Seismic interferometry-by- deconvolution for controlled-source and passive data Kees Wapenaar, Joost...

Seismic interferometry-by-deconvolution for controlled-source

and passive data

Kees Wapenaar, Joost van der Neut,Elmer Ruigrok, Deyan Draganov,

Juerg Hunzicker, Evert Slob,Jan Thorbecke

70th annual EAGE meetingJune 11, 2008

Rome

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

AxBx

S

ˆ2 { ( , , )}B AG x x* 22 ˆ ˆ( , , ) ( , , )B S A S SS

G G dc

x x x x x

Seismic interferometry by cross-correlation

( , , ) ( , , )B A B AG t G t x x x x22

( , , ) ( , , )B S A S SSG t G t d

c x x x x x

AxBx

S

Seismic interferometry by cross-correlation

( , , ) ( , , )B A B AG t G t x x x x

AxBx

S

Seismic interferometry by cross-correlation

( , ) ( , )B Ap t p t x x

Uncorrelated noise sources

target

virtualsource

Cross-correlation

1

( ) ( ) ( )N

k kk

D t S t S t

Seismic interferometry by cross-correlation

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Summary:

The correlation function is in a specific way related to the Green’s function

( , , )B AC tx x

( , , )B AG tx x

( , , ) ( , , ) ( , , )B A B A B AC t G t G t x x x x x xe.g.

Seismic interferometry by cross-correlation

Seismic interferometry by cross-correlation

Properties:

• Requires no knowledge about sources and medium • Trace-by-trace process

• Sources on closed surface (except on free surface)• Sensitive to irregular source distribution• Medium is assumed lossless

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

data data

data data

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

Correlation function

Deconvolution function

( , , ) :B AC tx x

( , , ) :B AD tx x

data data

data data

Wapenaar and Verschuur, 1996, DelphiAmundsen, 1999, SEG, Wapenaar et al., 2000, SEGHolvik and Amundsen, 2005, GeophysicsSchuster et al., 2006, Geophysics

Seismic interferometry by deconvolution

0( , , ) ( , , ) ( , , )B S B A A S Ap t R t p t d x x x x x x x

target (reservoir)

Reflectionresponse R+

Upgoing wavefield P-

Downgoing wavefield P+

OBC example (1996)

Seismic interferometry by deconvolution

( , , )A Sp t x x ( , , )B Sp t x x 0 ( , , )B AR t x x

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SC p q d x x x x x x x

Correlation approach:

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au D v d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SC p q d x x x x x x x

Correlation approach:

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au D v d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆU DV † † 2 1 †ˆ ˆ ˆ ˆ ˆ ˆ ˆ( ) D UV VV I UV

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SC p q d x x x x x x x

Correlation approach:

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au D v d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆU DV † † 2 1 †ˆ ˆ ˆ ˆ ˆ ˆ ˆ( ) D UV VV I UV

