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

                                           

GATE-2002

1. If a primary wave is incident on the Gutenberg discontinuity at an angle of 30 degrees to the normal, the angle at which it is refracted into the core is about..

a)7 degrees b) 17 degrees c)27 degrees d)37 degrees

Solution:

From Snell’s law

(sin i/sin r) = V1/V2-------------------------(1)

Gutenberg discontinuity : The Gutenberg discontinuity occurs within Earth’s interior at a depth of about 2900km below the surface, at this depth abrupt change in the seismic waves that travel through Earth.

Velocity of mantle( V1)=13.6 km/s

Velocity of outer core (V2) = 8.1 km/s

Incident angle (i) = 30˚

Substitute above values in equation(1)

(sin30˚ /sin r)=(13.6/8.1)

(sin r /sin30˚) = (8.1/13.6)

                            =0.5955

sin r= 0.5955 * 0.5                 (sin30˚=1/2 =0.5)

        = 0.297

    r= sin^-1(0.297)

    r= 17˚

Therefore refraction angle (r)=17˚