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Wave-equation common-angle gathers for converted waves

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Wave-equation common-angle gathers for converted waves Paul Sava & Sergey Fomel Bureau of Economic Geology University of Texas at Austin Imaging sketch Wavefield ... – PowerPoint PPT presentation

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Date added: 2 October 2019
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Title: Wave-equation common-angle gathers for converted waves


1
Wave-equation common-angle gathers for converted
waves
  • Paul Sava Sergey Fomel
  • Bureau of Economic Geology
  • University of Texas at Austin

2
Imaging sketch
R
S
3
Wavefield reconstruction
R
S
Source wavefield
Receiver wavefield
4
Imaging condition
Claerbout (1985)
Location mx,y,z
Space shift hhx,hy,hz
Rickett Sava (2002) Biondi Symes (2004) Sava
Fomel (2005)
5
Angle decomposition
Message images obtained by space-shift imaging
contain sufficient information for converted-wave
angle decomposition!
Location mx,y,z
Space shift hhx,hy,hz
Azimuth angle
Reflection angle
6
Angle decomposition
7
PP reflection geometry
ps
pr
8
PS reflection geometry
9
PS reflection geometry
10
PS reflection geometry
3 relations, can eliminate 2 variables
11
PS transformation
3 relations, can eliminate 2 variables.
Example eliminate w and .
Sava Fomel (2005)
12
PS transformation (2D)
3 relations, can eliminate 2 variables.
Example eliminate w and .
Weglein Stolt (1985) Sava Fomel (2003)
13
Angle decomposition algorithm
14
Example 1
distance
0
depth
15
vP2 km/s vS1 km/s
30
45
15
PP data
PS data
surface offset
surface offset
0
time
time
15
30
45
16
PP image
distance
0
depth
15
30
45
17
PS image
distance
0
depth
15
30
45
18
PP offset-gather
PS offset-gather
space-shift
space-shift
depth
depth
19
PP angle-gather
PS angle-gather
tan(q0)
tan(q0)
depth
depth
0
15
30
45
0
15
30
45
PP transformation
20
PP angle-gather
PS angle-gather
tan(q0)
tan(q)
depth
depth
0
15
30
45
0
15
30
45
PS transformation
21
Example 2
distance
Modified from Baina et al. (2005)
  • acquisition
  • shots 51 at 0.2km
  • receivers 401 at 0.025km

depth
22
PP data
PS data
surface offset
surface offset
time
time
23
PP image
PS image
distance
distance
Uneven amplitude
depth
depth
24
PP offset-gathers
PS offset-gathers
space-shift
space-shift
depth
depth
25
PP angle-gathers
PS angle-gathers
angle
angle
depth
depth
26
PP angle-gather
PS angle-gather
angle
angle
depth
depth
PP transformation
27
PP angle-gather
PS angle-gather
angle
angle
depth
depth
PS transformation
28
PP angle-gathers
PS angle-gathers
angle
angle
depth
depth
Normal polarity
29
PP angle-gathers
PS angle-gathers
angle
angle
depth
depth
Reversed polarity
30
PP stack
PS stack
distance
distance
depth
depth
31
Conclusions
  • Angle decomposition for converted-waves
  • Space-shift imaging condition
  • Independent of extrapolation method
  • Contains all required information
  • Real challenge what are the velocity models?
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