Gravity inversion method using <i>L</i><sub>0</sub>-norm constraint with auto-adaptive regularization and combined stopping criteria

Gebre, Mesay Geletu; Lewi, Elias

doi:https://doi.org/10.5194/se-14-101-2023

Articles | Volume 14, issue 2

https://doi.org/10.5194/se-14-101-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/se-14-101-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 2

Method article

|

03 Feb 2023

Method article |

| 03 Feb 2023

Gravity inversion method using L₀-norm constraint with auto-adaptive regularization and combined stopping criteria

Mesay Geletu Gebre and Elias Lewi

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Final revised paper (published on 03 Feb 2023)
Preprint (discussion started on 15 Nov 2022)

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-1202', Anonymous Referee #1, 13 Dec 2022

The authors present a sparsity constrained inversion method. The technical content of the paper is good and have both synthetic and field data illustrations. However, the paper has several typo and grammatical errors. The following are my comments to the paper.

- I suggest the title be shortened to “Gravity Inversion Method Using L₀-norm Constraint with Auto-adaptive Regularization and Combined Stopping Criteria”

- Could you discuss the possibility of extending the method to 3D?

- For the field data examples, can you show the conventional least square inversion results like the one shown in Fig. 7a.

- For the synthetic data examples, is the noise added in the gravity data or the model density? The description in the paper is not clear about this point.

- The noise added in the synthetic data is small. Can you show the robustness of the method by adding significant of noise in the data?

- What happens when the causative body is big in size but has a sharp boundary?

Citation: https://doi.org/10.5194/egusphere-2022-1202-RC1
- AC1: 'Reply on RC1', Mesay Geletu Gebre, 05 Jan 2023
  
  Dear Editor Nicolas Gillet and Anonymous Referee #1, please see attached file.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1202-AC1
RC2:
'Comment on egusphere-2022-1202', Anonymous Referee #2, 19 Dec 2022

Dear Editor and Authors, please see attached file.

Citation: https://doi.org/10.5194/egusphere-2022-1202-RC2
- AC2: 'Reply on RC2', Mesay Geletu Gebre, 05 Jan 2023
  
  Dear Editor Nicolas Gillet and Anonymous Referee #2, please see attached file.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1202-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Mesay Geletu Gebre on behalf of the Authors (05 Jan 2023) Author's response Author's tracked changes Manuscript

ED: Publish as is (10 Jan 2023) by Nicolas Gillet

ED: Publish as is (10 Jan 2023) by Susanne Buiter (Executive editor)

AR by Mesay Geletu Gebre on behalf of the Authors (13 Jan 2023) Manuscript

Short summary

In this work, a gravity inversion method that can produce compact and sharp images is presented. An auto-adaptive regularization parameter estimation method, improved error-weighting function and combined stopping rule are the contributions incorporated into the presented inversion method. The method is tested by synthetic and real gravity data, and the obtained results confirmed the potential practicality of the method.

Gravity inversion method using L0-norm constraint with auto-adaptive regularization and combined stopping criteria

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Interactive discussion

Peer review completion

Gravity inversion method using L₀-norm constraint with auto-adaptive regularization and combined stopping criteria