Seismic Velocities and Density of an Attenuating Earth

The dispersion that accompanies attenuation has been taken into account in many recent body wave studies. In free oscillation and surface wave investigations, however, the effect has been assumed to be of second order and, hence, has been ignored. Liu, Anderson, and Kanamori (1976) have recently re-examined this effect and have shown it to be first order across the seismic band. In order to compare data from different frequency bands, then, a frequency-dependent correction must be applied to the observed phase velocities. The corrected data will then be representative of the elastic properties of the earth at the selected reference frequency. In the case of the free oscillations and long-period surface waves corrected to body wave frequencies (about one cycle/s), this correction factor is of the order of 1%, many times larger than the uncertainty of the raw data.