Transient and impulse responses of a one-dimensional linearly attenuating medium — II. A parametric study

We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= t_u/Q_m where t_u is the travel time and Q_m the quality factor in the absorption band, and τ^(-1)_m, the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ_m. For very small τ_m, this model is shown to be very similar to previously proposed attenuation models. As τ_m grows past a critical value which depends on T*, the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a ‘one second’ earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves