the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Aug 2023
Three-Dimensional Analytical Solution of Self-potential from Regularly Polarized Bodies in Layered Seafloor Model
Abstract. The self-potential (SP) method is a sensitive geophysical means to locate seafloor polymetallic sulfide deposits. A reasonable SP forward modeling can provide a good foundation for inversion and interpretation of the measured data. We propose a method to solve the analytical solution of the SP generated by regularly polarized bodies in layered media. Based on the mirror image current theory, a new analytical formula was derived and clarified in detail for the models. We also discussed the analytical solution of layered models with different numbers of layers through numerical computation. Furthermore, a lab-based oxidation-reduction experiment was conducted to record the SP data. These data were used to simulate the SP generated by seafloor massive sulfide(SMS) deposits and assess the analytical solution previously. The result shows that the measured SP data matches the analytical solution well. That demonstrates the correctness of the proposed method and the corresponding analytical solution. It is significant to fast and precise forward modeling and inversion for SMS explorations.
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Status: closed
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RC1: 'Comment on gmd-2023-94', Anonymous Referee #1, 16 Mar 2024
General comments
The authors introduced a 3D analytical solution for forwarding modeling of self-potential from sulfide deposits. Although the topic is interesting and the overall flow of the paper, from the formulation to comparison with 2D analytical solution and experimental results, is great, I can hardly say the paper is well written in general and there seems to be a lot of room for improvement of the manuscript.
The motivation of the current model development is not compelling, especially given that (1) the system has not been proven to be applicable to the field (even though the authors attempted to validate the model with laboratory experiments, it does not necessarily mean it can be used in the field) and (2) complicated situations are likely to be more easily dealt with numerical tools/methods and there seem to be some published already.
Formulation is poorly explained especially given that deriving analytical solution for the system should be the essential part for a model development paper. I found it difficult to follow how the equations are derived. There can be several reasons for this, including (1) the papers cited (Li et al., 2005, He, 2012) for seemingly essential equations are not publicly available and not explained well, (2) the authors do not seem to use mathematical symbols in an organized way, including seemingly interchangeable and thus confusing use of uppercase/lowercase and/or Greek/English letters and/or vector/scalar expressions, and (3) figure to help the reader to understand formulation is lacking and/or not referenced.Especially, please consider making clearer explanations on (1) what is proved and how this is done in Section 2.1, (2) the mirror image method in general potentially with a specific diagram/schematic in Section 2.2 and (3) derivation of one of formulation from Table 1 in Section 2.3.
Specific comments
L9. “It is significant to fast and precise forward modeling and inversion for SMS explorations.”. I think English grammar here is not correct.
L22. What is “AUV”?
L34. What do you mean by “affection of the field source”?
L34. “which occur difficulty in solving the Poisson equation.” I think the authors should correct English.
L58. What is the definition of H?
L79. rho_0 must be a typo of r_0?
L82. “So we get the potential distribution along the surface of a uniformly polarized sphere is equivalent to an electric dipole.” I do not understand what this means.
L92. Is the use of permittivity correct here? In other words, do permittivity and conductivity have the same units?
L137. What do you mean by “the dipole moment is 1 D.”?
L138. 10-10 must mean 10^-10. What are units and adjustment term exactly?
L140. Do “exceptions” mean negative/positive peaks?
L142. Why tilted dipole is related to any depth?
L147. The authors should describe exactly what redox reaction is occurring.
Citation: https://doi.org/10.5194/gmd-2023-94-RC1 -
AC2: 'Reply on RC1', Pengfei Zhang, 05 Jul 2024
First and foremost, we would like to extend our sincere gratitude to Referee #1 for the insightful comments. We have carefully considered the feedback and revised the manuscript accordingly. All changes have been highlighted in the manuscript to facilitate the review process. Please find attached our detailed responses, where we have addressed each of the reviewer’s comments
Best regards,
Pengfei Zhang
On behalf of all authors
-
AC2: 'Reply on RC1', Pengfei Zhang, 05 Jul 2024
-
RC2: 'Formulas and Results', Anonymous Referee #2, 18 Jun 2024
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-94/gmd-2023-94-RC2-supplement.pdf
-
AC1: 'Reply on RC2', Pengfei Zhang, 05 Jul 2024
First of all, we would like to extend our sincere gratitude to Referee #2 for the insightful comments. We have carefully considered the feedback and revised the manuscript accordingly. All changes have been highlighted in the manuscript to facilitate the review process. Please find attached our detailed responses, where we have addressed each of the reviewer’s comments.
