Rapid estimation of converted wave velocities using...

Rapid estimation of converted wave velocities using prestack migration

John C. Bancroft, Thais Guirigay

Helen Isaac

30 November, 2012

1

0 500 1000 1500 2000 2500 30001

1.5

2

2.5

3

3.5

4

4.5

5

Depth (m)

Gam

ma γ

Gamma functions in depth from picked velocities

γ: Int. Vels. γ: RMS vels. γ: log

Motivation

2

Objectives Define a converted wave velocity Vc Use Vc to find Vs Create CCSP gathers

3

Outline • Objectives • Review EOM P-P and P-S, Vc • Estimating Vc • Estimation Vs • Formation of Gathers • Comments and Conclusion • Results next talk

4

Scatter point

SP R S MP

t/2

t0/2 or z0 hyperbola

x h h

2te

( ) ( ) 2 20

2

2 22 20 0

2 24 42

4ex h x ht tt h

VVt

V+ −

= + + + +=

E

Kirchhoff Prestack Migration

5

Equivalent Offset Migration

Scatter point

SP R S MP

t/2

t0/2 or z0 hyperbola

he

x h h

2te

( ) ( ) 2 20

2

2 22 20 0

2 24 42

4ex h x ht tt h

VVt

V+ −

= + + + +=

2 22 2 2

2 2

4eh x hx h

t V= + −

E

6

CMP or prestack migration gathe

h

t x

Forming a CSP gather

7

CMP Vs CSP gather

8

Gathers and semblance CMP

~CSP

CSP

Gather formed V = ∞

• Approximate Vp to form gathers

• More accurate Vp obtained from gathers

• For then m/s

• Not the case for converted wave data

• Need a more accurate starting velocity Vc

10

The point …

1Vp = ∞ 2 3200Vp =

Converted waves

11

P-P Source Receiver CMP

Z P

P

θ θ

P-S Source Receiver CMP

CCP

θ φ

Z P S

S R

Conversion Points

Asymptotic Approximation

Midpoint

Xp

2h

Most important up shallow X

Equivalent offsets: converted waves hr

hs

2 20 0

2

2 22 20 0

2 2

2

2

2

4 4 4 4p ps r

rms P rms P

s s

rm S

e

s r

e

ms S

ht th ht tV V V

htV

− −

− − −

− −

−

= + + + = + + +

12

Scatter point

SP R S MP

t/2

hyperbola

he

2te

E

t0p, t0s, z0

Vrms and Vave

0 0.5 1 1.5 21500

2000

2500

3000

3500

4000

4500

Time T0 (sec)

Vel

ocity

(m/s

)Comparison of Vp-rms, Vp-int, and Vp-ave.

Vp-intVp-rmsVp-ave

RMS velocity slightly higher than average velocity. 13

Vrms / Vave

0 0.5 1 1.5 20

0.5

1

1.5

Time T0 (sec)

ratio

Ratio Vp-rms/Vp-ave

P

0 0.5 1 1.5 20

0.5

1

1.5

Time T0 (sec)

ratio

Ratio Vp-rms/Vp-ave over Vs-rms/Vs-ave

P/S

0 0.5 1 1.5 20

0.5

1

1.5

Time T0 (sec)

ratio

Ratio Vs-rms/Vs-ave

S

14

2 2 2 2 20

2 2 20 00

1 1 1 ˆˆ ˆ ˆ1s r

rms p rms pe

rms s rme

s s

z hV V

t z h z hV

hV

z− −− −

= + + + +++=

2 20

2 ˆ ec

ztV

h+=

Assume rms p rms s

ave p ave s

V VkV V

− −

− −

≈ ≈

Define 0 0ˆ rms

ave

Vz zV

=

2220ˆ4

ceh t V z= −

2 rms p rms sc

rms p rms s

V VV

V V− −

− −

=+

15

Converted wave velocity Vc

• Initial Vc1 with Vp and • Limited range EO gathers • Pick new Vc2

• Estimate Vs

• Full EO gathers with Vp and Vs • Pick new Vc3

• Moveout correction with Vc3 • Stack to complete the prestack migration

2 rms p rms sc

rms p rms s

V VV

V V− −

− −

=+

γ

16

1. Using

2. Narrow range gather

Initial Vc can be formed

Estimating of Vc1

,p

s

VV

γ = 2γ =

maxx x

12(1 )

rms Pc

VVγ−=

+

( ) ( )2 22 20 0

1 1ˆ ˆrm rms Ss P

t z x h zV

x hV −−

= + + + + −

( ) ( )2 22 20 0 0

1 1ˆ ˆrms C m C

xr s

t z x hV V

z x h−

→−

≈ + + + + −

17

Supergather

A full EO method

Initial estimate of Vc

18

LCCSP gather

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Initial gather

Pick Vc2

Form few gathers using one velocity Vc1 Velocity analysis to find Vc2 Now find Vs

