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Multicomponent and source-free
converted-wave reverse-time
migration for VSP
Yue Du1, Yunyue Elita Li1, Jizhong Yang1, Arthur Cheng1, Xinding Fang2
Singapore Geophysics Project 1
1 Department of Civil & Environmental Engineering, National University of Singapore2 Department of Earth & Space Sciences, Southern University of Science and Technology, China
88th SEG Annual Meeting
17 October 2018
SOUTHERN UNIVERSITY OF SCIENCE AND TECHNOLOGY
Introduction: What is source-free?
Source Receivers
R(t)p
S(t)p
Reverse Time Migration (RTM)
Backward propagate
Receiver wavefieldI=0𝑇
*Forward propagate
source wavefield
Conventional PP image condition
2
R(t)s
Backward propagate
S Receiver wavefieldI=0𝑇
*Backward propagate
P Receiver wavefield
SFCW image condition
\PS
(Du et al., 2018)
(Li et al., 2018)
Outline
❖Theoretical basis• New set of elastic wave equations
• Elastic imaging using acoustic propagators
• SFCW image limitations
❖Numerical examples• Simple model
• A part of SEAM model
❖Conclusions and Discussions
3
Outline
❖Theoretical basis• New set of elastic wave equations
• Elastic imaging using acoustic propagators
• SFCW image limitations
❖Numerical examples• Simple model
• A part of SEAM model
❖Conclusions and Discussions
4
Seismology 101: mode conversion
Incident P Incident S
P SV P
SV P
solidsolid
SV
P
SV
P
SV
solidsolid
Are these mode conversion types unconditional?
✓New set of equations: clear mode conversion and its condition
5
New set of separated P- and S-wave equations
Source term
P-wave interacts with Vp boundary
P-wave interacts with Vs boundary
S-wave interacts with Vs boundary
P-wave propagation
6
(Li et al., 2018)
Source term
P-wave interacts with Vs boundary
S-wave propagation
S-wave interacts with Vs
boundary
New set of separated P- and S-wave equations
7
(Li et al., 2018)
Insights from the equations
✓ New set of equations: coupled but separated for P- and S-propagations in
heterogeneous (Lamé) media (constant density)
✓ Wave-medium interactions can be directly interpreted
✓ Mode-conversion only happens at S-wave discontinuities!
✓ Discontinuities only in Vp are transparent to S-wave
8
P P
P scatter
Elastic imaging using acoustic propagators
9
✓ Wave-equations reduce to fully decoupled P- and S-wave equations (acoustic wave
equations) for their potential fields
✓ They can be efficiently solved using acoustic propagators
✓ The elastic propagators can generate strong “in-situ” mode conversions when using
a rough S-velocity model.P
S scatter
SVSV
Velocity imprints by elastic propagators
10
Elastic Propagator Acoustic Propagator
? ? ?
Use a wrong
velocity model to
back propagate
SFCW Image
(Du et al., 2018)
Velocity imprints
SFCW Image Conventional PS Image
SFCW imaging limitations
11
2. Degraded resolution because of the narrow angle range between PP and PS-waves.
3. Strong artifacts due to the cross-talk of PP and PS-waves from different reflectors.
1. The SFCW image is a second-order approximation to the S-velocity perturbations.
Outline
❖Theoretical basis• New set of elastic wave equations
• Elastic imaging using acoustic propagators
• SFCW image limitations
❖Numerical examples• Simple model
• A part of SEAM model
❖Conclusions and Discussions
12
Simple Model
13
PP Image
Slow V
Avoid uncertain overburden structure
S(t)p
PS Image SFCW Image
R(t)s
R(t)p
A Part of SEAM Model
14
P velocity model PP Image
Image salt boundary without
salt model
Utilize full wavefields
Different illumination
A Part of SEAM Model
15
S velocity model PS Image
Higher resolution
less defined salt image
Different illumination
A Part of SEAM Model
16
S velocity model SFCW Image
Cannot image
far-offset
Near wellbore imaging
17
PP Image PS Image SFCW Image
18
PP Image PS Image SFCW Image
• The events in PP and PS images are pushed down by faster migration velocities.
• The overburden velocity error has stronger impact on the shallower layers.
Near wellbore imaging: fast overburden velocities
Conclusions and Discussions
• This work utilizes elastic imaging conditions with acoustic wave equations for VSP RTM to image complex structures.
➢Advantages of using acoustic propagators for elastic imaging
✓Lower memory and computational cost
✓Free of the artifacts caused by the unphysical wave mode conversion:
---Imprints of S-wave velocity model - “in-situ” mode conversions
➢Limitation: Need a clear P- and S-data separation in the recorded data
19
Conclusions and Discussions
• Joint interpretation of the PP and PS image can provide a better understanding for the subsurface structures due to different illuminations.
• PP image reflect both Vp and Vs perturbations while the PS and SFCW images only show Vs perturbations.
• The SFCW image is target oriented and is robust for the complex overburden velocity uncertainties, while it lacks illumination for the areas further away from the borehole.
20
21
Thank you!
Singapore Geophysics Project