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3D dipole borehole-source wavefieldsimulation
Junxiao Li, Kris Innanen, Laurence R. Lines
Kuo Zhang, and Guo Tao
Dec 3rd 2015
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Outline
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• 1 Introduction
• 2 3D staggered grid finite difference method
• 3 The hybrid perfectly matched layer
• 4 Numerical simulation for dipole source
• 5 Discussion
• 6 Conclusions
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Introduction
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• Great potential has been reviewed for acoustic reflection imaging logging todetect unconventional subtle reservoirs like fractures and vugs.
• Dipole source is capable of unveiling azimuth and dip information of structuresoutside borehole.
• 3D staggered-grid finite difference method with hybrid perfectly matched layerabsorbing scheme.
• Based on the convolutional model of received waveforms, the relationshipsbetween the reflection amplitude and the offset as well as the relationshipsbetween the reflection reception response and the azimuth angle areanalyzed.
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Staggered-grid finite difference
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xyxx xz x
yx yy yz y
zyzx zz z
V
x y z t
V
x y z t
V
x y z t
11 11 66 13
11 66 11 13
13 13 33
44
44
66
( 2 )
( 2 )
yxx x z
yy yx z
yxzz z
yz y z
xz x z
xy yx
VV Vc c c c
t x y z
VV Vc c c c
t x y z
VV Vc c c
t x y z
V Vc
t z y
V Vc
t z x
VVc
t y x
1
0
1 1, , ( 1, , ) ( , , )
2
Nn n n
x xx x y z m xx x y z xx x y z
m
l l l a l m l l l m l lx
yz
zV
iixV
xy
xz
yV
x
y
z
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The perfectly matched layer (PML) (Bérenger, 1994)
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Take x direction as an example
xxi k X t k
s Ae
xx xi
Drawbacks: 1. Requires the use of split fields2. Its efficiency becomes poor at grazing incidence
after discretization.
The convolutional-PML(C-PML) (Kuzuoglu and Mittra, 1996 )
xx x
x
ds
i
Drawbacks: Suffers instability either because of its frequency-dependent term or the convolution operations
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C-PML
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M-PML
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i
dmdmds
zyx
x
1
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H-PML
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x y z
x x
x
d m d m ds
i
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Snapshots in isotropic media
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Borehole wave field reception
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Dip
ole
Rec
eive
rs
Ref
lect
or
X
Z
Y
Unit: m
Borehole
5
5
6
dx=0.01m, dt=1us, f0=3k
(Meredith, 1990)
(Peng et al., 1993)
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Received reflections when azimuth is 0 and 90 degrees
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Received reflections when azimuth is 30 and 60 degrees
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0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Reflected waves received by R1 with an offset of 1.5 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Reflected waves received by R1 with an offset of 2.25 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Reflected waves received by R1 with an offset of 3.0 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Reflected waves received by R1 with an offset of 3.75 m
SH
SV
(c)
(a) (b)
(d)
S-SP-P
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0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Full waveforms received by R2 with an offset of 1.5 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Full waveforms received by R2 with an offset of 2.25 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Full waveforms received by R2 with an offset of 3.0 m
0 2000 4000 6000 8000 100000
2
4
6
8
Time(us)
Full waveforms received by R2 with an offset of 3.75 m
SH
SV
(c)
(a) (b)
(d)
S-SP-P
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Simulation for a dipole in VTI media
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dx=0.01m, dt=1us, f0=3k
Receiver spacing: 0.16 m
Offset of receivers: 1 to 5.64 m
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Conclusions
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• A hybrid PML based on the C-PML and M-PML is proposed and used in 3D staggered-grid FD method.
• The wavefield simulation for a directional dipole source in isotropic media isanalyzed. And a transition is detected between the SH-SH reflection and SV-SVreflection with the increase of the offset. Based on the cross-plot of maximumamplitude versus receiver offsets, both the distance between the borehole and thereflector and the critical angle can be calculated.
• For a further discussion, the wavefield simulation for a directional dipole source inVTI media is discussed. The SH-SH reflection coefficient in the VTI medium isintroduced and used to calculate the relationship between the incident angle andreflected amplitude.
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Discussion and future work
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SH-SH reflection imaging Coordinate Stretching scheme
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Acknowledgement
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• CREWES sponsors
• CREWES staff and students
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Questions & Comments