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