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WI T Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck, Tilman Klüver, Jürgen Mann * Geophysical Institute University of Karlsruhe Germany 8th Int. Congress, Brasilian Geophysical Society, Rio 2003
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Page 1: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T

Tomographic velocity model estimationwith data-derived first and second

spatial traveltime derivatives

Eric Duveneck, Tilman Klüver, Jürgen Mann∗

Geophysical InstituteUniversity of Karlsruhe

Germany

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 2: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TOverview

Introduction

Velocity determination with CRS attributes

A synthetic data example

A real data example

Extension to 3D

Advantages/Limitations

Conclusions

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 3: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIntroduction

Problem: Determination of velocity modelfor depth imaging

Tomographic approach based on CRS stack results

Smooth model description

Advantages:picking in simulated ZO section of high S/N ratiopick locations independent of each other⇒ very few picks required

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 4: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIntroduction

Problem: Determination of velocity modelfor depth imaging

Tomographic approach based on CRS stack results

Smooth model description

Advantages:picking in simulated ZO section of high S/N ratiopick locations independent of each other⇒ very few picks required

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 5: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIntroduction

Problem: Determination of velocity modelfor depth imaging

Tomographic approach based on CRS stack results

Smooth model description

Advantages:picking in simulated ZO section of high S/N ratiopick locations independent of each other⇒ very few picks required

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 6: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIntroduction

Problem: Determination of velocity modelfor depth imaging

Tomographic approach based on CRS stack results

Smooth model description

Advantages:picking in simulated ZO section of high S/N ratiopick locations independent of each other⇒ very few picks required

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 7: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TCRS stack – 3D data example

4000 −

2000 −

6000 −

8000 −

0 −

4000 −

2000 −

6000 −

8000 −

0 −

PreSDM PostSDM of CRS stack

Data courtesy of ENI E&P Division

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 8: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TCRS stack and attributes

t2 (ξm,h) =(

t0 + 2 sinαv0

(ξm−ξ ))2

+2 t0 cos2 α

v0

((ξm−ξ )2

RN+ h2

RNIP

)

ξ ξ

α α

NIP NIP

NIP NRR

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 9: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TCRS attributes and velocities

NIP

α

ξNIPR In the vicinity of a ZO ray:CRP-response can beapproximately described byt0, ξ , RNIP, α

Velocity model is consistentif RNIP = 0 at t = 0 for all con-sidered data points

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 10: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TCRS attributes and velocities

NIP

α

ξNIPR In the vicinity of a ZO ray:CRP-response can beapproximately described byt0, ξ , RNIP, α

Velocity model is consistentif RNIP = 0 at t = 0 for all con-sidered data points

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 11: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TTomography with CRS attributes

Data and model components

θ

ξ

α

MT

(x,z)

v(x,z)

Data: (T , M, α , ξ )i

Model: (x, z, θ )i, v jk

M = 1/v0RNIP

T = t0/2

v jk: B-spline coefficients

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 12: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TTomography with CRS attributes

Data and model components

θ

ξ

α

MT

(x,z)

v(x,z)

Data: (T , M, α , ξ )i

Model: (x, z, θ )i, v jk

M = 1/v0RNIP

T = t0/2

v jk: B-spline coefficients

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 13: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TForward modeling

Kinematic ray-tracing

⇒ T , α , ξ

Dynamic ray-tracing

⇒ Ray propagator matrix ΠΠΠ =

(Q1 Q2P1 P2

)

⇒ M = P2/Q2

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 14: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TForward modeling

Kinematic ray-tracing

⇒ T , α , ξ

Dynamic ray-tracing

⇒ Ray propagator matrix ΠΠΠ =

(Q1 Q2P1 P2

)

