Making CMP’s

1. Making CMP’s From chapter 16 “Elements of 3D Seismology” by Chris Liner

2. Outline • Convolution and Deconvolution • Normal Moveout • Dip Moveout • Stacking

3. Outline • Convolution and Deconvolution • Normal Moveout • Dip Moveout • Stacking

4. Convolution means several things: • IS multiplication of a polynomial series • IS a mathematical process • IS filtering

5. Convolution means several things: • IS multiplication of a polynomial series A * B = C E.g., A= 0.25 + 0.5 -0.25 0.75]; B = [1 2 -0.5]; C = [0.2500 1.0000 0.6250 0 1.6250 -0.3750]

6. Convolutional Model for the Earth output input Reflections in the earth are viewed as equivalent to a convolution process between the earth and the input seismic wavelet.

7. Convolutional Model for the Earth output input SOURCE * Reflection Coefficient = DATA (input) (earth) (output) where * stands for convolution

8. Convolutional Model for the Earth SOURCE * Reflection Coefficient = DATA (input) (earth) (output) where * stands for convolution (MORE REALISTIC) SOURCE * Reflection Coefficient + noise = DATA (input) (earth) (output) s(t) * e(t) + n(t) = d(t)

9. Convolution in theTIME domainis equivalent toMULTIPLICATION in theFREQUENCYdomain s(t) * e(t) + n(t) = d(t) FFT FFT FFT s(f,phase) x e(f,phase) + n(f,phase) = d(f,phase) Inverse FFT d(t)

10. CONVOLUTION as a mathematical operator signal has 3 terms (j=3) -1 2 -1/2 earth Reflection Coefficient has 4 terms (k=4) 1/4 1/4 time 1/2 z 1/2 -1/4 3/4 -1/4 3/4 Reflection Coefficients with depth (m)

11. 0 0 0 -1/2 2 1 0 0 0 0 0 0 0 0 0 0 x x x x x = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

12. 0 0 0 -1/2 2 -1 0 0 0 0 0 0 0 0 0 0 0 x x x x x = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

13. 0 0 0 -1/2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 x x x x x x x = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

14. 0 0 0 -1/2 2 1 0 0 0 0 0 0 0 1/4 0 0 0 0 1/4 x x x x x x x x = = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

15. 0 0 0 1/2 1/2 0 0 0 0 1 0 0 0 -1/2 2 1 0 0 0 0 x x x x x x x x x = = = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

16. 0 0 0 -1/8 1 -1/4 0 0 0 0 5/8 x x x x x x x x x x = = = = = = = = = = 0 0 0 -1/2 2 1 0 0 0 0 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 +

17. 0 0 0 0 -1/4 -1/2 3/4 0 0 0 0 x x x x x x x x x x = = = = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 0 0 0 -1/2 2 1 0 0 0 0 +

18. 0 0 0 1/8 1 1/2 0 0 0 1 5/8 x x x x x x x x = = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 + 0 0 0 -1/2 2 1 0 0 0 0

19. 0 0 0 -3/8 0 0 0 -3/8 x x x x x x x = = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 + 0 0 0 -1/2 2 1 0 0 0 0

20. 0 0 0 0 0 0 0 x x x x x x = = = = = = 0 0 0 1/4 1/2 -1/4 3/4 0 0 0 + 0 0 0 -1 2 -1/2 0 0 0 0

21. MATLAB %convolution a = [0.25 0.5 -0.25 0.75]; b = [1 2 -0.5]; c = conv(a,b) d = deconv(c,a) c = 0.2500 1.0000 0.6250 0 1.6250 -0.3750 matlab

22. Outline • Convolution and Deconvolution • Normal Moveout • Dip Moveout • Stacking

23. Normal Moveout Hyperbola: x T

24. Normal Moveout x T “Overcorrected” Normal Moveout is too large Chosenvelocity for NMO is too (a) large (b) small

25. Normal Moveout x T “Overcorrected” Normal Moveout is too large Chosenvelocity for NMO is too (a)large (b) small

26. Normal Moveout x T “Under corrected” Normal Moveout is too small Chosenvelocity for NMO is (a) too large (b) too small

27. Normal Moveout x T “Under corrected” Normal Moveout is too small Chosenvelocity for NMO is (a) too large (b) too small

28. Vinterval from Vrms Dix, 1955

29. Vrms V1 V2 Vrms < Vinterval V3

30. Vinterval from Vrms

31. Primary seismic events x T

32. Primary seismic events x T

33. Primary seismic events x T

34. Primary seismic events x T

35. Multiples and Primaries x M1 T M2

36. Conventional NMO before stacking x M1 NMO correction V=V(depth) e.g., V=mz + B T M2 “Properly corrected” Normal Moveout is just right Chosenvelocity for NMO is correct

37. Over-correction (e.g. 80% Vnmo) x x M1 M1 NMO correction V=V(depth) e.g., V=0.8(mz + B) T T M2 M2

38. f-k filtering before stacking (Ryu) x x M1 NMO correction V=V(depth) e.g., V=0.8(mz + B) T T M2 M2

39. Correct back to 100% NMO x x M1 M1 NMO correction V=V(depth) e.g., V=(mz + B) T T M2 M2

40. Outline • Convolution and Deconvolution • Normal Moveout • Dip Moveout • Stacking

41. Outline • Convolution and Deconvolution • Normal Moveout • Dip Moveout • Stacking

42. Dip Moveout (DMO) (Ch. 19; p.365-375) How do we move out a dipping reflector in our data set? m Offset (m) TWTT (s) z

43. Dip Moveout • A dipping reflector: • appears to be faster • its apex may not be centered Offset (m) For a dipping reflector: Vapparent = V/cos dip TWTT (s) e.g., V=2600 m/s Dip=45 degrees, Vapparent = 3675m/s

44. CONFLICTING DIPS Different dips CAN NOT be NMO’d correctly at the same time Offset (m) 3675 m/s TWTT (s) 2600 m/s Vrms for dipping reflector too low & overcorrects Vrms for dipping reflector is correct but undercorrects horizontal reflector

45. DMO Theoretical Background (Yilmaz, p.335) (Levin,1971) is layer dip “NMO”

46. DMO Theoretical Background (Yilmaz, p.335) (Levin,1971) “DMO”

47. Three properties of DMO “DMO” “NMO” (1) DMO effect at 0 offset = ? (2) As the dip increases DMO (a) increases (B) decreases (3) As velocity increases DMO (a) increases (B) decreases

48. Three properties of DMO “DMO” “NMO” (1) DMO effect at 0 offset = 0 (2) As the dip increases DMO (a) increases(B) decreases (3) As velocity increases DMO (a) increases(B) decreases

49. Application of DMO aka “Pre-stack partical migration” • (1) DMOafter NMO (applied to CDP/CMP data) • but before stacking • DMO is applied to Common-Offset Data • Is equivalent to migration of stacked data • Works best if velocity is constant

50. DMO Implementation before stack -I Offset (m) (1) NMO using background Vrms TWTT (s)