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 .