⇒ M = P2/Q2

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 15: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TInversion procedure

nonlinear least-squares problem

⇒ iterative solution, linearize locally

model update ∆m: least-squares solution of

F∆m = ∆d

with ∆d : data misfitF : Fréchet derivatives

calculation of Fréchet derivatives:ray perturbation theory

regularization ⇒ F̂∆m = ∆d̂(minimization of second derivatives of velocity)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 16: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TInversion procedure

nonlinear least-squares problem

⇒ iterative solution, linearize locally

model update ∆m: least-squares solution of

F∆m = ∆d

with ∆d : data misfitF : Fréchet derivatives

calculation of Fréchet derivatives:ray perturbation theory

regularization ⇒ F̂∆m = ∆d̂(minimization of second derivatives of velocity)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 17: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TInversion procedure

nonlinear least-squares problem

⇒ iterative solution, linearize locally

model update ∆m: least-squares solution of

F∆m = ∆d

with ∆d : data misfitF : Fréchet derivatives

calculation of Fréchet derivatives:ray perturbation theory

regularization ⇒ F̂∆m = ∆d̂(minimization of second derivatives of velocity)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 18: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TInversion procedure

nonlinear least-squares problem

⇒ iterative solution, linearize locally

model update ∆m: least-squares solution of

F∆m = ∆d

with ∆d : data misfitF : Fréchet derivatives

calculation of Fréchet derivatives:ray perturbation theory

regularization ⇒ F̂∆m = ∆d̂(minimization of second derivatives of velocity)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 19: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TA synthetic data example

Original velocity model

-1500 500 2500 4500 6500x [m]

-3000

-2000

-1000

0

z [m

]

2000

3000

4000

5000

m/s

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 20: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TSynthetic data example

0

1

2

t [s]

0 2 4 6x [km]

0

1

2

t [s]

0 2 4 6x [km]

0

5

10

Rni

p [k

m]

0

1

2

t [s]

0 2 4 6x [km]

-20

0

20

angl

e [°

]

CRS stack RNIP section α section

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 21: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TSynthetic data example

Picked input data for the inversion

−2000 0 2000 4000 6000 8000

0

200

400

600

800

1000

1200

1400

Xo [m]

T [1

0−3

s]

−2000 0 2000 4000 6000 80000

200

400

600

800

1000

1200

1400

1600

1800

Xo [m]

M [1

0−9

s/m

2 ]

−2000 0 2000 4000 6000 8000−30

−20

−10

0

10

20

30

Xo [m]

alph

a [

o ]

T M α

Model parametrization:B-spline knot spacing ∆x = 500 m, ∆z = 300 m

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 22: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TSynthetic data example

Residual data error after 12 iterations

−2000 0 2000 4000 6000 8000−6

−4

−2

0

2

4

6

Xo [m]

Del

ta T

[10

−3 s

]

6

4

2

0

−2

−4−6

−2000 0 2000 4000 6000 8000−8

−6

−4

−2

0

2

4

6

8

10

Xo [m]

Del

ta M

[10

−9 s

/m2 ]

8

4

0

−4

−8−2000 0 2000 4000 6000 8000

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

Xo [m]

Del

ta a

lpha

[ o ]

0.02

0.01

0

−0.01

−0.02

∆T [10−3s] ∆M [10−9 s/m2] ∆α [◦]

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 23: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TSynthetic data example

Inversion result

-1500 500 2500 4500 6500x [m]

-3000

-2000

-1000

0

z [m

]

2000

3000

4000

5000

m/s

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 24: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TSynthetic data example

Inversion result

-1500 500 2500 4500 6500x [m]

-3000

-2000

-1000

0

z [m

]

2000

3000

4000

5000

m/s

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 25: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReconstructed vs. original model

Reconstructed velocity and reflector elements

-1500 500 2500 4500 6500x [m]

-3000

-2000

-1000

0

z [m

]

2000

3000

4000

5000

m/s

Original velocity and reconstructed reflector elements

-1500 500 2500 4500 6500x [m]

-3000

-2000

-1000

0

z [m

]

2000

3000

4000

5000

m/s

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 26: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TPrestack migration results

1

2

3

z [k

m]

