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Supervisors:
Dr. Larry Lines
Dr. Robert Ferguson
Convergence of a full waveform inversion scheme based on PSPI
migration and forward modeling-free approximation: procedure
and validation
Presenter:
Marcelo Guarido de Andrade

? Reduce the cost of a gradient descent FWI routine preserving its
resolution at most
? Replacing the RTM by a PSPI migration
? Reducing cost to estimate the step length
? Re-interpretation of the gradient
Objective
5

? Introduction
? Steepest-descent (gradient) method
? Trial-and-error line search vs. Pica et al. (1990) approximation
? Monochromatic averaged gradient
? Initial model
? Conjugate gradient
? Impedance inversion of the gradient
? Forward modeling-free gradient
? Pre-stack
? Post-stack
? Well calibration of the gradient
? Same initial model
? Conclusions
? Future work
Outline
6

Introduction
C ? �� ?? ?
2Minimize
Least Squares
? ??? ? ? ???
8

?(?+?) = ?(?) ? ?(?) ?(?)
m0
?dm
g0
m1
��0
9

Introduction
Velocity(m/s)
Velocity(m/s)
10

Steepest-descent (gradient) method
11

96 simulated shots
(��real model��)
Initial model
(smoothed
velocity)
Synthetic Data
Residuals
PSPI Migration
(Deconvolution
Imaging Condition)
Step length
(linear search and
quadratic fit)
Update ModelConvergence?
Final Model
Yes
No
Mute and Stack
12

Acquisition
Type Marine
Number of shots 96
Shot spacing 100m
Shot depth 30m
# of receivers 401
Receiver spacing 10m
Receiver depth 0m
Frequency 10Hz
Processing
Starting frequency 1-6Hz
Iterations per frequency < 16Hz 10
Iterations per frequency > 15Hz 5
Frequency increment < 25Hz 1Hz
Frequency increment > 24Hz 5Hz
Mute Yes
Water bottom mute Yes
Scale factor tests 21
13

Model
Depth 3km
Width 10km
Resolution 10m
Min. velocity 1500m/s
Max. velocity 3900m/s
Velocity(m/s)
14

Velocity(m/s)
15

16

17

18

19

20

21

22

Velocity(m/s)
23

Velocity(m/s)
24

Velocity(m/s)
25

26

? Trial-and-error
? Try several step lengths
? Update the model
? Synthetic shot
? L2-norm
? Quadratic fit (3 points)
? Lowest error
? Expensive
27

? Least Squares:
? Step length:
28

Velocity(m/s)
Velocity(m/s)
Initial Model CorrectModel
29

Trial-and-error line search
30

Pica et al. (1990) approximation
31

32

Acquisition
Model Marmousi
Number of shots 101
Shot spacing 100m
Shot depth 0m
# of receivers 401
Receiver spacing 10m
Receiver depth 0m
Frequency 10Hz
Processing
Starting frequency 1-4Hz
Iterations per frequency < 13Hz 5
Iterations per frequency > 12Hz 2
Frequency increment < 13Hz 1Hz
Frequency increment > 12Hz 5Hz
Mute Yes
Smooth Yes
Scale factor tests 21
33

Velocity(m/s)
34

Velocity(m/s)
35

Velocity(m/s)
36

37

Monochromatic averaged gradient
38

? Monochromatic PSPI migration of the residuals
? Gradient for each frequency
? One step for each gradient
? Average scaled monochromatic gradients
39

? Starting: low frequency
? Increase frequency band
? Convergence
? By 2Hz
? Maximum: 60Hz
? More migrations as
frequency band gets larger
40

Velocity(m/s)
41

Velocity(m/s)
42

Velocity(m/s)
43

44

Velocity(m/s)
45

Velocity(m/s)
46

Velocity(m/s)
47

Velocity(m/s)
48

Velocity(m/s)
49

Velocity(m/s)
50

51

Velocity(m/s)
52

Velocity(m/s)
53

Velocity(m/s)
54

Velocity(m/s)
55

56

57

Impedance inversion of the gradient
58

? Gradient -> reflection coefficients or impedance?
? Impedance inversion
? FWI as seismic processing tools
? I �C impedance inversion
? S �C stacking
? M �C migration
59

? Band-Limited Impedance Inversion (BLIMP)
? Depth-to-time and time-to-depth conversions
? Initial model as pilot impedance
? One migration step per iteration
60

61

62

63

64

65

Forward modeling-free gradient
66

And:
Step length requires 2 forward modeling
Linear operators
67

68

69

70

71

72

? Commuting the Migration and Stacking operators
73

? Invert frequencies > 4Hz
? Step length: biased by position
? Select random shot
? Can��t control objective function
74

75

76

77

78

79

80

81

82

83

Well calibration of the gradient
84

? Sonic log
? Storage difference of sonic log and current model (what the
gradient should be)
? Compute gradient
? Compute matching filter between gradient and stored
difference of sonic log and current model
? Convolve matching filter with the whole gradient
? Inverting frequencies > 4Hz
85

86

87

88

89

90

91

92

Advantages of a forward modeling-free inversion:
? No source (wavelet) estimation
? No need to for any forward modeling
? Cheaper
? More robust to work on real data?
93

? Simulation of a velocity analysis
? Divide Marmousi in 5 horizontal areas
? Pick one random position inside each area
? Linear interpolation
? Repeat for all columns
? Smooth
Same initial model
95

Same initial model
96
Repeat for all columns

? Steepest-descent: works well on simple models
? Least squares step length: cheaper and good
? Monochromatic averaged gradient: higher resolution with high cost
? Conjugate gradient: improved resolution
? Impedance inversion of the gradient: great resolution reducing costs
? Forward modeling-free gradient: pre and post-stack approximations,
cheaper with good resolution
? Well calibration of the gradient: 100% forward modelling-free FWI,
lowest cost with improved resolution
Conclusions
104

? Reverse time migration (RTM)
? Multi-parameter (if possible)
? Extend to 3D
? Real data
? Deep learning (Neural Networks?)
Future work
105

?Dr. Larry Lines
?Dr. Rob Ferguson
?NSERC
?CREWES Sponsors
?Students and staff
?Dr. Kris Innanen
?Dr. Daniel Trad
?Dr. Gary Margrave
?Dr. Babatunde Arenrin
?Dr. Raul Cova
?Dr. Wenyong Pan
?FWI group
?Laura Baird
?Soane Mota dos Santos
Acknowledgments
106

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PhD Final Presentation by Marcelo Guarido

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PhD Final Presentation by Marcelo Guarido