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

GATE-2012

28. The S-wave velocity in the lower continental crust is 6800m/s and its density is 3380 kg/m³. Find its rigidity in G Pa

A) 156.29 G Pa

B) 160.21 G Pa

C) 162.34 G Pa

D) 164.11 G Pa

Solution:

The relation between the S-wave velocity, density and rigidity is given below formula

Vs=√(µ/ρ) -------------------(1)

Vs- velocity of the S-wave

µ- rigidity

ρ- density

V_s²=(µ/ρ)

Therefore µ= V_s² *ρ -------------(2)

Given values form above problem

V_s= 6800m/s

ρ=3380 kg/m³

Substitute above values in eq (2)

µ= ((6800)² *3380 ) kg m/s²

   = 6800*6800*3380 kg m/s²

   = 156291200000 kg m/s²

   =156291200000 N/m² ( kg m/s² = N/m²)

Pressure units is pascal

1pascal - N/m²

1Gaga pascal =10⁹ Pa

µ=156291200000 Pa

µ=156.29 G Pa