Addressing Reviewer Concerns on Fairness of Numerical Comparisons

We appreciate the reviewer's thorough review of our manuscript and their insightful comments regarding the fairness of the numerical comparisons. We acknowledge that some comparisons in our numerical tests were not entirely fair, as pointed out by the reviewer. For example, the auxiliary parameters used in comparisons with different regularization methods were not always the same. As the reviewer noted, the 'beta' values used in Fig. 5 (c) and Fig. 5 (d) differed significantly. We understand that these parameters can indeed have a substantial impact on the inversion results, and we regret any confusion this may have caused.

We want to clarify that the discrepancies in auxiliary parameters were primarily due to [explain the reasons, e.g., experimental design, limitations of the chosen approach, etc.]. However, we recognize that this does pose a challenge in ensuring a fair comparison. We are committed to addressing this issue and have already begun to explore various solutions to ensure fairness in our numerical tests.

Moving forward, we propose the following improvements in the revised manuscript:

1. Standardization of Auxiliary Parameters: We will standardize the auxiliary parameters across different regularization methods and experimental conditions to ensure a fair comparison.

2. Sensitivity Analysis: We will conduct a sensitivity analysis to assess the impact of different auxiliary parameter values on the inversion results. This will provide a more comprehensive understanding of the influence of these parameters and allow us to determine the optimal settings for each regularization method.

3. Expanded Discussion: We will expand the discussion section to address the concerns raised by the reviewer and provide further justification for the chosen parameter settings and the impact of parameter variation on the inversion results.

By implementing these changes, we aim to ensure that the numerical comparisons in the revised manuscript are more rigorous, fair, and reliable. We are confident that these improvements will enhance the clarity and credibility of our findings.