First Arrival Traveltime and Waveform Inversion of Refraction Data

$Page 1: First Arrival Traveltime and Waveform Inversion of Refraction Data$
First Arrival Traveltime and First Arrival Traveltime and Waveform Inversion of Waveform Inversion of

Refraction DataRefraction Data

Jianming Sheng and Gerard T. SchusterJianming Sheng and Gerard T. Schuster

University of UtahUniversity of UtahOctober, 2002October, 2002

OutlineOutline• MotivationMotivation• First arrival traveltime and waveform First arrival traveltime and waveform

inversioninversion• Numerical examplesNumerical examples• SummarySummary

MotivationMotivationTraveltime and waveform Traveltime and waveform of CDP refraction dataof CDP refraction data

Given:Given:

Goal:Goal: High resolution tomogram High resolution tomogram

Problem:Problem: Can waveform tomography Can waveform tomography provide better resolution than provide better resolution than

ray-based tomography?ray-based tomography?

Ray-based Tomography vs. Ray-based Tomography vs. Full Waveform InversionFull Waveform Inversion

Ray-based Ray-based tomographytomography

Efficient and robustEfficient and robust Resolution limited by Resolution limited by high-freq. assumptionhigh-freq. assumption

Full Full waveform waveform tomographytomography

No high-freq. limitationNo high-freq. limitation Slow convergence andSlow convergence andlocal minima problemlocal minima problem

First-arrival Traveltime andFirst-arrival Traveltime andWaveform InversionWaveform Inversion

Ray-basedRay-basedtraveltime traveltime tomographytomography

Efficient and robustEfficient and robust

First-arrival First-arrival waveform waveform inversioninversion

No high-freq. limitationNo high-freq. limitation

Better convergence andBetter convergence andmild nonlinearmild nonlinear

Initial modelInitial model



First Arrival Traveltime and First Arrival Traveltime and Waveform InversionWaveform Inversion

• Step 1:Step 1: Preprocessing the raw data: Preprocessing the raw data: band-pass, 3D to 2D band-pass, 3D to 2D transform, trace normalizationtransform, trace normalization

• Step 2:Step 2: Picking first-arrival Picking first-arrival traveltimes and muting out traveltimes and muting out other waves except first other waves except first arrivalsarrivals

• Step 3:Step 3:

First arrival traveltime First arrival traveltime tomography tomography

Minimizes traveltime residualMinimizes traveltime residual

Initial modelInitial model

2 preobs

• Step 4:Step 4: First arrival First arrival waveform inversionwaveform inversion

ObservedObservedPredictedPredicted

, , 2,

obs pres g s g

s g

D DMisfit Misfit functionfunction

Multigrid TomographyMultigrid Tomography• Traveltime tomography:Traveltime tomography:

Dynamic smoothing schemeDynamic smoothing scheme(to attack local minima problem)(to attack local minima problem)

(Nemeth, T., Normark, E. and Qin, F., 1992)(Nemeth, T., Normark, E. and Qin, F., 1992)



Numerical ExamplesNumerical Examples

• Synthetic data I: Three-layerSynthetic data I: Three-layer

• Synthetic data II: WesternGeco (Blind Synthetic data II: WesternGeco (Blind

test)test)

• Redmond mine survey dataRedmond mine survey data

Synthetic Model ISynthetic Model I00

2020

4040

6060

Dep

th (m

)D

epth

(m)

00 200200100100Distance (m)Distance (m)

25002500

19581958

14161416

873873

331331(m/s)(m/s)

Source Freq. 60 HzSource Freq. 60 HzAvg. Velocity 2400 m/sAvg. Velocity 2400 m/s

Source Wavelength 40 mSource Wavelength 40 m

Suggested by Suggested by Konstantin OsypovKonstantin Osypov

00

2020

4040

6060

Dep

th (m

)D

epth

(m)


25002500

19581958

14161416

873873

331331(m/s)(m/s)

40 m40 m

Synthetic Model ISynthetic Model I

Synthetic Data ISynthetic Data I• Synthetic data set was calculated Synthetic data set was calculated

by 2-D FD acoustic wave equation by 2-D FD acoustic wave equation solversolver

• Twenty-one shots and 51 traces Twenty-one shots and 51 traces per shot were used. per shot were used. • Computational grid dimension was Computational grid dimension was 401*121.401*121.

