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Full Waveform Inversion algorithm using Common Scatter Points gathers using Common Scatter Points gathers Hassan Khaniani*, John C. Bancroft and Gary F. Margrave 2011 CREWES Annual Sponsors Meeting December,02,2011 1

Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

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Page 1: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Full Waveform Inversion algorithm using Common Scatter Points gathersusing Common Scatter Points gathers

Hassan Khaniani*, John C. Bancroft and Gary F. Margrave2011 CREWES Annual Sponsors Meeting

December,02,2011

1

Page 2: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Outline

• Review of Full Waveform InversionReview of Full Waveform Inversion• PSTM Full Waveform Inversion algorithm

l• Examples • Discussions• Conclusions

2

Page 3: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Review

• Nonlinear geophysical optimization process

• Born in mid 1980s due to pioneering work of p gLailly(1983) & Tarantola (1984,1986,1988), well developed in more than two decades

• Forward modeling tool including wave equation modeling

• Inverse problem can be solved with gradient based linear iterative methods

3

Page 4: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Theory of PSDM FWI0 4000

(m)

0

5003500

4000

dept

h (

10002500

3000

21

PSDM FWI

lateral position (m) 4600 4800 5000 5200 54001500 2000

fwI in

, 2

1min ( , )2

sx xu x tφ δ=

1

m)

0

5003500

4000fwI in

3

1( , ) ( ) ( ( , ))k t f t kbsk

x z dt P u x tv

γ δ= ∂ ∂

( ) ( ) ( )

Tarantola, 1984, Vigh, 2008

dept

h (m

10002500

30001( , ) ( , ) ( , )k k k kv x z v x z x zα γ+ = −

Sh d i l i ilateral position (m)

4600 4800 5000 5200 54001500 2000Shot records simulation using

solution of wave equationPSDM

4

Page 5: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

R S

Prestack Time FWI pt

h (m

)

0

500

3000

3500

4000

me

(s)

0

0.5

3000

3500

4000

me

(s)

0

0.50.1

R

lateral position (m)

dep

4600 4800 5000 5200 5400

1000

1500 2000

2500

lateral position (m)

tim

4600 4800 5000 5200 5400

1

1.5 2000

2500

lateral position (m)

tim

4600 4800 5000 5200 5400

1

1.5 0

0.05Depth Time Rc

Forward Modeling

time

Forward Modeling

Migration/Inversion

DSR equation

Lateral position

X= Distance between scatterpoint and S/R CMP

h=Half S/R offset 5

Page 6: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

CSP gather

CSP gather

Offset domain Equivalent Offset domain

τ

X= Distance between scatterpoint and S/R CMP

2 2 2 2

2 2

( X h ) ( X h )t( S ,G )4 v 4 v

τ τ+ −= + + +2

2 e2h( )v

,t S G τ +

=

X Distance between scatterpoint and S/R CMP

h=Half S/R offset

Page 7: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

PSTM FWI Inversion

21 1( , ) ncR x Lτ ∂= − ( , )4 ( , )c x

v xτ

τ τ ∂

21 1 2 ( )v o vδ δ= − +near

izatio

n

2 2 3 ( )( ) ( , ) ( , )

o vv v v x v x

δδ τ τ

= ++

22 4hδ

lin

22

3

4( ', )( , , ) ( ) '.

( ', )

e

e

hv x tvu x h t K s d dh dx

v x

δ τδ τ τ

τ

= − = × ∗

( )γ τ7

( , )xγ τ

Page 8: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Gradient ComputationPSTM vs PSDM

True di

initial True gradientinitial Velocity gradientVelocityVelocitygradientVelocity

1z

dept

h

time

2z2τ

PSDM FWI PSTM FWIInnanen, 2011, Geophysical inversion II: seismic inversion:U of Calgary, unpublished course notes. 8

Page 9: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Algorithm of PSTM FWICalculate ( x, )γ τ

startingv ( x, )τ

Scan for optimum No

αrmsv ( x, )τ

Update v( x, )τcalculate small

enough?

u( x,t )δu( x,t )δ

( , )

?

yes

End

9

Page 10: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

21 shot records

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s 1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP0 500 1000 1500 2000 2500 3000 3500

1.6

1.8

2

1.6

1.8

2

true velocity in time initial velocity in time

10

Page 11: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 5

11

Iteration 5

Page 12: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 15

12

Iteration 15

Page 13: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 25

13

Iteration 25

Page 14: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 30

14

Iteration 30

Page 15: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 35

15

Iteration 35

Page 16: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8

)

0.2

0.4

0.6

0.8

Tim

e (s

1

1.2

1.4

1 6

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 40

16

Iteration 40

Page 17: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0 20 2

)

0.2

0.4

0.6

0.8)

0.2

0.4

0.6

0.8

Tim

e (s

)

1

1.2

1.4

Tim

e (s 1

1.2

1.4

1 6

CMP3500 4000 4500 5000 5500 6000 6500

1.6

1.8

2

1.6

1.8

2

true velocity in time updated velocityIteration 55

17

Iteration 55

Page 18: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Synthetic Example

0true velocity45 it ti d t d l it

0.5

45 iterations updated velocitystarting model

1

time

(s)

