3D dipole borehole-source wavefieldsimulation
Junxiao Li, Kris Innanen, Laurence R. Lines
Kuo Zhang, and Guo Tao
Dec 3rd 2015
www.crewes.org
Outline
www.crewes.org
• 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
Introduction
www.crewes.org
• 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.
Staggered-grid finite difference
www.crewes.org
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
The perfectly matched layer (PML) (Bérenger, 1994)
www.crewes.org
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
C-PML
www.crewes.org
M-PML
www.crewes.org
i
dmdmds
zyx
x
1
H-PML
www.crewes.org
x y z
x x
x
d m d m ds
i
Snapshots in isotropic media
www.crewes.org
Borehole wave field reception
www.crewes.org
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)
Received reflections when azimuth is 0 and 90 degrees
www.crewes.org
Received reflections when azimuth is 30 and 60 degrees
www.crewes.org
www.crewes.org
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
www.crewes.org
www.crewes.org
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
www.crewes.org
www.crewes.org
Simulation for a dipole in VTI media
www.crewes.org
dx=0.01m, dt=1us, f0=3k
Receiver spacing: 0.16 m
Offset of receivers: 1 to 5.64 m
www.crewes.org
www.crewes.org
www.crewes.org
Conclusions
www.crewes.org
• 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.
Discussion and future work
www.crewes.org
SH-SH reflection imaging Coordinate Stretching scheme
Acknowledgement
www.crewes.org
• CREWES sponsors
• CREWES staff and students
www.crewes.org
Questions & Comments
Top Related