(a) Show how (8.9) follows from (6.46) and (6.59) by proving that if
(b) Model the crust as a simple layer over a half-space as in Figure 8.2, with h =
40 km, ρ1 = 2.7 g/cm3, ρ2 = 3.3 g/cm3, β1 = 3.5 km/s, and β2 = 4.5 km/s.
Find the lowest value of ω (i.e., the fundamental mode) that satisfies equation
(8.10) at values of phase velocity (c = 1/p) of 3.8, 4.0, 4.2, and 4.4 km/s.
Convert ω to period, T , and list your results in a table with the c and T values.
Hint: Make sure that you use consistent units in computing the µ values in
(8.10).
(c) (COMPUTER) Make a plot of the c(ω) dispersion curve for the fundamental
and first two higher modes for values of c from β1 to β2. Include many more
points than your result from (b).