An Accelerated Algorithm for 3D Inversion of Gravity Data Based on Improved Conjugate Gradient Method

Round 1

Reviewer 1 Report

The paper proposes a novel approach to improve the efficiency of the three-dimensional inversion algorithm for gravity data based on a smooth model constraint. The authors successfully address the issues of high memory consumption and prolonged computation time when dealing with large datasets and model parameters. They achieve this by representing the diagonal weight matrix through vectorization and replacing the large matrix intermediate variables with a combination of a small matrix and vector.

 

The use of the conjugate gradient method, optimized to minimize the number of stored vectors during iteration, further contributes to reducing memory consumption during the operation process. The experimental results demonstrate the successful development of a fast 3D inversion algorithm for gravity data.

 

The most significant contribution of this work is achieving an average speed of ~1.5s per iteration for a 100 × 100 × 20 mesh number inversion, which provides an effective strategy for the fast inversion of large-scale data. Overall, the paper is well-written, and the proposed approach shows promising results in enhancing the efficiency of gravity data inversion, making it suitable for practical applications. However, further validation and comparison with existing methods would strengthen the paper's conclusions.

 

 

 

 

Comments and Questions:

 

1. The paper's introduction effectively introduces the problem and the proposed solution. However, it would be helpful to know the specific motivations or practical applications for this fast 3D inversion algorithm. Are there any specific industries or fields where this method could have significant implications?

 

2.The new formulas that are part of your contribution must be mentioned otherwise add the source references. For example the equations (1)-(2)-(3)-(4).....

 

3. Could you elaborate on the traditional three-dimensional inversion algorithm's limitations that necessitated the development of this fast algorithm? Understanding the shortcomings of existing methods can help readers appreciate the importance of the proposed solution.

 

4. The mention of the application effect being comparable to existing matrix compression methods is intriguing. It would be beneficial to provide some quantitative comparison results between the proposed method and these existing techniques in terms of efficiency, accuracy, and other relevant metrics.

 

5. The use of Python tools and PyQt for the implementation is noteworthy. Could the authors provide some insight into the advantages of choosing these tools for developing the 3D gravity data inversion software and GUI?

 

6. In the abstract, the authors mention representing the diagonal weight matrix by vectorization and replacing the intermediate variable of the large matrix type with a combination of a small matrix and vector. Could they elaborate on the rationale behind these choices and how they contribute to reducing memory consumption and computation time?

 

7. The experimental results show that the accelerated algorithm achieves an average speed of ~1.5s per iteration for a 100 × 100 × 20 mesh number inversion. How does this speed compare to the traditional algorithm's iteration time for the same mesh number?

 

8. The abstract mentions "providing an effective strategy for the fast inversion of large-scale data." What is considered "large-scale" data in this context, and how does the proposed algorithm handle data scalability?

 

 

 

9. The authors may consider discussing any potential limitations or challenges associated with the proposed approach to provide a more balanced perspective on the method's applicability and potential pitfalls.

 

 

Overall, the paper addresses an essential problem in the field of 3D inversion algorithms for gravity data and proposes an intriguing solution. The inclusion of more specific experimental results, comparisons with existing methods, and discussions on practical applications would further strengthen the paper's impact.

I recommend accepting the paper after considering the comments above.

Author Response

Please see the attachment for the reply to the question and the modification of the article.

Author Response File: Author Response.pdf

Reviewer 2 Report

Summary

Three-dimensional inversion of gravity data is essential for geological applications, but the commonly used inversion method can suffer from the issues of high memory consumption and prolong computation time. Here, Zhou et al., proposed to optimize the conventional smooth model constraint inversion algorithm mainly by using vectorization, small matrix and vector to replace the large diagonal weight matrix and its related intermediate variable. With those optimizations, they found improved computation efficiency required for the inversion. The innovation is okay for me, but I have the following concerns mainly related to the experimental results. Here I listed my specific comments.

Specific comments

11)     Abstract, line 23-24, showing the exact computation time for each iteration is less meaningful since the readers can hardly understand how much improvement is achieved and the number depends on multiple factors such as the specfic CPU used. Instead, the speedup could be more meaningful. In addition, the main text showed no results about computation memory used, then why mention the high computation memory issue?

22)     Line 57, “density distribution” is unclear. The density distribution for what?

33)     Line 58-59, revise “times” as “time”

44)     Section 3.1, the authors said that their algorithm reduced memory usage, but they did not list the memory usage for each algorithm used.

55)     For Table 2 and Table 3, for the traditional method, why not list the calculation time used for pre-processing and iteration for mesh number-100x100x20?

66)     Line 323-325, why not compare the computation time of the GPU-based method with the method of this study for the pre-processing and iteration stages, respectively? Why not compare their efficiency for different mesh numbers? It seems not systematic and less rigorous for the current comparison.

77)     Section 3.2, since the major contribution of this study is the improved computational efficiency for 3D inversion, why not compare the proposed method with the traditional method and GPU-based method on the real data?

Please see my comments above

Author Response

Please see the attachment for the reply to the question and the modification of the article.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thanks for the authors' efforts on addressing my concerns. The current version is okay for me.

Author Response

Pleased see the attached file.