研究目的
To provide a new derivation of the Kramers-Kronig relations based on the Sokhotski-Plemelj equation and to verify these relations on experimental data of sound attenuation in seabottom sediments.
研究成果
The study provides a new derivation of the Kramers-Kronig relations using the Sokhotski-Plemelj equation, clearly analyzing the conditions for their validity. The Zener model is shown to fit experimental data of wave velocity and attenuation in ocean bottom sediments, while the Maxwell and Kelvin-Voigt models have limitations in satisfying the relations.
研究不足
The Kelvin-Voigt and constant-Q models do not satisfy the Kramers-Kronig relations due to lack of regularity and square-integrability. The Zener model does not capture the high-frequency behavior of the attenuation, suggesting the need for more complex models like those based on the Biot theory.
1：Experimental Design and Method Selection:
The study uses mathematical derivations based on the Sokhotski-Plemelj equation to explore the Kramers-Kronig relations in the context of viscoelasticity and wave propagation.
2：Sample Selection and Data Sources:
Experimental data of sound attenuation in seabottom sediments from Zhou et al. (2009) are used to verify the Kramers-Kronig relations.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned in the paper.
4：Experimental Procedures and Operational Workflow:
The paper details the mathematical derivation of the Kramers-Kronig relations and their application to the Zener, Maxwell, and Kelvin-Voigt viscoelastic models.
5：Data Analysis Methods:
The analysis involves comparing the theoretical predictions of the Kramers-Kronig relations with experimental data to validate the models.
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