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# Presentation Chapter 5: NMO for Two-Layer Configuration

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### Presentation Chapter 5: NMO for Two-Layer Configuration

1. 1. NMO for 2-layer conﬁguration (Ta3520) Transmission loss correction – p. 1/
2. 2. Conﬁguration x d1 α R x 2 d β 2 Transmission loss correction – p. 2/
3. 3. Normal Move-out (NMO) for morethan 1 interfaceTraveltime for two layers given by: 2 2 1/2 2 1/2 (x − x2 ) + 4d1 ) x2 2 + 4d2 ) T = + c1 c2 2 1/2 1/2 2d1 (x − x2 ) 2d2 x22 = 1+ + 1 + 2 c1 4d2 1 c2 4d2 1/2 1/2 x2 1 x2 = T1 1 + + T2 1 + 22 2 T 1 c2 2 1 T 2 c2 Ti = zero-offset traveltime trough layer i Transmission loss correction – p. 3/
4. 4. Expand square root: x2 1 x2 2 T T1 + 2 + T2 + 2. 2T1 c1 2T2 c2This can be rewritten as follows: x2 1 x2T 2 = (T1 + T2 )2 + (T1 + T2 ) + 22 + O(x4 ) T 1 c2 T 2 c2 1 x1 Approximate: sin α ≈ tan α = 2d1 x2 sin β ≈ tan β = 2d2 Transmission loss correction – p. 4/
5. 5. Snell’s Law reads: sin α sin β = c1 c2Substituting the approximation from above: x1 x2 = 2d1 c1 2d2 c2or x1 x2 2 = T c2 T 1 c1 2 2 Transmission loss correction – p. 5/
6. 6. Using x = x1 + x2 and x2 = (T2 c2 )/(T1 c2 )x1 : 2 1 T 1 c2 x1 = x 2 1 2 2 T 1 c1 + T 2 c2Idem for x2 : T 2 c2 x2 = x 2 2 2 2 T 1 c1 + T 2 c2 Transmission loss correction – p. 6/
7. 7. Using approximations and Snell’s law: T 1 c2 + T 2 c2 1 2 T 2 ≈ (T1 + T2 )2 + (T1 + T2 )x2 (T1 c2 + T2 c2 )2 1 2 (T1 + T2 ) 2 2 ≈ (T1 + T2 ) + 2 + T c2 x T 1 c1 2 2This is of the form: x2 T 2 = Ttot (0)2 + 2 crmsThis is the equation of a hyperbola ! Transmission loss correction – p. 7/
8. 8. Compare : x2 T2 = Ttot (0)2 + 2 crms (T1 + T2 ) 2 T2 2 ≈ (T1 + T2 ) + 2 + T c2 x T 1 c1 2 2cRM S is given by: N 1 c2 rms = c2 Ti (0) i Ttot (0) i=1 Transmission loss correction – p. 8/
9. 9. Approximation 0 0.5 time (s) 1 1.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 offset (m) Transmission loss correction – p. 9/
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