GATE-2018 (24) :Wyllie – Time average equation

GATE-2007

Q.49:- A P-wave incident on a horizontal interface between two layers at an angle of 30° generates a reflected S-wave .What is the angle of reflection of the S-wave ?( The P and S-wave velocities in the top layers are 4km/s and 2.5km/s respectively).

Solution:

Formula: using Snells law

1. $\frac{Sin I}{Sin r}=\frac{V1{}}{V2}$ ( is called the law of refraction for plane seismic waves)

2. $\frac{Sin Ip}{Vp1}=\frac{Sin Is}{Vs1}=\frac{Sin Rp}{Vp2}=\frac{Sin Rs}{Vs2}$

Using the second formula $\frac{Sin Ip}{Vp1}=\frac{Sin Rs}{Vs2}$

Rs is the angle of reflection of the S- wave

Given values are:-

Incident angle of P- wave =30º

Velocities of P-and S waves are

Vp= 4km/s and Vs=2.5 km/s

$\frac{Sin 30}{4}=\frac{Sin Rs}{2.5}$

$\frac{0.5}{4}=\frac{Sin Rs}{2.5}$

$Sin Rs =\frac{2.5*0.5}{4}$

$Rs=\arcsin(0.3125)$

Rs=18.179

Angle of reflection of a S-wave is =18.179º