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

CSIR-NET 2012

101.The two-way travel time in the case of two horizontal reflectors are 10ms and 12ms respectively and the RMS velocities are 2500m/s and 3500m/s respectively. Then the interval velocity between two reflectors is 

A) 6500 m/s           

B) 2500 m/s            

C) 3500 m/s           

D) 1000 m/s

Solution:

Interval velocity(V_int): Is the constant velocity of a single layer.

V_int can be approximately calculated from V_rms using the Dix formula.

From Dix formula interval velocity

V_int= √( ( ( V₂² *t₂) – (V₁²*t₁) ) / (t₂-t₁) ) ------------------(1)

Where,

V_int= interval velocity

t₁= travel time of the first reflector = 10 ms 

    =10,000s

t₂= travel time of the second reflector =12 ms

 = 12,000s

V_rms1= root mean square velocity of the first reflector

       = 2500 m/s

V_rms2 = root mean square velocity of the second reflector

         = 3500 m/s

substitute above values in eq(1)

V_int= √( ( ( 3500)² *12,000) – (2500)²*10,000) ) / (12,000-10,000) )

=√( ( ( 147,000,000,000) – (62,500,000,000) ) / (2000) )

=√( ( 84,500,000,000 ) / (2000) )

=√(42,250,000 )

V_int = 6500 m/s