Long‐period Love numbers and their frequency dependence due to dispersion effects

In a dispersive medium the Love numbers are frequency dependent. These effects are small over the range of frequencies usually encountered (from about 12 hours to 430 days) in tidal and rotational studies. Models of dispersion predict that at periods of 18.6 years the effect may become quite significant. A preliminary analysis of the long period tidal perturbations in the motion of the LAGEOS satellite indicates that k2 ≃ 0.36 compared with an elastic value of 0.30. This value is in agreement with a mantle shear Q that is proportional to (frequency)β with β of the order 0.3 to 0.4.

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