Three-Dimensional Joint Inversion of the Resistivity Method and Time-Domain-Induced Polarization Based on the Cross-Gradient Constraints

Round 1

Reviewer 1 Report

Dear Editor and authors, I send you my comments and observations on the manuscript. I hope that my comments will useful to the authors.

General Comments

The manuscript "Three-Dimensional Joint Inversion of the Resistivity Method and Time-Domain-Induced Polarization Based on the Cross-Gradient Constraints" presents an interesting proposal to solve the joint inversion of resistivity and time-domain induced polarization data based on the cross-gradient method. This is a topic of interest due to the possibilities of both methods in various applications. The authors make a detailed presentation of the formulation employed and the parameters used to measure the quality of the results. In addition, they present the application on three synthetic cases and one real case. However, the authors should complete and clarify some points in detail. My recommendation is a minor revision.

Specific comments that I believe should be clarified and/or completed are included in the pdf document.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Excellent paper. 

Author Response

Thank you for affirming our article

Reviewer 3 Report

 

In this manuscript, the author has developed a 3D joint inversion method for resistivity and Time-Domain Induced Polarization (TDIP) data, utilizing a cross-gradient coupling constraint. The synthetic examples demonstrate that joint inversion improves the recovery of model parameters and boundaries, and the method has been successfully applied to groundwater detection. The manuscript is generally well written and aligns with the scope of this journal. Before acceptance, the authors should address the following comments: 

1.           Equation 1: It is unclear whether “I” represents electric current and what its unit (A) is. If the unit is different, please use distinct symbols. 

2.           Line 107: Please provide references for the finite difference method. 

3.           Equations 13 and 15: The gradient of the data misfit term is missing V^-1. 

4.           Is the nonlinear method used for the TDIP inversion as described by Oldenburg et al. (1994)? 

5.           Provide relevant references for the calculation of the sensitivity matrix, particularly for the sensitivity matrix of polarization. 

6.           In the joint inversion process, are resistivity and polarization updated simultaneously or alternately? 

7.           The inversion results show all positive polarization values (Figure 3, Figure 4, Figure 6, and Figure 8). Please explain how the author ensures that polarization values remain positive and do not include negative values. 

8.           The author has described the calculation method for the RMS. It would be helpful to include the trend of RMS values during the inversion process. 

9.           Evaluate the match between predicted and observed data in the synthetic study to assess the quality of the inversion results. 

10.        Describe the method used for updating the regularization parameters. 

11.        Explain why the results of the resistivity inversion exhibit slight redundant structures in the synthetic examples, while the polarization inversion results are better. 

12.        Use the same colormap throughout the manuscript to maintain consistency. For example, Figure 8 uses the JET colormap, while Figure 9 uses different ones. 

13.        Clarify in Figure 9 which results correspond to separate inversion and joint inversion. The same clarification is needed for Figure 3 to Figure 5. 

14.        Discuss whether artifacts may arise from the joint inversion when there is no correlation between resistivity and polarization. 

15.        Improve the resolution and quality of the figures. 

16.        Further refine the language used in the manuscript.

17.        To enhance readability and maintain consistent line spacing, it is recommended to utilize the equation tools in MS Word for symbols and equations embedded in the text.

 

Author Response

Please see the attachment.

Author Response File: Author Response.docx