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0CIG location [km]

common-image gatherscommon-image gathers (maximum offset=2000m)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 27: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIncluding additional constraints

. . . important in the case of data gaps!

v(x,z) values at arbitrary locations (x,z)

spatially dependent regularization(smoothness of velocity model)

force velocity structure to follow local reflectorstructure

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 28: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIncluding additional constraints

. . . important in the case of data gaps!

v(x,z) values at arbitrary locations (x,z)

spatially dependent regularization(smoothness of velocity model)

force velocity structure to follow local reflectorstructure

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 29: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TIncluding additional constraints

. . . important in the case of data gaps!

v(x,z) values at arbitrary locations (x,z)

spatially dependent regularization(smoothness of velocity model)

force velocity structure to follow local reflectorstructure

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 30: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

0

1

2

3

t [s]

0 1 2 3 4 5 6x [km]

CRS stack

0

1

2

3t [

s]

0 1 2 3 4 5 6x [km]

coherence

0

0.1

0.2

0.3

0.4

0.5

CRS stack section coherence section(semblance)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 31: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

0

1

2

3

t [s]

0 1 2 3 4 5 6x [km]

Rnip

0

2

4

6

8

10

0

1

2

3t [

s]

0 1 2 3 4 5 6x [km]

angle

-40

-20

0

20

40

RNIP section [km] angle section [◦]

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 32: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

Picked input data for the inversion

0 1000 2000 3000 4000 5000 6000

0

200

400

600

800

1000

1200

1400

x [m]

T [

10−3

s]

0 1000 2000 3000 4000 5000 60000

200

400

600

800

1000

1200

1400

1600

1800

x [m]

M [

10−9

s/m

2 ]

0 1000 2000 3000 4000 5000 6000−20

−15

−10

−5

0

5

x [m]

angl

e [

o ]

T M α

Model parametrization:B-spline knot spacing ∆x = 500 m, ∆z = 300 m

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 33: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

Residual data error after 12 iterations

0 1000 2000 3000 4000 5000 6000−20

−15

−10

−5

0

5

10

15

x [m]

Del

ta T

[10

−3 s

]

0

10

−10

0 1000 2000 3000 4000 5000 6000−80

−60

−40

−20

0

20

40

60

x [m]

Del

ta M

[10

−9 s

/m2 ]

0

−40

40

0 1000 2000 3000 4000 5000 6000−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

x [m]

Del

ta a

ngle

[ o ]

0

−0.1

0.1

∆T [10−3s] ∆M [10−9 s/m2] ∆α [◦]

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 34: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

Inversion result0

1000

2000

3000

4000

5000

z [m

]0 1000 2000 3000 4000 5000 6000

x [m]

inversion result

2000

3000

4000

5000

velo

city

[m/s

]

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 35: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TReal data example

Inversion result0

1000

2000

3000

4000

5000

z [m

]0 1000 2000 3000 4000 5000 6000

x [m]

inversion result

2000

3000

4000

5000

velo

city

[m/s

]

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 36: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TPoststack migration

0

1000

2000

3000

4000

5000

z [m

]

0 1000 2000 3000 4000 5000 6000x [m]

inversion result

2000

3000

4000

5000

velo

city

[m/s

]

1

2

3

4

5

z [k

m]

0 1 2 3 4 5 6x [km]

CRS poststack migration

Reconstructed velocity Poststack migrationmodel and dip bars of CRS stack result

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 37: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TPrestack migration results

1

2

3

4

5

z [k

m]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0CIG location [km]

common-image gatherscommon-image gathers (maximum offset=2000m)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 38: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D CRS attributes

t2 (∆ξξξ ,h) =(

t0 + 2pξ ·∆ξξξ)2

+2t0

(∆ξξξ T Mξ ∆ξξξ + hT Mh h

)

pξ = 12∂ t/∂ξξξ = 1

v0(sinα cosψ ,sinα sinψ)T

Mh = 12∂ 2t/∂h2 = 1

v0DKNIPDT

Mξ = 12∂ 2t/∂ξξξ 2 = 1

v0DKNDT

Independent of near-surface velocity v0 !8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 39: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D CRS attributes

t2 (∆ξξξ ,h) =(

t0 + 2pξ ·∆ξξξ)2

+2t0

(∆ξξξ T Mξ ∆ξξξ + hT Mh h

)

For a tomographic inversion, only

one azimuth φ of Mh is required: Mφ !

