Consider a simple homogeneous layer over half-space model (as plotted in Fig. 7.22) with P velocity α1 and S velocity β1 in the top layer and P velocity α2 in the bottom layer. (a) Assuming a layer...

Consider a simple homogeneous layer over half-space model (as plotted in

Fig. 7.22) with P velocity α1 and S velocity β1 in the top layer and P velocity α2 in the bottom layer.

(a) Assuming a layer thickness of h and a ray parameter of p, derive an equation

for the differential time (TPs − TP ) between P and Ps at the surface. Hint:

the travel time is equal along the wavefront shown by the dashed line in the

bottom layer.

(b) What is TPs − TP for h = 40 km, α1 = 6.3 km/s, β1 = 3.6 km/s, α2 = 8 km/s,

and p = 0.06 s/km?