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1 2024

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Algorithms for time-frequency imaging and analysis: introduction to mixed-model spectral decomposition

Pant Animesh, Ghosal Dibakar, Puryear Charles, Verma Shashank Narayan

Acta Geophysica

2024

Vol. 72, no. 2

637--653

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 windowbased 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 windowbased 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.