⇒ Data: (T ,Mφ , pξx, pξy

,ξx,ξy)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 40: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D inversion with CRS attributes

Data and model components

(ξ ,ξ )

x

x y

y

yx φ

(x,y,z)

(e ,e )

M(p ,p )T

v(x,y,z)

Data:(T , Mφ , pξx

, pξy, ξx, ξy)i

Model:(x, y, z, ex, ey)i, v jkl

T = t0/2

v jkl: B-spline coefficients

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 41: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D inversion with CRS attributes

Data and model components

(ξ ,ξ )

x

x y

y

yx φ

(x,y,z)

(e ,e )

M(p ,p )T

v(x,y,z)

Data:(T , Mφ , pξx

, pξy, ξx, ξy)i

Model:(x, y, z, ex, ey)i, v jkl

T = t0/2

v jkl: B-spline coefficients

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 42: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D synthetic example

Cut through original and reconstructed 3D models

Model

v [k

m/s

]

5

43

2

34

5

x [km]

01

y [km]2

16

1.5

4.3

original model

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 43: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D synthetic example

Cut through original and reconstructed 3D models

Inversion result

v [k

m/s

]

5

43

2

34

5

x [km]

01

y [km]2

16

1.5

4.3

inversion result

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 44: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D synthetic example

Depth slice at z=1500 m

Model

0

1

2

3

4

5

1 2 3 4 5 6y [km]

4.3

z = 1500 m

x [km]

v [k

m/s

]

1.5

original model8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 45: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T3D synthetic example

Depth slice at z=1500 m

Inversion result

0

1

2

3

4

5

1 2 3 4 5 6y [km]

4.3

x [km]

v [k

m/s

]

z = 1500 m

1.5

inversion result8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 46: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 47: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 48: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 49: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 50: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 51: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 52: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 53: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAdvantages/Limitations

Input is a by-product of CRS stack

Very few picks are required

Picking in ZO section of increased S/N ratio

No assumptions about reflector continuity

Smooth model (ideal for ray-tracing)

Smooth velocity description must be valid

Limited lateral variation within CRS aperture(approximately hyperbolic traveltimes)

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 54: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TConclusions

CRS stack yields information useful fordetermination of smooth velocity modelsfor depth imaging

Tomographic inversion method based onCRS attributes

Implementation in 2D and 3D

Applied to 2D real data

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 55: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TConclusions

CRS stack yields information useful fordetermination of smooth velocity modelsfor depth imaging

Tomographic inversion method based onCRS attributes

Implementation in 2D and 3D

Applied to 2D real data

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 56: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TConclusions

CRS stack yields information useful fordetermination of smooth velocity modelsfor depth imaging

Tomographic inversion method based onCRS attributes

Implementation in 2D and 3D

Applied to 2D real data

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 57: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TConclusions

CRS stack yields information useful fordetermination of smooth velocity modelsfor depth imaging

Tomographic inversion method based onCRS attributes

Implementation in 2D and 3D

Applied to 2D real data

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 58: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I TAcknowledgment

This work has been supported by the sponsors of theWave Inversion Technology (WIT) consortium.

W I T

8th Int. Congress, Brasilian Geophysical Society, Rio 2003

Page 59: Tomographic velocity model estimation with data-derived ... · Tomographic velocity model estimation with data-derived first and second spatial traveltime derivatives Eric Duveneck,

W I T

8th Int. Congress, Brasilian Geophysical Society, Rio 2003


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