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

1. A zero-offset reflection event at 1.00 s has a normal move out (NMO) of 0.005 s at 200 m offset. What is the stacking velocity?

Solution:

The stacking velocity (Vst) is defined as that velocity value which 

produces the maximum amplitude of the reflection event in the 

stack of traces. This successful removal of NMO.

t_x²= t₀² + (x²/ v_st²) -------------------(1)

t₀ = 1s

t_x= 0.005 s

offset (x) = 200 m

v_st =?

substitute above values in eq(1)

(0.005)² = (1)²+( (200)²/ (v_st²) )

0.000025 = 1+ (40,000 / v_st²)

40,000/ v_st² = -0.9999

v_st² =- (40,000 / 0.999)

v_st² = -40,002

v_st = √ 40,002

v_st = 200 m/s