COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING
description
Transcript of COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING
COMPARISON OF COMPARISON OF WAVE EQUATION WAVE EQUATION MIGRATION METHODS WITH PHASE MIGRATION METHODS WITH PHASE
ENCODINGENCODING
Jianhua Yu
University of Utah
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
INTRODUCTIONINTRODUCTIONMigration methods includes two classes:
. Ray-based migration method
Features:
a. Computational efficiency
b. Capability of irregular acquisition
geometry and target-processing
INTRODUCTIONINTRODUCTION
c. Depend on ray-tracing algorithm
d. Less accurate image for complex area
INTRODUCTIONINTRODUCTION
Wave equation methods:
Solution for two-way or one-way equations
Features:
a. Accurate wavefield extrapolation
b. High quality image for complex area
c. Expensive computational cost
OBJECTIVEOBJECTIVE
Compare various wave-equation methods
Compare phase encoding algorithms
The final purpose is to develop an efficient wave equation method for 3D migration image in complex area
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
METHODOLOGYMETHODOLOGY
Phase-shift based wave equation methods:
a. SSF
b. PSPI
c. FFD (SSF+FD)
Why use phase-shift based Why use phase-shift based method?method?
Less memory requirement
Compressed data in frequency domain
dzikyxyx
zezkkPdzzkkP ),,,(),,,(
Phase shift Method
Basic equation for wavefield extrapolation is
This equation can not handle velocity lateral variation !!
SSF METHOD
Basic steps include:
Split velocity field: Vi=V0+dVi
Wavefiled extrapolation with V0 in frequency-wavenumber domain
Phase correction with dVi in frequency-space domain
PSPI METHOD
Basic steps of PSPI consist of:
Introduce several reference velocities: Vi
Wavefiled extrapolation with each Vi in frequency-wavenumber domain
Interpolating reference wavefield in frequency- space domain
),
11(1
minvvd
Pddvk
vi
z
P x )211(2
2min
2
min
,2
)1(22bu
ua
vd
SSF+FD(FFD) METHODBasic equation for FFD migration is:
SSF FD
FFD = SSF+FD
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
,),(),( n
ns SS xx n
.),(),( n
ns DD xx n
Where Sn is source term; Dn is nth shot gather; Ss and Ds are the encoded source term and super shot gather; n is the index of shot gather
PHASE ENCODING ALGORITHM
nHOW TO GET ?
nin e
Generate random coefficients with valuem of 1 or -1
Generate random coefficients with Gaussian sampling
can be obtained by following ways: n
Generate random coefficients with range [0,2 ]
Strategy I:
HOW TO PHASE ENCODE ?
G1 Gn Gm-n Gm
Phase encoding
G’k
Migrating Output
Phase encoding
G’1 K<M
Strategy II:
HOW TO PHASE ENCODE?
G1 G2 Gi Gm
Phase Encoding
Gsuper
Migrating Output
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
NUMERICAL RESULTS FOR SEG/EAGE NUMERICAL RESULTS FOR SEG/EAGE SALT MODEL DATASALT MODEL DATA
X (km)0
0
3
Dep
th (
km
)
15
TEST1: Comparison of Four Migration TEST1: Comparison of Four Migration MethodsMethods
X (km)
00
3
Dep
th (
km
)
15
Kirchhoff SSF
X (km)0 15
Without Multiples
TEST1: Comparison of Four Migration TEST1: Comparison of Four Migration MethodsMethods
X (km)
00
3
Dep
th (
km
)
15
PSPI SSF+FD
X (km)0 15
Without Multiples
TEST1: Comparison of Four Migration TEST1: Comparison of Four Migration MethodsMethods
X (km)
00
3
Dep
th (
km
)
15
Kirchhoff SSF
X (km)0 15
With Multiples
