables, equations and calculations. Results are relevant to the research goals and objectives of this study.
The Discussion interpreted the major outcomes of this study. The advantages of the obtained results are described and compared with other studies.
The Conclusion summarized the study with interpretation of facts.
The clarity of the text logic and organization of the paper is sufficient.
The paper is well organized with structured sections. It demonstrates the consistent interpretation of the results with detailed explanations.
A comparison of the results with previous studies is presented.
The academic contribution is clear: the paper increases the knowledge in applied geology, geostatistical data modelling and engineering.
The importance and novelty consists in technical approach of assessment of drill hole patterns using large dataset on Zn and methods of geostatistical analysis with a special case of ellipsoid anisotropy.
Figures are of good quality, easy to read, relevant and suitable, well illustrate the results, relevant to the content, have sufficient resolution, appropriately described and labeled.
The paper combines technical, geostatistical, geological and mathematical approaches which presents a multi-disciplinary study well deserved to be published in Applied Sciences.

The detailed report can be found in the attached PDF file. I recommend to accept the manuscript .

With kind regards, - Anonymous reviewer.

28.06.2022.

Comments for author File: Comments.pdf

Author Response

We thank you very much for the review results and accepting our manuscript to be published in Applied Sciences.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper “Application of three-dimensional direct least square method for ellipsoid anisotropy fitting model of highly irregular drill hole patterns” indicates a methodology for fitting a three-dimensional ellipsoidal model for spatial prediction. The methodology that the authors used is the expansion of the 2D least square fitting to the 3D case.

The Review of the Manuscript:

1-      Although one can clearly see the mathematical explanation and implementation of the methodology, the comparison shown in the manuscript does not seem to clearly indicate the superiority of the proposed methodology. The authors made the comparison using the isotropic and anisotropic cases, but given that the deposit exhibits strong anisotropy, the kriging using the isotropic variogram model will definitely result in erratic estimates compared to the anisotropic case. I suggest the authors make the comparison considering traditional and their proposed methodology or justify the methodology clearly.

2-      The experimental variogram was calculated in 8 different directions considering the horizontal plane and 8 different cases (different azimuth bearing and dips) in the downhole (or tertiary) direction. I have understood the strategy for the directions selected considering the horizontal plane, but I think that the authors should clearly explain why or how they selected the mentioned azimuth bearings and dip angles in the downhole direction. Is there any strategy for selecting these numbers?

3-      I could not read the axes shown in Figure 3. Also, the data variance should be shown as a sill in each experimental variogram unless the experimental variograms have been standardized.

4-      There appears to be some grammatical errors in many parts of the manuscript. I suggest the authors do another proofreading to ensure that the final version of the manuscript is error free.

 Finally, the issues mentioned above should be addressed by the authors before the manuscript can be considered for publication.

 

Author Response

We thank you very much for the constructive comments and suggestions to improve our manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have addressed all my comments and I am happy with the changes they have made. I do not have any further comments.