1.5

1500 2000 2500 3000 3500 4000 45002velocity (m/s)

true l itvelocity

18

Page 19: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

E l 2Example 2Hussar current results

19

Page 20: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

iteration# 0

initial velocitySW NWiteration# 0

0.2

0 4 4000

4500

5000SW NWTi

me

(s)

0.4

0.6

0.83000

3500

T

1

1.2

1500

2000

2500

500 1000 1500 2000 2500 3000

1.4

1000

1500

20

Page 21: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

iteration# 1

updated velocitySW NWiteration# 1

0.2

0 4 4000

4500

5000SW NWTi

me

(s)

0.4

0.6

0.83000

3500

T

1

1.2

1500

2000

2500

CMP

500 1000 1500 2000 2500 3000

1.4

1000

1500

21

Page 22: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

iteration# 8

updated velocitySW NWiteration# 8

0.2

0 4 4000

4500

5000SW NWTi

me

(s)

0.4

0.6

0.83000

3500

T

1

1.2

1500

2000

2500

CMP

500 1000 1500 2000 2500 3000

1.4

1000

1500

22

Page 23: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

updated velocityiteration# 70SW NW

0.2

0 4 4000

4500

5000iteration# 70

0.2

0 4 4000

4500

5000SW NWTi

me

(s)

0.4

0.6

0.83000

3500

Tim

e (s

)

0.4

0.6

0.83000

3500

T

1

1.2

1500

2000

2500

T

1

1.2

1500

2000

2500

CMP

500 1000 1500 2000 2500 3000

1.4

1000

1500

CMP

500 1000 1500 2000 2500 3000

1.4

1000

1500

23

Page 24: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

iteration# 0 5000

iteration# 70 5000

me

(s)

0.2

0.4

0.6

0 83000

3500

4000

4500

me

(s)

0.2

0.4

0.6

0 83000

3500

4000

4500

Tim 0.8

1

1.2

1.41500

2000

2500Ti

m 0.8

1

1.2

1.41500

2000

2500

CMP

500 1000 1500 2000 2500 3000

1000

CMP

500 1000 1500 2000 2500 3000

1000

24

Page 25: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Hussar example

γ(x,t) sonic log 1435initial velocity

0.1 0.1

initial velocitysonic velocity

me

(s) 0.2

0 3

0.2

0 3

Tim 0.3

0.4

0.3

0.4

CMP500 1000 1500

0.52000 3000 4000

0.5

l it ( / )CMP velocity (m/s)

25Gredient function In time

Page 26: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Shot records comparison

real data

26

Page 27: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Shot records comparison

predicted data

27

Page 28: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Discussions

real data

28

Page 29: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Comments

• Converted waveConverted wave • Anisotropic modeling /inversion

29

Page 30: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Conclusions

Developed a PSTM FWI algorithms for velocityDeveloped a PSTM FWI algorithms for velocity inversion.Use CSP gathers for initial velocity modelUse CSP gathers for initial velocity model.Not accurate for complex structures because

f i i i i f d d iof using time migration forward and inverse process.Faster.

30

Page 31: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Acknowledgments

• CREWES Sponsors for supports• Dr. Kristopher Innanen• Naser Yousefzadeh• Marcus Wilson• Marcus Wilson• Ben Wards

THANK YOU !THANK YOU !31

Page 32: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

hyperbola tilt

Page 33: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Image Enhancements

Regular PSTM PSTM + removed Tilt

0

500

10004500

5000

5500

) 000

1500

20002500

3000

3500

4000

Dept

h (m

Tim

e (s

)

3000 3500 4000 4500

2500

3000 1500

2000

2500

Page 34: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Image Enhancements

Regular PSTM PSTM + removed Tilt

0

500

10004500

5000

5500

) 000

1500

20002500

3000

3500

4000

Dept

h (m

Tim

e (s

)

3000 3500 4000 4500

2500

3000 1500

2000

2500

Page 35: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Image Enhancements

Regular PSTM PSTM + removed Tilt

0

500

10004500

5000

5500

) 000

1500

20002500

3000

3500

4000

Dept

h (m

Tim

e (s

)

3000 3500 4000 4500

2500

3000 1500

2000

2500

Page 36: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Image Enhancements

Regular PSTM PSTM + removed Tilt

0

500

10004500

5000

5500

) 000

1500

20002500

3000

3500

4000

Dept

h (m

Tim

e (s

)

3000 3500 4000 4500

2500

3000 1500

2000

2500

Page 37: Full Waveform Inversion algorithm using Common Scatter ... · Full Waveform Inversion algorithm using Common Scatter Points gathers Author: Hassan Khaniani*,John C. Bancroft and Gary

Image Enhancements

Regular PSTM PSTM + removed Tilt

0

500

10004500

5000

5500

) 000

1500

20002500

3000

3500

4000

Dept

h (m

Tim

e (s

)

3000 3500 4000 4500

2500

3000 1500

2000

2500