TEST1: Comparison of Four Migration TEST1: Comparison of Four Migration MethodsMethods
X (km)
00
3
Dep
th (
km
)
15
PSPI SSF+FD
X (km)0 15
With Multiples
TEST1: CPU Time of Four Mig. MethodsTEST1: CPU Time of Four Mig. Methods
TEST2: Comparison of Three Phase TEST2: Comparison of Three Phase Encoding MethodsEncoding Methods
0
X (km)0
3
Dep
th (
km)
15
00
3
Dep
th (
km)
15
X (km)0 15
(a)
(b)
(c)
a. Random distribution
b. Linear encoding
c. Gaussian distribution
TEST3: Comparison of SSF Migration TEST3: Comparison of SSF Migration with Phase Encoding Strategy Iwith Phase Encoding Strategy I
X (km)
00
3
Dep
th (
km)
15 X (km)0 15
0
3
Dep
th (
km)
(a). encode=2
(b). encode=4
(c). encode=10
(d). no encoding(320)
TEST3: CPU Time of SSF Migration with TEST3: CPU Time of SSF Migration with Phase Encoding Strategy IPhase Encoding Strategy I
TEST3: Comparison of SSF Migration TEST3: Comparison of SSF Migration with Phase Encoding Strategy IIwith Phase Encoding Strategy II
X (km)
00
3
Dep
th (
km)
15 X (km)0 15
0
3
Dep
th (
km)
(a). nmig=100
(b). nmig=80
(c). nmig=60
(d). no encoding(320)
TEST3: CPU Time of SSF Migration with TEST3: CPU Time of SSF Migration with Phase Encoding Strategy IIPhase Encoding Strategy II
TEST4: Comparison of SSF+FD Migration TEST4: Comparison of SSF+FD Migration with Phase Encoding Strategy Iwith Phase Encoding Strategy I
X (km)
00
3
Dep
th (
km)
15 X (km)0 15
0
3
Dep
th (
km)
(a). encode=2
(b). encode=4
(c). encode=10
(d). no encoding(320)
TEST4: CPU Time of SSF+FD Migration with TEST4: CPU Time of SSF+FD Migration with Phase Encoding Strategy IPhase Encoding Strategy I
TEST4: Comparison of SSF+FD Migration TEST4: Comparison of SSF+FD Migration with Phase Encoding Strategy IIwith Phase Encoding Strategy II
X (km)
00
3
Dep
th (
km)
15 X (km)0 15
0
3
Dep
th (
km)
(a). nmig=100
(b). nmig=80
(c). nmig=80
(d). no encoding(320)
TEST4: CPU Time of SSF+FD Migration with TEST4: CPU Time of SSF+FD Migration with Phase Encoding Strategy IIPhase Encoding Strategy II
TEST5: CPU Time of SSF+FD Migration with TEST5: CPU Time of SSF+FD Migration with Phase Encoding Strategy IIPhase Encoding Strategy II
10 nodes
1 node
X (km)
00 4
10
Dep
th (
km)
X (km)0 4
Velocity slice (depth=1.6 km) Migration image (depth=1.6 km)
TEST6: Preliminary Result of 3D SSF TEST6: Preliminary Result of 3D SSF Migration with Salt Model(zero offset data)Migration with Salt Model(zero offset data)
TEST4: Preliminary Result of 3D SSF TEST4: Preliminary Result of 3D SSF Migration with Salt Model(zero offset data)Migration with Salt Model(zero offset data)
X (km)
00 4
10
Dep
th (
km)
(c). nmig=80
Velocity slice (depth=2 km)
X (km)0 4
Migration image (depth=2 km)
CONTENTSCONTENTS. Introduction
. Brief Description of Wave Equation
Methods: SSF, PSPI, FFD (SSF+FD)
. Phase Encoding Algorithm
. Numerical Results
. Conclusion and future work
CONCLUSION
Phase encoding can reduce computational effort of wave equation migration by factor three or more
SSF+FD yields best image result.
The test results show:
Future Work
We will mainly focus on developing an efficient wave equation method with phase encoding and other type compression technique for 3D migration
3D prestack migration method is being tested on SALT model data
ACKNOWLEDGEMENTS
I greatly appreciate the sponsors of UTAM Consortium for their financial support
I also thank all the people who give me suggestions and help for this work