CSIR_NET_2018_
DECEMBER
115)
A P-wave is
incident at an angle of 300
upon a horizontal interface separating two media which are both
poissions solid. If the P-wave velocity of the first layer is 3
km/sec and the critical angle is 600
, then the angle
of reflection of the shear wave is
A)
\arcsin(\frac{1}{6})
B) \arcsin(\frac{1}{4})
C)
\arcsin(\frac{1}{3})
D) \arcsin(\frac{1}{2})
(Thanks to Chandrasekhar, ANU)
Solution:
Here
we use two formulas
-
\frac{V_{P}}{V_{S}}= \sqrt{\frac{2(1-\nu)}{(1-2\nu)}}
-
\frac{Sin Ip}{Vp1}=\frac{Sin Is}{Vs1}=\frac{Sin Rp}{Vp2}=\frac{Sin Rs}{Vs2}
Poissions solid value (\nu) =0.25
Velocity of the P-wave (V )= 3 km/s
\frac{V_{P}}{V_{S}}=
\sqrt{\frac{2(1-\nu)}{(1-2\nu)}}
\frac{3}{V_{S}}=\sqrt{\frac{2(1-0.25)}{(1-2*0.25)}}
\frac{3}{V_{S}}=\sqrt{\frac{2*0.75}{0.5}}
\frac{3}{V_{S}}=\sqrt{3}
V_{S}=\frac{3}{\sqrt{3}}
V_{S}=\sqrt{3}km/sec
i.e
V_{s_{1}}=\sqrt{3}km/sec
now
we use the 2nd
formula
\frac{Sin Ip}{Vp1}=\frac{Sin
Is}{Vs1}=\frac{Sin Rp}{Vp2}=\frac{Sin Rs}{Vs2}
Ip - incident and reflected angles of P wave
Is - reflected angle of S-wave
Vp1 - P-wave velocity of the upper layer
Vs1 - S wave velocity of the upper layer
Vp2 - P wave velocity of the lower layer
Vs2 - S wave velocity of the lower layer
from this we can write
\frac{Sin Ip}{Vp1}=\frac{Sin Is}{Vs1}
Sin Is=Sin
Ip(\frac{Vs_{1}}{Vp_{1}})
Sin Is=Sin 30(\frac{\sqrt{3}}{3})
Sin Is=\frac{1}{2}(\frac{\sqrt{3}}{3})
Sin Is=\frac{1}{3.4}
References : Fundamentals of Geophysics , William Lowrie
Post a Comment
Post a Comment