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Reverse Time Migration of Prism Waves for Salt Flank Delineation. Wei Dai, WesternGeco Gerard T. Schuster, King Abdullah University of Science and Technology. Sep 25, 2013. Outline. Introduction and motivation Theory Numerical Results L model Salt model Summary. Introduction. - PowerPoint PPT Presentation
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Reverse Time Migration of Prism Waves for Salt Flank Delineation
Wei Dai, WesternGecoGerard T. Schuster, King Abdullah University
of Science and Technology
Sep 25, 2013
Outline• Introduction and motivation
• Theory
• Numerical Results
L model
Salt model
• Summary
Introduction• Problem: Vertical boundaries (salt flanks) are
difficult to image because they are usually not illuminated by primary reflections.
• Solution: Prism waves contain valuable information.
Conventional Method• When the known boundaries are embedded in
the velocity model, conventional RTM can migrate prism waves correctly.
Recorded Trace
Time (s) 20
Horizontal Reflector Embedded in the Velocity0
Z (k
m)
3
0 X (km) 6
0Z
(km
)3
Conventional RTM Image
Reverse Time Migration Formula
𝒎𝒎𝒊𝒈(𝒙)=∑𝝎𝝎𝟐𝑾 ∗(𝝎 )𝑮∗ (𝒙|𝒔 )𝑮∗ (𝒙|𝒈 )𝒅 (𝒈|𝒔 )
Angular Freq. Source SpectrumGreen’s functions
Input Data
0Z
(km
)3
𝒙
𝑮 (𝒙|𝒔 )=𝑮𝒐 (𝒙|𝒔 )+𝑮𝟏(𝒙∨𝒔)𝑮 (𝒙|𝒈 )=𝑮𝒐 (𝒙|𝒈 )+𝑮𝟏(𝒙∨𝒈 )
+ 𝑮𝒐∗ (𝒙|𝒔 )𝑮𝒐
∗ (𝒙|𝒈 ) 𝒅𝟐 (𝒈|𝒔 )
+ +
+ + + Other terms.]
0 X (km) 6
0Z
(km
)3
Ellipses
Rabbit Ears
Prism Wave Kernels
𝒎𝒎𝒊𝒈=∑𝝎𝝎𝟐𝑾 ∗ (𝝎 )𝑮𝟏
∗ (𝒙|𝒔 )𝑮𝒐∗ (𝒙|𝒈 )𝒅𝟐 (𝒈|𝒔 )
𝑮𝟏❑ (𝒙|𝒔 )=∫𝝎𝟐𝒎 (𝒙 ′)𝑮𝒐 (𝒙 ′|𝒔 )𝑮𝒐 ( 𝒙′|𝒙 )𝒅𝒙 ′
Born Modeling
0Z
(km
)3
0 X (km) 6
Migration of Prism Waves
Migration of Prism Waves0
Z (k
m)
30
Z (k
m)
3 0 X (km) 6
𝑥𝑠𝑥𝑔
𝑥1
𝑥2
|𝑥𝑠−𝑥2 ′|𝑐 +
|𝑥2−𝑥𝑔|𝑐 =𝜏𝑠𝑔
𝑥2❑ ′
𝒎𝒎𝒊𝒈=∑𝝎𝝎𝟐𝑾 ∗ (𝝎 )𝑮𝒐
∗ (𝒙|𝒔 ) 𝑮𝟏∗ (𝒙|𝒈 )𝒅𝟐 (𝒈|𝒔 )
𝑮𝟏❑ (𝒙|𝒈 )=∫𝝎𝟐𝒎 ( 𝒙′ )𝑮𝒐 (𝒙 ′|𝒔 )𝑮𝒐 (𝒙 ′|𝒙 )𝒅𝒙 ′
Born Modeling
0Z
(km
)3
0 X (km) 6
Migration of Prism Waves
Migration of Prism Waves0
Z (k
m)
30
Z (k
m)
3 0 X (km) 6
Outline• Introduction and motivation
• Theory
• Numerical Results
L model
Salt model
• Summary
0Z
(km
)3 0 X (km) 6
The L Model• Model size: 301 x 601 • Source freq: 20 hz• shots: 32 • geophones: 601
0Ti
me
(s)
6.4
0 X (km) 6
A Shot Gather of the L Model
0Z
(km
)3
0 X (km) 6
0Z
(km
)3
Prism Wavepath
0Z
(km
)3
0 X (km) 6
0Z
(km
)3
Migration Image of Prism Waves
RTM Image /w Smooth Velocity
The Salt Model
• Model size: 601 x 601
• Source freq: 20 hz
• shots: 601
• geophones: 601
0 X (km) 6
0Z
(km
)6
0Ti
me
(s)
10
0 X (km) 6
A Shot Gather of the Salt Model
0 X (km) 6
0Z
(km
)6
0 X (km) 6
Migration Velocity
RTM with Smooth VelocityRTM Image
RTM Image
0 X (km) 6
0Z
(km
)6
0 X (km) 6
Migration Velocity
If the Horizontal Reflectors are embedded in the velocity
0 X (km) 60 X (km) 6
0Z
(km
)6
Migration Velocity
New Method
RTM Image
0Z
(km
)6
Prism Wave ImageConv. RTM Image
0 X (km) 6
0Z
(km
)6
Migration Velocity
New Method
Filtered RTM Image
0Z
(km
)6 0 X (km) 6
Prism Wave Image
Final Image
0 X (km) 6
Final Image
0 X (km) 6
0Z
(km
)6
Horizontal
Vertical
0Z
(km
)6
RTM Image
Summary• I propose a new method to migrate prism waves
separately.
Limitations• Computational cost is doubled.
Avoid the modification of migration velocity.
Reduce cross interference between different waves by
migrating different waves in separated steps.
Thanks