1

AVO INVERSION OF LONG-OFFSET SYNTHETIC PP DATA

BASED ON EFFECTIVE REFLECTION

COEFFICIENTS

10 April 2008

Lyubov Skopintseva

Milana Ayzenberg, Martin Landrø

Tatyana Nefedkina, Arkady Aizenberg

AVO-analysis. What is that?

Conventional AVO analysis:

•Range of incidence angles: 0-400

•Weak contrasts at reflector

0 10 20 30 40 50 60 70 80 900

0.2

0.4

0.6

0.8

1

incidence angle, degree

amp

litu

de

Pre-critical region

Critical angle

Post-critical region

2 2( ) (Re ( )) (Im ( ))A x K x K x

1

1 2

sin 1

Vp Vp

Plane-wave reflection coefficient

Effective reflection coefficient (ERC)

Incident wave

Plane-wave decomposition

Division by incident wave

Multiplying by plane-wave reflection

coefficient (PWRC)

Summation

ERC versus PWRC

• PWRC valid for plane waves

• ERC generalize PWRC for point sources

- incidence angle - frequency

- wavefront curvature - wave velocity

K x K x

;R x

x xV

2 f

V R x

x

ERC versus PWRC

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150 200 250 300 350 400Offsets, km

Am

pli

tud

e

PWRCERC(2 Hz)ERC (5 Hz)ERC (10 Hz)ERC (20 Hz)

Model parameters

0 1250 2500 3750 5000

1000

0

H=1000 m

L=5000 m

x=25 m

Vp1=2000 m/s

Vs1=1100 m/s

1=1800 kg/m3

Vp2=2800 m/s

Vs

2=1600 m/s

2=2100 kg/m3

Offset, m

Dep

th, m

Wavelet: F(t)=-sin(2ft)e-(2ft)

Dominant frequency (f): 32 Hz

Z-component from reflectivity modeling

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0 1000 2000 3000 4000 5000

offsets, m

tim

e,

s

AVO response

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Offsets,m

Am

plit

ud

e

SpectrogramF

requ

ency

, H

z

Offsets,m

1000 2000 3000 4000 5000

10

20

30

40

50

60

2

4

6

8

10

12

14

16

x 10-3

AVO response comparison with ERC and PWRC

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Offsets,m

Am

plit

ud

e

AVO-response

AVO-function (29-44Hz)

AVO-function (22-51Hz)AVO-function (all frequencies)

AVO function based on PWRC

Vs1

Vp1

1 600 2 000 2 400900

1000

1100

1200

1300

0 0.2 0.4 0.6 0.8

ro1

Vp1

1600 2000 24001400

1600

1800

2000

0 0.2 0.4 0.6 0.8

ro1

Vs1

900 1100 13001400

1600

1800

2000

0.2 0.4 0.6 0.8

ro2

Vs2

1400 1600 1800

1800

2000

2200

2400

0 0.2 0.4 0.6 0.8

Vs1

Vp1

1500 2000 2500

800

1000

1200

1400

0.2 0.4 0.6 0.8

ro1

Vp1

1500 2000 2500

1500

2000

2500

0.2 0.4 0.6 0.8

ro1

Vs1

800 1100 1 400

1500

2000

2500

0.2 0.4 0.6 0.8ro

2

Vs2

1000 1500 2000

1500

2000

2500

0.2 0.4 0.6 0.8

Plane-wave reflection coefficient

Effective reflection coefficient

Cost functions comparison (pre-critical offsets)

Vs1

Vp1

1600 2000 2400900

1000

1100

1200

1300

0 0.2 0.4 0.6 0.8

ro1

Vp1

1600 2000 24001400

1600

1800

2000

0 0.2 0.4 0.6 0.8

ro1

Vs1

900 1100 13001400

1600

1800

2000

0 0.2 0.4 0.6 0.8

ro2

Vs2

1400 1600 1800

1800

2000

2200

2400

0 0.2 0.4 0.6 0.8

Vs1

Vp1

1500 2000 2500

800

1000

1200

1400

0.2 0.4 0.6 0.8

ro1

Vp1

1500 2000 2500

1500

2000

2500

0.2 0.4 0.6 0.8

ro1

Vs1

800 1100 1400

1500

2000

2500

0.4 0.6 0.8ro

2

Vs2

1000 1500 2000

1500

2000

2500

0.5 0.6 0.7 0.8 0.9

Cost functions comparison (all offsets)

Effective reflection coefficient

Plane-wave reflection coefficient

AVO inversion results

ERC solution PWRC solution

Pre-critical offsets Post-critical offsets 0

2

4

6

8

10

12

14

16

18

20

22

24

Rel

ativ

e er

ror

in e

last

ic p

aram

eter

s, %

Vp1

Vs1

1

Vp2

Vs2

2

Pre-critical offsets Post-critical offsets0

2

4

6

8

10

12

14

16

18

20

22

24

Rel

ativ

e er

ror

in e

last

ic p

aram

eter

s, %

Vp1

Vs1

1

Vp2

Vs2

2

15

Conclusion

• ERC give better estimates than PWRC

• Rapid variations in reflection amplitude for post-critical offsets improve inversion results

• Long-offset data allow accurate estimation of Vp and Vs