Absorption and the low velocity zone

Abstract

It is well known that elastic wave velocities are independent of frequency only for a non-dissipative medium. In a real solid dispersion must accompany absorption. This effect has been emphasised by Randall and Liu et al. The effect is small when the seismic quality factor Q is large or unimportant if only a small range of frequencies is being considered—that is, the spectra of P waves. Even in these cases, however, the measured velocities, or inferred elastic constants, are not the true elastic properties but lie between the high frequency and low frequency limits or the so-called 'unrelaxed' and 'relaxed' moduli. The magnitude of the effect depends on the nature of the absorption band and the value of Q. When comparing data taken over a wide frequency band the effect of absorption can be considerable especially considering the accuracy of present body-wave and free-oscillation data. Thus, Jeffreys questions conclusions based on free oscillation data, particularly where they differ from body-wave results which are based on much shorter periods. Carpenter and Davies and Davies attempted to reconcile body-wave and surface-wave Earth models by allowing for physical dispersion using Futterman's and Kolsky's dispersion–absorption relationships. Jeffreys used Lomnitz' relationships. Liu et al. have shown that dispersion depends to first-order on absorption in the seismic frequency band and derived a linear superposition model that gives a Q that is independent of frequency. It can be shown that all of the above theories give equivalent absorption–dispersion relations for moderate absorption. Liu et al. and Anderson et al. have shown how to correct surface-wave and free-oscillation data for physical dispersion. Much of the support for the existence of an upper mantle low velocity zone has come from the inversion of normal mode data that have been uncorrected for physical dispersion due to absorption. In the light of these developments, we decided to re-examine the question of a shearwave low velocity zone.

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