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

 CSIR-NET 2017

94. The energy of an S-wave travelling through the mantle and incident on the mantle-core boundary is

A) totally reflected back

B) partly reflected and partly refracted into the core towards the Earth’s centre

C) partly reflected and partly refracted into the core away from the Earth’s centre

D) totally refracted into the core to travel partly as a P-wave and partly as an S-wave.

Answer: C

1. V₂ > V₁ , if velocity of the overlying layer less then the the underlying layer, the refracted ray is bent away from the normal to the boundary, giving an angle of refraction that is grater than the angle of incidence ( r > i).

2. V₂ < V₁ , if velocity of the overlying layer grater then the underlying layer, the refracted ray is bent back toward the normal and the boundary, giving an angle of refraction that is less then the angle of incidence (r < i).

3. A P-wave incident on the boundary between mantle and fluid outer core is refracted towards the normal to the interface, because the P-wave velocity drops from about 13 km/s to about 8 km/s at the boundary. This shadow zone is called a PKP wave ( P-wave refracted through mantle- outercore-mantle (PKP)).

4. An S-wave incident at the same point has a lower mantle velocity of about 7 km/s part of incident energy is converted to a P-wave of outercore, which has a higher velocity of 8 km/s. ( S-wave refracted though mantle- outercore- mantle (SKS)).

Reference : Fundamentals of Geophysics, william lowrie