Synthetic Shot Gather Synthetic Shot Gather 0.00.0

0.10.1

Tim

e (s

ec.)

Tim

e (s

ec.)

-80-80 120120Offset (m)Offset (m)

Air WaveAir Wave

Traveltime TomogramTraveltime Tomogram 00

2020

4040

6060

Dep

th (m

)D

epth

(m)


25002500

19581958

14161416

873873

331331(m/s)(m/s)


2020

4040

6060

Dep

th (m

)D

epth

(m)


25002500

19581958

14161416

873873

331331(m/s)(m/s)

Traveltime ResidualTraveltime Residual

11 3030IterationsIterations

2.02.0

1.01.0

0.00.0

Tra

vel ti

me

Res

idu a

l (s e

c .)

Tra

vel ti

me

Res

idua

l (s e

c .)

Waveform TomogramWaveform Tomogram00

2020

4040

6060

Dep

th (m

)D

epth

(m)


25002500

19581958

14161416

873873

331331(m/s)(m/s)


2020

4040

6060

Dep

th (m

)D

epth

(m)


25002500

19581958

14161416

873873

331331(m/s)(m/s)

Waveform ResidualWaveform Residual


12,00012,000

00

8,0008,000

4,0004,000

Wa v

e for

m R

esid

u al

Wa v

e for

m R

esid

ual




test)test)


True Velocity ModelTrue Velocity Model

0.00.0

1.01.0

Dep

th (k

m)

Dep

th (k

m)

0.00.0 2626Horizontal distance (km)Horizontal distance (km)

1000 m/s1000 m/s

2050~2500 m/s2050~2500 m/s

True Density ModelTrue Density Model0.00.0 2626Horizontal distance (km)Horizontal distance (km)

0.00.0

1.01.0

Dep

th (k

m)

Dep

th (k

m)

Recorded CSG # 150Recorded CSG # 150-3000-3000 30003000Offset (m)Offset (m)

0.00.0

2.02.0

Tim

e (s

ec.)

Tim

e (s

ec.)

Guessed Density ModelGuessed Density Model

10001000 50005000Velocity (m/s)Velocity (m/s)

34003400

14001400

Den

sity

(kg/

mD

ensi

ty (k

g/m

33 ))

0.5

21001981.2v

Source WaveletSource Wavelet400400

Am

plitu

deA

mpl

itude 00

-600-6000.00.0 0.250.25Time (sec.)Time (sec.)

Waveform MatchingWaveform MatchingA

mpl

itude

Am

plitu

de

0.00.0 0.20.2Time (sec.)Time (sec.)

OffsetOffset(m)(m)-50-50

2525

5050

00

-25-25

Traveltime TomogramTraveltime Tomogram

27122712

22842284

18561856

14281428

10001000

m/sm/s0.00.0 2626Horizontal distance (km)Horizontal distance (km)0.00.0

1.01.0

Dep

th (k

m)

Dep

th (k

m)

Traveltime TomogramTraveltime Tomogram

24092409

20572057

17051705

13521352

10001000

m/sm/s5.05.0 8.758.75Horizontal distance (km)Horizontal distance (km)0.00.0

0.40.4

Dep

th (k

m)

Dep

th (k

m)

0.10.1

0.20.2

0.30.3

Waveform TomogramWaveform Tomogram

27002700

22752275

18501850

14251425

10001000

m/sm/s5.05.0 8.758.75Horizontal distance (km)Horizontal distance (km)0.00.0

0.40.4

Dep

th (k

m)

Dep

th (k

m)

0.10.1

0.20.2

0.30.3

Migration sectionMigration section5.05.0 8.758.75Horizontal distance (km)Horizontal distance (km)

0.00.0

0.40.4

Dep

th (k

m)

Dep

th (k

m)

0.10.1

0.20.2

0.30.3

Predicted CSG #150Predicted CSG #150

0.00.0

2.02.0

Tim

e (s

ec.)

