1. PS, SSP, PSPI, FFD KM
SSP
PSPI
FFD

2. P(x,z,w) = P(x,0 ,w) e k = k 1 – k ~ k (1 – k + ..) k k k k 2 z ik(x)

3. PS, SSP, PSPI, FFD k = k 1 – k k k ~ k(1 – k ) ~ k (1 – .43k ) 1 -.5z 2 k x
P(x,z,w) = P(x,0 ,w) e z
ik(x) -1 1 .2 k z
~ k(1 – k ) 2 x
~ k (1 – .43k )
1 -.5
; k = k k z k x

4. SSP Migration k = k(x) 1 – k k(x) = k 1 – k k - Dk
P(x,z,w) = P(x,0 ,w) e z
ik(x)
k = k(x) 1 – k z 2
k(x) x
= k 1 – k 2 k x
- Dk
Thin lens

5. FFD Migration k = k(x) 1 – k k(x) = k 1 – k k - Dk
P(x,z,w) = P(x,0 ,w) e z
ik(x)
k = k(x) 1 – k z 2
k(x) x
= k 1 – k 2 k x
- Dk
Thin lens

6. FFD Migration k = k(x) 1 – k k(x) = k 1 – k k - Dk
P(x,z,w) = P(x,0 ,w) e z
ik(x)
k = k(x) 1 – k z 2
k(x) x
= k 1 – k 2 k x
- Dk
Thin lens

7. FFD Migration
P(x,z,w) = P(x,0 ,w) e z
ik(x)

8. FFD Migration
P(x,z,w) = P(x,0 ,w) e z
ik(x)
other term

9. FFD Migration P(x,z,w) = P(x,0 ,w) e other term PDE associated with
ik(x)
other term
PDE associated with
other term
Rearrange PDE

10. Substitute FD approximations into above
FFD Migration
P(x,z,w) = P(x,0 ,w) e z
ik(x)
Substitute FD approximations into above

11. Substitute FD approximations into above
FFD Migration
P(x,z,w) = P(x,0 ,w) e z
ik(x)
Substitute FD approximations into above

12. FFD Migration k = k(x) 1 – k k(x) = k 1 – k k - Dk
P(x,z,w) = P(x,0 ,w) e z
ik(x)
k = k(x) 1 – k z 2
k(x) x
= k 1 – k 2 k x
- Dk
Thin lens

13. PS, SSP, PSPI, FFD

14. PS, SSP, PSPI, FFD

15. Summary
Cost:
Accuracy: KM
SSP
PSPI
FFD

16. Course Summary m(x)= a(g,s,x) G(g|x)d(g|x)G(x|s)dgds
g,s,w
G(g|x) = G(g|x) + G(g|x)
d(g|x) = d(g|x) + d(x|g)
Filter
G(g|x) = G(g|x)
d(g|x) = d(g|x)
RTM
Asymptotic G
+ Fresnel Zone
Asymptotic G
1-way G
KM Phase Shift Beam

17. Multisource Seismic Imagingvs
CPU Speed vs Year
100000
10000
copper
1000
Aluminum
Speed
VLIW
100
Superscalar 10
RISC 1
1970
1980
1980
1990
2000
2010
2020
Year

18. OUTLINE
Theory I
Numerical Results
Theory II

19. RTM Problem & Possible Soln.
Problem: RTM computationally costly
Solution: Multisource LSM RTM
Preconditioning speeds up by factor 2-3
LSM reduces crosstalk
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 19 5 19

20. Multisource Migration:
Multisource Least Squares Migration d { L {
d +d =[L +L ]m 1 2
Forward Model:
Multisource Migration:
mmig=LTd T T
=[L +L ](d + d ) 1 2
Standard migration T T T T
= L d +L d + 1 2
L d +L d 2 1
Crosstalk noise

21. Multisource Least Squares Phase-encoded Migration
Orthogonal phase encoding s.t. <N* N >=0 1 2
=[N L +N L ](N d + N d ) 1 2 * T *
mmig T
Crosstalk noise
=N*N L d +N*N L d + N*N L d + N*N L d 1 2 T T T T
If <N N > = d(i-j)
i j
= L d + L d 1 2
Standard migration

22. Key Assumption + ~ ~ ~ [S(t) +N(t) ] d(t) = N(t ) <N(t)> ~
Zero-mean white noise: <N(t)>=0; <N(t) N(t’) >=0
k=1 M
[S(t) +N(t) ]
d(t) = M
M vs M
M= Stack Number
Amplitude +
k=1 M
N(t )
(k)
<N(t)> ~ 1 M
k=1 M
[ S(t) ] 2
(k)
[ S(t) ] M 2 2
[ S(t) ] M 2 2
SNR ~ ~ ~
k=1 M
[ N(t) ] 2
k=1 M
[ N(t) ] 2
(k)
(k)
M s

23. Multisource S/N Ratio d , d , …. d +d +…. L [d + d +.. ]1 2 1 2 1 2 1 2
# CSGs
# geophones/CSG

24. MS S-1 M ~ MS MI MS vs vs Multisrc. Migration vs Standard Migration
# geophones/CSG
# CSGs MS
S-1 M ~ vs MS
Iterative Multisrc. Migration vs Standard Migration
# iterations vs MI MS

25. Summary T T
L d +L d 2 1
Time Statics
1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing w, randomness,
dimension, iteration #, and decreasing depth
Time+Amplitude Statics
3. Crosstalk decrease can now be tuned
QM Statics
4. Some detailed analysis and testing needed to refine
predictions.