D̂ ˆ ( , , )B AD x x ( , , )B AD tx x

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

van der Neut et al., Thursday 14:55P272

black = directly modeled red = retrieved

Cross-Correlation

PP reflection

Deconvolution

black = directly modeled red = retrieved

PP reflection

Cross-Correlation

directly modeled

retrievedblack = directly modeledred = retrieved

PP reflection

directly modeled

retrieved

Deconvolution

black = directly modeledred = retrieved

PP reflection

black = directly modeled red = retrieved

PS reflection

Cross-Correlation

black = directly modeled red = retrieved

PS reflection

Deconvolution

directly modeled

retrieved

Cross-Correlation

black = directly modeledred = retrieved

PS reflection

directly modeled

retrieved

Deconvolution

black = directly modeledred = retrieved

PS reflection

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

USArray

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au G u d x x x x x x x

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au G u d x x x x x x x

Sx

AxBx

Cross-correlation

Deconvolution

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

ˆˆˆ ( , , ) ( , , ) ( , , )m B S mj B A j A S Av G t d x x x x x x x

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

ˆˆˆ ( , , ) ( , , ) ( , , )m B S mj B A j A S Av G t d x x x x x x x

Sx

AxBx

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

ˆˆˆ ( , , ) ( , , ) ( , , )m B S mj B A j A S Av G t d x x x x x x x

ˆˆ ˆ( , , ) ( , , ) ( , , )m B S m B S m B Sv v v x x x x x x

Sx

AxBx

with

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

ˆˆˆ ( , , ) ( , , ) ( , , )m B S mj B A j A S Av G t d x x x x x x x

ˆˆ ˆ( , , ) ( , , ) ( , , )m B S m B S m B Sv v v x x x x x x

Sx

AxBx

with

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

ˆˆˆ ( , , ) ( , , ) ( , , )m B S mj B A j A S Av G t d x x x x x x x

ˆˆ ˆ( , , ) ( , , ) ( , , )m B S m B S m B Sv v v x x x x x x

Sx

AxBx

with

▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼

1 … 26 … 51

3 33ˆ ˆˆ ( , , ) ( , , ) ( , , )B S B A A S Av G p d x x x x x x x

3 3 3ˆˆ ˆ( , , ) ( , , ) ( , , )B S B S B Sv v v x x x x x x

Sx

AxBx

with

(a) Correlation

t (s

)

Cross-correlation

t (s

)

(b) DeconvolutionDeconvolution

Ground Truth: Cross-correlation:

Ground Truth: Deconvolution:

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

The correlation function and thedeconvolution function are eachin a specific way related to the Green’s function

( , , )B AC tx x( , , )B AD tx x

( , , )B AG tx x

( , , ) ( , , ) ( , , )B A B S A S SC t p t q t d x x x x x x x

Correlation approach:

( , , ) ( , , ) ( , , )B S B A A S Au t D t v t d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SC p q d x x x x x x x

Correlation approach:

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au D v d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆU DV † † 2 1 †ˆ ˆ ˆ ˆ ˆ ˆ ˆ( ) D UV VV I UV

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SD u v d x x x x x x x

Review of seismic interferometry by cross-correlation

Seismic interferometry by deconvolution

• Introduction• Theory• Controlled-source data (‘virtual source’)• Passive data (surface wave retrieval)• Passive data (transmission-to-reflection)• Theory (revisited)

Conclusions

Contents

Seismic interferometry by cross-correlation

• Requires no knowledge about sources and medium • Trace-by-trace process

Seismic interferometry by deconvolution

• Requires no knowledge about sources and medium • Can deal with one-sided illumination• Irregular source distribution• Dissipation allowed (e.g. CSEM)

59

CSEM by deconvolution (Slob et al.)

2D TM-examples for shallow and deep seaBlue curves: no reservoirRed curves: with reservoir

60

Electric field Magnetic field

61

Down going Up going

62

Deconvolved result not dependent on sea depth

CSEM by deconvolutionSolve:

0ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Ap R p d x x x x x x x

and are decomposed diffusion fields.

Correlation method not applicable

ˆ ( , , )B Sp x xˆ ( , , )A Sp x x

64

Numerical example: Seabed Logging in shallow seaoverburden effect

2D TM-examples for receivers in horizontal wellBlue curves: no reservoirRed curves: with reservoir

65

Electric field Magnetic field

66

Down going Up going

67

Deconvolved result not dependent on overburden

Random source distribution

100 sources+ 20 in cluster A + 30 in cluster B

Center freq of wavelet: 20 Hz

Dispersion 10

21 receivers in array 1

21 receivers in array 2

ˆ ˆ ˆ( , , ) ( , , ) ( , , )B A B S A S SC p q d x x x x x x x

Correlation approach:

ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Au D v d x x x x x x x

Deconvolution approach:

ˆ ˆ ˆU DV † † 2 1 †ˆ ˆ ˆ ˆ ˆ ˆ ˆ( ) D UV VV I UV

0ˆ ˆ ˆ( , , ) ( , , ){ ( , , )}B A B S A S SR p p d x x x x x x x

‘Virtual source’ by cross-correlationEvaluate:

‘Virtual source’ by deconvolutionSolve:

0ˆˆ ˆ( , , ) ( , , ) ( , , )B S B A A S Ap R p d x x x x x x x

Cross-correlation method is an approximation of deconvolution method

Conclusions

Correlation method: trace-by-trace process

Deconvolution method: Regular receiver gridIrregular source distributionDissipation allowed