Physics of Seismic and Tidal Attenuation

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The theory of elasticity and internal friction in Earth’s materials is most important for seismology, materials science, and studies of terrestrial and planetary tides. We argue that despite its long and broad use, the conventional viscoelastic model is insufficient for two reasons. First, this model is based on postulated mathematical concepts such as the creep function, quality factors (Q), time-dependent moduli, and the correspondence principle which lack explanations from first-principle physical laws. Second, this model is insufficiently general, and inelasticity within the heterogeneous Earth does not always reduce to an effect of a Q. For example, in rocks containing pore fluids (the primary cause of seismic attenuation in sedimentary rocks), secondary P-waves are always present. These secondary waves contribute to all observable phenomena, such as wave velocity dispersion, reflection amplitudes in layered media or strain/stress phase lags in laboratory measurements. Nevertheless, secondary wave modes are not included in the viscoelastic model, which only considers the Q factors for the primary modes.