Fresnel-zone Traveltime Fresnel-zone Traveltime Tomo. for INCO and Mapleton Tomo. for INCO and Mapleton Data Data Jianming Sheng Jianming Sheng University of Utah University of Utah Feb. 5, 2004 Feb. 5, 2004
Dec 21, 2015
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 .