Tim

e (s

ec.)

-3000-3000 30003000Offset (m)Offset (m)

Recorded CSG # 150Recorded CSG # 150-3000-3000 30003000Offset (m)Offset (m)

0.00.0

2.02.0

Tim

e (s

ec.)

Tim

e (s

ec.)




test)test)



Salt Diapir DataSalt Diapir Data • Thirty-one shots and 120 traces Thirty-one shots and 120 traces total 3188 traveltimes picked. total 3188 traveltimes picked. Shot interval: 20 m Shot interval: 20 m geophone interval 5 mgeophone interval 5 m

• Source frequency 40 Hz. Source frequency 40 Hz.

• Record length 1 sec. Record length 1 sec. sample interval 0.5 millisecond . sample interval 0.5 millisecond .

CSG for Field Data CSG for Field Data After PreprocessingAfter Preprocessing

11 120120Geophone #Geophone #

00

0.20.2

Tim

e (s

ec.)

Tim

e (s

ec.)

CSG for Field Data CSG for Field Data After MutingAfter Muting


00

0.20.2

Tim

e (s

ec.)

Tim

e (s

ec.)

Wavelet ExtractedWavelet Extracted00

0.10.1

Tim

e (s

ec.)

Tim

e (s

ec.)

Traveltime TomogramTraveltime Tomogram00

130130

Dep

th (m

)D

epth

( m)


55005500

45004500

35003500

25002500

15001500

500500

(m/s)(m/s)

TunnelTunnel

20 m20 m

55 m55 m

SALTSALT

Traveltime ResidualTraveltime Residual


2.02.0

1.01.0

0.00.0

Tra

vel ti

me

Res

idu a

l (s e

c .)

Tra

vel ti

me

Res

idua

l (s e

c .)

00

130130

Dep

th (m

)D

ept h

(m)

Waveform TomogramWaveform Tomogram


55005500

45004500

35003500

25002500

15001500

500500

(m/s)(m/s)

TunnelTunnel55 m55 m

20 m20 m

SALTSALT

Traveltime TomogramTraveltime Tomogram00

130130

Dep

th (m

)D

epth

( m)


55005500

45004500

35003500

25002500

15001500

500500

(m/s)(m/s)

TunnelTunnel

20 m20 m

55 m55 m

SALTSALT

Waveform ResidualWaveform Residual


6,0006,000

00

4,0004,000

2,0002,000

Wa v

e for

m R

esid

u al

Wa v

e for

m R

esid

ual

Predicted CSGPredicted CSG


00

0.20.2

Tim

e (s

ec.)

Tim

e (s

ec.)

CSG for Salt Data CSG for Salt Data After MutingAfter Muting


00

0.20.2

Tim

e (s

ec.)

Tim

e (s

ec.)

22

Log

10 A

mpl

itude

Log

10 A

mpl

itude

00

-2-2

-4-400 400400Offset (m)Offset (m)

Logarithmic Amplitude Vs. OffsetLogarithmic Amplitude Vs. Offset

SyntheticSynthetic

ObservedObserved

ProblemsSeismic attenuationSeismic attenuation

Surface wave noiseSurface wave noise

Source wavelet inversion Source wavelet inversion & objective function & objective function



SummarySummary• Synthetic results show that the Synthetic results show that the

waveform tomogram is much more waveform tomogram is much more resolved;resolved;

• The preliminary results for the field data The preliminary results for the field data are not as good as expected, and further are not as good as expected, and further work is needed.work is needed.

AcknowledgmentAcknowledgmentI thank the sponsors of the 2002 University I thank the sponsors of the 2002 University of Utah Tomography and Modeling of Utah Tomography and Modeling /Migration (UTAM) Consortium for their /Migration (UTAM) Consortium for their financial support . I thank Konstantin financial support . I thank Konstantin Osypov for providing the data set.Osypov for providing the data set.

Documents

First Arrival Traveltime and Waveform Inversion of Refraction Data