Use the values for Qα plotted in Figure 6.15 for the PREM model to:
(a) Estimate the attenuation for waves of 30 s period (0.033 Hz) for PcP ray paths
at vertical incidence. Consider only the intrinsic attenuation along the ray
paths; do not include the reflection coefficient at the core–mantle boundary
or geometrical spreading. Be sure to count both the surface-to-CMB and
CMB-to-surface legs. You can get the PREM P velocities from Figure 1.1
or the values tabulated in Appendix A. You may estimate the travel times
through the different Q layers in PREM by assuming a fixed velocity within
each layer (e.g., use the average velocity between 3 and 80 km, the average
between 80 and 220 km, etc.). Note that in this case the “surface’’ is assumed
to be the bottom of the ocean at 3 km depth. Compute t
∗ for PcP. Finally
give the attenuated amplitude of the PcP ray assuming the ray had an initial
amplitude of one.
(b) Using the approximation t
∗
β = 4t
∗
α, compute the attenuated amplitude of ScS
at 30 s period.
(c) Repeat (a) and (b) for 1 s period (1 Hz) PcP and ScS waves.
(d) Repeat your calculations for the PcP and ScS attenuated amplitudes at 1 Hz,
but this time use the Warren and Shearer (2000) Qα values from Figure 6.15.
How do the predicted amplitudes compare to the PREM model predictions?
What do these results predict for the observability of teleseismic S arrivals
at 1 Hz?