Estimating Vs from Vc2

2 rms S

rms

rms Prms C

r s P Sm

VVV V

V −−−

− −

=+

2rms C rms

rmP

rms P rs S

ms C

V VV

VV

−

− −−

−=−

20

2 20

2 ˆrms C

p s et hV

z−

− = +

2 2 2 20 0

1 1ˆ ˆ( ) ( )rmsm S

p sr s P

t z x h z x hV V −

−−

= + + + + −

Full CCSP gathers

Use he to form CCSP gathers

21

Full CCSP gather

22

Full EO

Pick Vc3

• is defined with Vint and depth

• Vp, Vs, and Vc are also defined in depth

• Using map depth to tc

• Keep all times in tc

We have ignored t times 2 ( ) ( )

( ) ( )srms P rms S

rms Cr

p

pP sms rms S

tV VV

tV Vt t

− −−

− −

=+

Time t consideration

γ

Ave RMSV V≈

z

zz

•

z

23

Matching the traveltime for P- and C-wave data

Method 1 1. Convert Vrms-p(top) to interval Vint-p (top)

2. Use interval velocities to map the times to depth

3. Get average velocity Vave-p of Vrms-p

0opt z⇒

0 0.5 1 1.5 2 2.5 3 3.5 42000

3000

4000

5000

6000

Time T0 (sec)

Vel

ocity

(m/s

)

Comparison of Vp-rms, Vp-int, and Vp-ave.

Vp-rmsVp-intVp-ave

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Method 1 (continued) 4. Scale the amplitude Vint-c to Vint-p at z (same as top)

using 4. Use Vint-c (z) and the corresponding depth

increments, compute the C time at each depth.

5. Resample Vint-c from irregular times to equal time increments

6. Convert the interval C velocities to RMS C velocities

7. Get the depth of every Vc time sample using Vint-c


λ

25


Method 2 1. Using the corresponding average velocities

2. Resample Vrms-c(n) to Vrms-c(m) using equal increments of m

2 ( )(1 ( ))

rms prms c

V zV

zγ−

− =+

12oc opt t γ+

≈ 12

m nλ+=

26

0 1 2 3 4 5 61500

2000

2500

3000

Time T0 (sec)

Vel

ocity

(m/s

)

Comparison of Vc-rms1 and Vc-rms2

Vc-rms1Vc-rms2

Estimating the C velocities

27

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

Depth (m)

Vel

ocity

(m/s

)

Comparison of interval velocities in depth

Vp-int(z)Vc-int(Gz)Vc-int(Pz)

Estimating the C velocities

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Method 1 1. From the Vc picked:

2. Convert shear interval Vint-s from depth to time

3. Convert Vint-s in S time into Vrms-s

4. Convert tos to top

5. Get the RMS gamma function in time

6. Convert RMS gamma to depth assuming Vrms = Vave

int intint

int int

( )2

p cs

p c

V VV z

V V− −

−− −

=−

2int

00

0

( )( )

N

s nn

rms s s N

nn

V n tV t

t

−=

−

=

=∑

∑

Estimating the S velocities

( )( )

( )rms p p

rmsrms s p

V tt

V tλ −

−

=

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0 1 2 3 4 50

1000

2000

3000

4000

5000

6000

Time T0 (sec)

Vel

ocity

(m/s

)

Comparison of interval velocities in time

Vp-intVc-int(P)Vs-int(P)


30

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

Depth (m)

Vel

ocity

(m/s

)

Comparison of interval velocities in depth

Vp-int(z)Vc-int(Pz)Vs-int(Pz)


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0 2000 4000 6000 8000 100001

1.5

2

2.5

3

3.5

4

4.5

Depth (m)

Gam

ma

Comparison of interval Gamma functions

Gamma from Vp-rms(Gz)Gamma from picked Vc-rms(Pz)Gamma from well-log


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Another project in N.E. BC

0 500 1000 1500 2000 2500 30001

1.5

2

2.5

3

3.5

4

4.5

5

Depth (m)

Gam

ma γ

Gamma functions in depth from picked velocities

γ: Int. Vels. γ: RMS vels. γ: log

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• Not yet • Next talk • Posters

Examples of data

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• Use EO concepts to process P-S data • Need approximate velocity starting velocities

Vp and Vs • Can use a single velocity Vc most of the time • Simple process to estimate of Vc and Vs

– Vc1 from Vp and – Vc2 from initial gather – Vs from Vp and Vc2

• Produced reasonable values for

Comments and conclusions

γ

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γ

γ






γ

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γ

γ






γ

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γ

γ






γ

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γ

γ






γ

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γ

γ






γ

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γ

γ




• Produced reasonable values for • Can approximate Vave with Vrms


γ

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γ

γ

Acknowledgments

All CREWES staff CREWES sponsors

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Thanks 43

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