I wonder if there is a correlation between the attenuation of a seismic wave and its propagation speed in a medium, all other things being equal.
Hello,
In general, there is a link between velocity and attenuation. A link can be retrieved through Kramers-Kronigs equations. Here is an example of sources.
Waters, K. R., Hughes, M. S., Mobley, J., Brandenburger, G. H. & Miller, J. G. On the applicability of Kramers–Krönig relations for ultrasonic attenuation obeying a frequency power law Kendall. 108, 556–563 (2000).
In the case of viscoelastic propagation, the relations are also related to the same viscoelastic parameters, described in the corresponding rheological models. In the case of Kelvin-Voigt model, equations can be found in:
Catheline, S. et al. Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: An inverse problem approach. The Journal of the Acoustical Society of America 116, 3734–3741 (2004).
Best regards.
Thank you for your replies s. N. Mulev and Bruno Giammarinaro.
Please provide a detailed answer, s. N. Mulev.
Скорость распространения волны зависит от модуля упругости горных пород и в меньшей степени от плотности. Затухание зависит от частоты волны в однородном массиве.
Затухание и скорость независимые величины.
Considering the wavespeed depends only on elastic moduli means that the medium is purely elastic. In general, it is not the case and some rheological models need to be considered. They will add viscosity parameters which will impact attenuation and wave speed dispersion. The link between both can be retrieved using Kramers-Kronig relations.
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