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

Summary. 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.