the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Multi-dimensional, Multi-Constraint Seismic Inversion of Acoustic Impedance Using Fuzzy Clustering Concepts
Abstract. In the process of transforming seismic data into vital information about subsurface rock and fluid properties, seismic inversion is a crucial tool. This motivates researchers to develop several seismic inversion methods and software. Since the seismic data are band-limited, seismic inversion is ill-posed, and the results are not unique, each method tries to use initial information and assumes expected conditions for the results. Satisfying a general low-frequency trend and having a smooth model or step-wise results are some of the assumptions that these methods add as constraints to the inversion process. Well-logs, geological studies, and models from other geophysical methods can add important insight into the seismic inversion results. We introduce an objective function that applies the clustering properties of the prior information as a constraint to the seismic inversion process as well as other common constraints. An optimal solution to the objective function is explained. We applied the Gustafson-Kessel fuzzy C-means as one of the possible clustering methods for clustering term. Numerical synthetic and real data examples show the efficiency of the proposed method in the inversion of seismic data. In addition to the acoustic impedance model, the proposed seismic inversion method creates reliable deconvolved and denoised versions of the input seismic data. Additionally, the membership section output from the inversion process shows high potential in the seismic interpretation. Further research on selecting an optimum fuzziness, updating wavelet, and the potential of the membership sections to track horizons, distinguish sequences and layers, identify possible contents of the layers, and other possible applications are recommended.
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Status: open (until 10 Nov 2024)
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RC1: 'Comment on npg-2024-12', Anonymous Referee #1, 02 Aug 2024
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Dear Authors,
I believe your work has potential. However, there are several issues that need to be discussed in more detail and with greater clarity. I have included my comments in the text file.
Here are some main concerns:
- How do you choose the parameters for the objective function (Equation 14), and what criteria do you use to select these parameters?
- How do you choose the parameters for clustering, and what criteria do you use to select them?
- Could you please provide results of the inversion with different noise levels and different starting models, and compare these results with those obtained using Hampson-Russell?
Kind Regards,
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CC1: 'Reply on RC1', Hosein Hashemi, 09 Aug 2024
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Dear Reviewer,
Thank you for your thorough review and insightful comments on our manuscript. We appreciate the time and effort you have invested in providing detailed feedback. Below, we address each of your observations and comments.
We hope the attached answers, explanations, and examples meet your expectations.
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AC1: 'Reply on RC1', Hosein Hashemi, 20 Aug 2024
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In addition to the previous file, the attached file answers the comments in the manuscript.
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RC2: 'Reply on AC1', Anonymous Referee #1, 04 Oct 2024
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The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2024-12/npg-2024-12-RC2-supplement.pdf
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AC2: 'Reply on RC2', Hosein Hashemi, 05 Oct 2024
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Thank you for your valuable feedback.
We have carefully considered and addressed each of your comments. The responses are provided in the attached file.
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AC2: 'Reply on RC2', Hosein Hashemi, 05 Oct 2024
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RC2: 'Reply on AC1', Anonymous Referee #1, 04 Oct 2024
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