Transcript Multiple Removal by Joint Least Square Migration

Wavefield Prediction
of Water-layer Multiples
Ruiqing He
University of Utah
Oct. 2004
Outline
• Introduction
• Theory
• Synthetic experiments
• Application to real data
• Conclusion
Introduction
•Multiple classification.
•Free-surface multiples (FSM).
- Delft, multiple series theories, etc.
•Water-layer multiples (WLM).
- Berryhill, Wiggins, et al.
Berryhill’s Approach
•The prediction of WLM is obtained by propagating
the received data once within the water layer.
- Kirchhoff integral, Finite-Difference,
Gaussian beams, Phase-shift, etc.
•The prediction is emulation.
- Part of WLM.
- Half is exact; the other half is not exact.
•Multiple subtraction.
Outline
• Introduction
• Theory
• Synthetic experiments
• Application to real data
• Conclusion
Seismic Wave Representation
Source : S  gS  S *
Primaries  Interbeds : PI  fS *  gfS *
1st  order  FSM : fgfS *  gfgfS *
2nd  order  FSM : fgfgfS *  gfgfgfS *
...
PI  ( f  gf ) S *

FSM  ( f  gf ) ( gf ) n S *
n 1

Data : W  PI  FSM  ( f  gf ) ( gf ) n S *
n 0
gS: Ghost-source.
s*: Twin-source.
f: visit of subsurface once.
g: Receiver-side ghosting.
Berryhill’s Emulation

FSM  ( f  gf ) ( gf ) n S *
n 1

W  ( f  gf ) ( gf ) n S *
n 0
Emulation:


FSM '  gf (W )  gf ( f  gf ) ( gf ) S  ( f  gf ) ( gf ) n S *  FSM
n
n 0
if:gf  fg
then:FSM '  FSM
*
n 1
FSM Prediction
PI  ( f  gf ) S *  fS *  gfS *  PI u  PI g



FSM  ( f  gf ) ( gf ) S  f  ( gf ) S  gf  ( gf ) n S *  FSM u  FSM g
n
n 1
*
n
n 1
*
n 1
W  PI  FSM  PI u  FSM u  PI g  FSM g  Wu  Wg
Steps:

1:receiver_side_ghost_decomposition:D  PI g  FSM g   ( gf ) n S *
n 1

2:forward_modeling:f ( D)  f  ( gf ) n S *  FSM u
n 1
3 : PI u  W  D  FSM u
Subscript g: Receiver-side ghosts (RSG).
Subscript u: Upcoming data that generate RSG.
Multiple Classification
• Level 1:
– Water-Layer Multiple (WLM).
– Non-WLM multiples (NWLM).
• Level 2 (WLM):
– Last reverberation WLM (LWLM).
– First reverberation WLM (FWLM).
– Middle reverberation WLM (MWLM).
• Definition priority.
• Water-Bottom-Multiple (WBM).
Types of Water-Layer Multiples
LWLM
FWLM
Water surface
Water bottom
Subsurface reflector
MWLM
Seismic Data Classification
Level
Seismic Data (W)
0
Level
Upcoming Waves (U)
1
Level
WLM
NWLM
2
Level LWLM FWLM MWLM
3
Note: Converted waves are not considered,
and direct waves have been removed.
D
P
LWLM Prediction
Data (W)
+
Upcoming
waves (U)
g
Downgoing
ghosts (D)
f
LWLM
-
For synthetic data, the operator g, f can be exactly known.
By this design, LWLM can be exactly predicted.
Outline
• Introduction
• Theory
• Synthetic experiments
• Application to real data
• Conclusion
Synthetic Model
0
water
Hydrate
Depth
(m)
Salt dome
Sandstone
1500
0
Offset (m)
3250
Synthetic Data
400
Time
(ms)
2500
0
Offset (m)
3250
Predicted LWLM
400
Time
(ms)
2500
0
Offset (m)
3250
Waveform Comparison
between Data & RSG+LWLM
Data
Amplitude
RSG + LWLM
600
Time (ms)
2400
Elimination of RSG & LWLM
by Direct Subtraction
400
Time
(ms)
2500
0
Offset (m)
3250
Further Multiple Attenuation
by Deconvolutions
400
Time
(ms)
2500
0
Offset (m)
3250
Outline
• Introduction
• Theory
• Synthetic experiments
• Application to real data
• Conclusion
A Mobil data
Predicted LWLM
Waveform Comparison
WLM Attenuation
with Multi-Channel Deconvolution
Migration before demultiple
Migration after demultiple
A Unocal Data
Predicted LWLM
Waveform Comparison
At a geophone above non-flat water bottom
At a geophone above flat water bottom
WLM Attenuation
with Multi-channel Deconvolution
Migration before demultiple
Migration after demultiple
Outline
• Introduction
• Theory
• Synthetic experiments
• Application to real data
• Conclusion
Conclusion
• Berryhill’s approach does not need to know the
source signature, and can be performed in a single
shot gather, but the prediction is emulation.
• This method improves Berryhill’s approach by
making clear classification among WLM, and
using receiver-side ghosts to predict LWLM.
• This method exactly eliminates LWLM for
synthetic data, and successfully suppresses WLM
by multi-channel de-convolutions for field data .
Thanks
• This research is benefited from the
discussions with Dr. Yue Wang and Dr.
Tamas Nemeth of ChevronTexaco Co..
• I am also thankful to 2004 members of
UTAM for financial support.