26. OUTLINE
Theory I
Numerical Results
Theory II

27. The Marmousi2 Model
Z k(m) 3
X (km) 16
The area in the white box is used for S/N calculation.

28. Conventional Source: KM vs LSM (50 iterations)
Z k(m) 3
X (km) 16
Z (km) 3
X (km) 16

29. 200-source Supergather: KM vs LSM (300 its.)
Z k(m) 3
X (km) 16
Z (km) 3
X (km) 16

30. I S/N = S/N Number of Iterations
The S/N of MLSM image grows as the square root of the number of iterations. 7
S/N 1
Number of Iterations
300

31. Multisource Technology
Fast Multisource Least Squares Phase Shift.
Multisource Waveform Inversion (Ge Zhan)
Theory of Crosstalk Noise (Schuster) 8

32. The True Model use constant velocity model with c = 2.67 km/s
center frequency of source wavelet f = 20 Hz

33. Multi-source PSLSM 645 receivers and 100 sources, equally spaced
10 sets of sources, staggered; each set constitutes a supergather
50 iterations of steepest descent

34. Single-source PSLSM 645 receivers and 100 sources, equally spaced
Jerry,
The multi-source and single-source approaches have used different strategies for the step length. Therefore direct comparison of their misfit error is not applicable. Sorry about that.
645 receivers and 100 sources, equally spaced
100 individual shots
50 iterations of steepest descent

35. Multi-Source Waveform Inversion Strategy
(Ge Zhan)
Generate multisource field data with known time shift
144 shot gathers
Initial velocity model
Generate synthetic multisource data with known time shift from estimated velocity model
Using multiscale, multisource CG to update the velocity model with regularization
Multisource deblurring filter

36. 3D SEG Overthrust Model (1089 CSGs)
15 km
3.5 km
15 km

37. Dynamic Polarity Tomogram
Numerical Results
3.5 km
Dynamic QMC Tomogram
(99 CSGs/supergather)
Static QMC Tomogram
(99 CSGs/supergather)
15 km
Dynamic Polarity Tomogram
(1089 CSGs/supergather)

38. OUTLINE
Theory I
Numerical Results
Theory II

39. Multisource Least Squares Migration
Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics 36

40. Summary 37 1. Multisource crosstalk term analyzed analytically
Time Statics
1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing w, randomness,
dimension, and decreasing depth
Time+Amplitude Statics
3. Crosstalk decrease can now be tuned
QM Statics
4. Some detailed analysis and testing needed to refine
predictions. 37

41. Multisource Migration:
Multisource Least Squares Migration d { L {
d +d =[L +L ]m 1 2
Forward Model:
Phase encoding
Multisource Migration:
mmig=LTd
Kirchhoff kernel
Standard migration
Crosstalk term 34

42. Multisource Least Squares Migration
Crosstalk term 35

43. Multisource Least Squares Migration
Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics 36

44. Crosstalk Term L d +L d T T Time Statics Time+Amplitude Statics2 1
Time Statics
Time+Amplitude Statics
QM Statics

45. Summary 37 1. Multisource crosstalk term analyzed analytically
Time Statics
1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing w, randomness,
dimension, and decreasing depth
Time+Amplitude Statics
3. Crosstalk decrease can now be tuned
QM Statics
4. Some detailed analysis and testing needed to refine
predictions. 37

46. Multisource FWI Summary
(We need faster migration algorithms & better velocity models)
Stnd. FWI Multsrc. FWI
IO vs 1/20
Cost vs /20 or better
Sig/MultsSig ?
Resolution dx vs 1

47. Key Assumption + n n <d(t)>= <S(t)> + <N(t)> N(t )
Zero-mean white noise: <N>=0; <N N >=0
i j
<d(t)>= <S(t)> + <N(t)>
n= Stack Number
Amplitude +
k=1 n
N(t )
(k)
<N(t)> ~ n n
1/n 2 2 2
<N(t) > ~ 2
k=1 n
[ N(t ) ]
(k)
1/n
<N(t)> ~
<S(t)> ~
<N(t) > ~ 2
k=1 n
[ N(t ) ]
(k)
1/n