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

CSIR-NET 2014

108.A Seismic survey over a horizontal reflector brought out a two way travel time of 1.0 sec at the shot point , While the refraction survey brought out the intercept of 0.8sec .A detector place at 1.8km distance from the shot point received the reflected and refracted waves simultaneously . The depth to the reflector is

A) 0.8 km          
B) 1.2 km            
C)1.6 km                
D)2.0km


Solution:

From above problem, this is a horizontal reflector

So, using NMO (norma move out)

Formula:

Δt_n= X² / (2*V²*t_i) -----------------(1)

Δt_n= reflector travel time – intercept time

     = 1.0-0.8

Δt_n = 0.2 s

Offset distance (X)= 1800m

t_i = intercept time = 0.8 s

Substitute these values in eq (1)

above formula velocity (V) = X / (2*t_i* Δt_n)^1/2 ----------------------(2)

                                         = 1800/ ( 2*0.8*0.2)^1/2

V= 3185 m/s

Therefore the depth to the reflector h = (V*t_i)/2

                                                    = (3185 *0.8) / 2

                                                    = 1274 m

                                                    = 1.274 km