Sincerely,
Pengfei ZHANG
On behalf of all authors
-
AC1: 'Reply on RC2', Pengfei Zhang, 05 Jul 2024
Status: closed
-
RC1: 'Comment on gmd-2023-94', Anonymous Referee #1, 16 Mar 2024
General comments
The authors introduced a 3D analytical solution for forwarding modeling of self-potential from sulfide deposits. Although the topic is interesting and the overall flow of the paper, from the formulation to comparison with 2D analytical solution and experimental results, is great, I can hardly say the paper is well written in general and there seems to be a lot of room for improvement of the manuscript.
The motivation of the current model development is not compelling, especially given that (1) the system has not been proven to be applicable to the field (even though the authors attempted to validate the model with laboratory experiments, it does not necessarily mean it can be used in the field) and (2) complicated situations are likely to be more easily dealt with numerical tools/methods and there seem to be some published already.
Formulation is poorly explained especially given that deriving analytical solution for the system should be the essential part for a model development paper. I found it difficult to follow how the equations are derived. There can be several reasons for this, including (1) the papers cited (Li et al., 2005, He, 2012) for seemingly essential equations are not publicly available and not explained well, (2) the authors do not seem to use mathematical symbols in an organized way, including seemingly interchangeable and thus confusing use of uppercase/lowercase and/or Greek/English letters and/or vector/scalar expressions, and (3) figure to help the reader to understand formulation is lacking and/or not referenced.Especially, please consider making clearer explanations on (1) what is proved and how this is done in Section 2.1, (2) the mirror image method in general potentially with a specific diagram/schematic in Section 2.2 and (3) derivation of one of formulation from Table 1 in Section 2.3.
Specific comments
L9. “It is significant to fast and precise forward modeling and inversion for SMS explorations.”. I think English grammar here is not correct.
L22. What is “AUV”?
L34. What do you mean by “affection of the field source”?
L34. “which occur difficulty in solving the Poisson equation.” I think the authors should correct English.
L58. What is the definition of H?
L79. rho_0 must be a typo of r_0?
L82. “So we get the potential distribution along the surface of a uniformly polarized sphere is equivalent to an electric dipole.” I do not understand what this means.
L92. Is the use of permittivity correct here? In other words, do permittivity and conductivity have the same units?
L137. What do you mean by “the dipole moment is 1 D.”?
L138. 10-10 must mean 10^-10. What are units and adjustment term exactly?
L140. Do “exceptions” mean negative/positive peaks?
L142. Why tilted dipole is related to any depth?
L147. The authors should describe exactly what redox reaction is occurring.
Citation: https://doi.org/10.5194/gmd-2023-94-RC1 -
AC2: 'Reply on RC1', Pengfei Zhang, 05 Jul 2024
First and foremost, we would like to extend our sincere gratitude to Referee #1 for the insightful comments. We have carefully considered the feedback and revised the manuscript accordingly. All changes have been highlighted in the manuscript to facilitate the review process. Please find attached our detailed responses, where we have addressed each of the reviewer’s comments
Best regards,
Pengfei Zhang
On behalf of all authors
-
AC2: 'Reply on RC1', Pengfei Zhang, 05 Jul 2024
-
RC2: 'Formulas and Results', Anonymous Referee #2, 18 Jun 2024
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-94/gmd-2023-94-RC2-supplement.pdf
-
AC1: 'Reply on RC2', Pengfei Zhang, 05 Jul 2024
First of all, we would like to extend our sincere gratitude to Referee #2 for the insightful comments. We have carefully considered the feedback and revised the manuscript accordingly. All changes have been highlighted in the manuscript to facilitate the review process. Please find attached our detailed responses, where we have addressed each of the reviewer’s comments.
Sincerely,
Pengfei ZHANG
On behalf of all authors
-
AC1: 'Reply on RC2', Pengfei Zhang, 05 Jul 2024
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