Abstract
Time–frequency algorithms help discern and filter hidden information from signals but their growing abundance induces non-uniqueness thus, complicating selection. Classification of these algorithms into approaches can bring simplification and structure to improve our selection and estimates. This study focuses on algorithms we classify here as fixed window-based projection approach, wavelet-based projection approach, greedy-based approach and combinational-based approach while omitting heuristic-based approach and numerical-autoregressive-based approach classes. It describes the basic theory of transforms under the classes and compares them for effective stability, effective localization and resolution capabilities of time–frequency spectra for wavelet estimation and interfering beds with results demonstrating subtle advantages for each depending on nature of signal and model behind the algorithm. The combinational-based mixed-model approach wavelet-assisted constrained least squares spectral analysis concatenates a wavelet-based approach with a fixed window-based approach and effectively functions to reassign complex amplitude coefficients from their apparent positions to their true positions. A comparison of the results suggests that it demonstrates good scope as an effective alternative general tool for hydrocarbon detection and resolution of thin beds.
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Acknowledgements
The authors would like to thank Prof. Yanghua Wang, Imperial College London for validation and comments on results from SFMPD. The authors also thank Prof. J.P. Castagna for help on CLSSA. We also take this opportunity to thank the research group at Crustal Imaging Laboratory (CIL), Indian Institute of Technology Kanpur for access to computational resources. We thank dGB Earth Sciences for providing open access to Penobscot Bay dataset.
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Animesh Pant- Conducted literature review, formal algorithm writing, coding, writing and summary of the work. Dr. Dibakar Ghosal- Conducted supervision and review of the work. Dr. Charles I. Puryear- Conducted review of the work. Shashank Narayan- Conducted review of the work.
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Edited by Prof. Ali Gholami (ASSOCIATE EDITOR) / Prof. Gabriela Fernández Viejo (CO-EDITOR-IN-CHIEF).
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Pant, A., Ghosal, D., Puryear, C. et al. Algorithms for time–frequency imaging and analysis: introduction to mixed-model spectral decomposition. Acta Geophys. 72, 637–653 (2024). https://doi.org/10.1007/s11600-023-01108-2
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DOI: https://doi.org/10.1007/s11600-023-01108-2