Fresnel-zone Traveltime Tomo. for Fresnel-zone Traveltime Tomo. for INCO and Mapleton Data INCO and Mapleton Data

Jianming Sheng Jianming Sheng

University of UtahUniversity of Utah

Feb. 5, 2004Feb. 5, 2004

MotivationMotivationRay-based Traveltime Tomo.Ray-based Traveltime Tomo.

Biased towards high-velocitiesBiased towards high-velocities

High-frequency assumptionHigh-frequency assumption

Ray DistributionRay Distribution00

454500 8080

Dep

th (

m)

Dep

th (

m)

Distances (m)Distances (m)

80008000

40004000

00

60006000

20002000

MotivationMotivationRay-based Traveltime Tomo.Ray-based Traveltime Tomo.

Biased towards high-velocitiesBiased towards high-velocities

High-frequency assumptionHigh-frequency assumption

Solution 1: Wavepath traveltime tomo.Solution 1: Wavepath traveltime tomo.Bandlimited, unbiased, multipathBandlimited, unbiased, multipath

Wave-equationWave-equation

Solution 2: Fresnel-zone traveltime tomo.Solution 2: Fresnel-zone traveltime tomo.Paraxial ray approximationParaxial ray approximation

Wavepath or Fresnel-zoneWavepath or Fresnel-zone

ss

gg

Fresnel ZoneFresnel Zone

2

TTTT sgxgsx xx

First-break and first-peak Tomo. First-break and first-peak Tomo.

OutlineOutline

Mapleton DataMapleton Data

SummarySummary

INCO Synthetic Data INCO Synthetic Data

PrinciplePrinciple

ss

gg

First-break: high velocityFirst-break: high velocity

First-peak: diffraction stackingFirst-peak: diffraction stacking

• First-arrivals result from First-arrivals result from diffraction stackingdiffraction stacking

Misfit FunctionMisfit Function

22 calbreak

obsbreak

calpeak

obspeak ttWttme

{{ {{

First-peakFirst-peak First-breakFirst-break

Fresnel-zone TraveltimeFresnel-zone Traveltime

Vasco et al. (1995)Vasco et al. (1995)

ddc

11

ss

gg

My Quick andMy Quick and dirty way:dirty way: sgsxgsxgshiftsxg ttwAtt

N 1

ttshiftshift

W(t)W(t) xgsx

sg

rr

r

Sensitivity Function (first-peak)Sensitivity Function (first-peak)Rytov Approx. (Woodward, 1992)Rytov Approx. (Woodward, 1992)

dxttAcc sgsxgsxg sin1

Im 2

Phase Phase residualresidual

SlownessSlowness GeometricalGeometricalspreadingspreading

Im

t

sgsxgsxg ttAc

c

t

sin1

1ss

gg

xxttsgsg

ttsxgsxg

xgsx

sg

rr

r

Backprojecting First-break Res.Backprojecting First-break Res.

454500 8080

Dep

th (

m)

Dep

th (

m)

Distances (m)Distances (m)

40004000

00

60006000

20002000

0000

4545

Dep

th (

m)

Dep

th (

m)

25002500

500500

m/sm/s00 8080 00 8080

00

4545

Dep

th (

m)

Dep

th (

m)

25002500

500500

m/sm/s00 8080 00 8080

ss

gg

Smoothing along Smoothing along a fat-raya fat-ray

First-break and first-peak Tomo. First-break and first-peak Tomo.

OutlineOutline

Mapleton DataMapleton Data

SummarySummary

INCO Synthetic Data INCO Synthetic Data

INCO Synthetic ModelINCO Synthetic Model00

8080

Dep

th (

m)

Dep

th (

m)

X (m)X (m)

45004500

35003500

25002500

15001500

m/sm/s00 590590

INCO Synthetic DataINCO Synthetic Data00

0.150.15

Tim

e (s

ec.)

Tim

e (s

ec.)

296 shots (2m)296 shots (2m)591 rec. (1m)591 rec. (1m)

Dt: 0.05 msDt: 0.05 msLength: 0.3sLength: 0.3s

200200 400400X (m)X (m)

Freq.: 90HzFreq.: 90Hz

Zhiyong JiangZhiyong Jiang

INCO Synthetic ModelINCO Synthetic Model00

8080

Dep

th (

m)

Dep

th (

m)

X (m)X (m)

45004500

35003500

25002500

15001500

m/sm/s00 590590

V=900 m/sV=900 m/sL=10 mL=10 m

L=16.7 mL=16.7 mV=1500 m/sV=1500 m/s

V=2500 m/sV=2500 m/sL=28 mL=28 m

V=4500 m/sV=4500 m/sL=50 mL=50 m

Ray-based TomogramRay-based Tomogram00

8080

Dep

th (

m)

Dep

th (

m)

X (m)X (m)

45004500

35003500

25002500

15001500

m/sm/s00 590590

INCO Synthetic ModelINCO Synthetic Model00

8080

Dep

th (

m)

Dep

th (

m)

X (m)X (m)

45004500

35003500

25002500

15001500

m/sm/s00 590590

10 m10 m

16.7 m16.7 m

28 m28 m

50 m50 m

Fat-Ray TomogramFat-Ray Tomogram00

8080

Dep

th (

m)

Dep

th (

m)

X (m)X (m)

45004500

35003500

25002500

15001500

m/sm/s00 590590

First-break and first-peak Tomo. First-break and first-peak Tomo.

OutlineOutline

Mapleton DataMapleton Data

SummarySummary

INCO Synthetic Data INCO Synthetic Data

Mapleton, Utah DataMapleton, Utah Data

00

0.150.15

Tim

e (s

ec.)

Tim

e (s

ec.)

2020 160160

168 shots168 shots168 receiver168 receiver

Interval: 5mInterval: 5m

dt: 0.5 msdt: 0.5 mslength: 1slength: 1s

First-break Fat-ray Tomo.First-break Fat-ray Tomo.00

4545

Dep

th (

m)

Dep

th (

m)

25002500

500500

m/sm/s00 8080Distances (m)Distances (m)

First-break + First-peak First-break + First-peak

00

4545

Dep

th (

m)

Dep

th (

m)

25002500

500500

m/sm/s00 8080Distances (m)Distances (m)

Migration ImageMigration Image00

4545

Dep

th (

m)

Dep

th (

m)

300300

00 8080Distances (m)Distances (m)

200200

100100

00

100100

-200-200

First-break and first-peak Tomo. First-break and first-peak Tomo.

OutlineOutline

Mapleton DataMapleton Data

SummarySummary

INCO Synthetic Data INCO Synthetic Data

SummarySummary

• A first-break and first-peak tomo. is designed. A first-break and first-peak tomo. is designed.

• Mapleton Data:Mapleton Data:

• INCO Synthetic data:INCO Synthetic data:

Fat-ray tomo. provides a better tomogramFat-ray tomo. provides a better tomogram

This method can image complex models;This method can image complex models;

More tests are necessary. More tests are necessary.

AcknowledgmentAcknowledgment

I thank the sponsors of the 2003 UTAM I thank the sponsors of the 2003 UTAM Consortium for their financial support . Consortium for their financial support .