Moveout Correction and Migration of Surface-related Resonant Multiples

Bowen Guo*,1, Yunsong Huang2 and Gerard Schuster1

1King Abdullah University of Science and Technology2CGG

Outline

Conclusions and future work

Introduction and motivation

Theory and workflow

Numerical results

Introduction What is a surface-related resonant

multiple ?Free surface

Reflector

Raypaths overlap

Raypaths overlap

Introduction Why migrate resonant multiples ? Super-resolution

Case 1: migrate primary reflections

Where did this come from ?

𝑡𝑝

𝑧𝑝1

𝑧𝑝1=𝑣𝑡𝑝 /2

𝑡𝑝+T

𝑧𝑝2

𝑧𝑝2=𝑣 (𝑡¿¿𝑝+𝑇 )/2¿

∆

t

𝛌 /𝟐𝑣

Motivation Why migrate resonant multiples ? Super-resolution

Where did this come from ?

𝑧𝑚1𝑧𝑚 2

𝑡𝑚

+T

𝑧𝑚1=𝑣𝑡𝑚/4𝑧𝑚 2=𝑣 (𝑡 ¿¿𝑚+𝑇 )/4 ¿

∆

Case 2: migrate resonant multiples

t

∆

𝑣𝑧𝑝1𝑧𝑝2𝛌 /𝟐

Super-resolution by migrating resonant multiples

Problem Only received by near-offset traces low SNR

Motivation

Freesurface

Reflector

Freesurface

Reflector

Multiple Image

Primary Image

Z (km

)

X (km)

X (km)Schuster and Huang (2014)

0.69

0.8533.5 36.533.5 36.5

Problem: Low SNR

t (s)

X (km)

1.5

6.0

0 30

COG offset=107 m

Solution: Step 1: CMP moveout correction. Step 2: Stacking to improve SNR.

t

offset

CMPt

offset

CMP

Pre-resonant multiples

Resonant multiples

Before stackingAfterstacking

Resonant multiple

Primary reflection

Motivation

Introduction and motivation

Theory

Numerical results

Conclusions and future work

Outline

Theory: Pre-resonant Multiples

Free surface

Reflector 1

Reflector 2

Multiples from dissimilar interface

Pre-resonant multiples from similar interface

Free surface

Reflector

𝛼

h

Resonant multiples

Theory: Moveout Correction

Moveout correction based on moveout formla

Free surface

Reflector

𝛼

Pre-resonant multiples 𝜏0𝜏

Valid for homogeneous velocity model

Theory: Moveout Correction

Free surface

Reflector

𝛼

𝜏 𝒔𝒈′𝑝

Moveout correction based on Fermat’s principle

𝒔 𝒈𝒈 ′

𝜏𝒈′𝒈𝑝

Indentify for different offsets Stack into zero-offsets

𝜏 𝒔𝒈𝑚 =min

𝒈′(𝜏 𝒔𝒈′

𝑝 +𝜏 𝒈′𝒈𝑝 )

Valid for heterogeneous velocity model

Theory: Migration of Resonant Multiples Migration of post-stack resonant multiples

𝑥

2𝜏𝑥𝑔 2𝜏𝑥𝐴

Free surface

𝑔 𝐴

m() =c(, ) d( , t-2-2)

Primary Reflection Migration Image

Horizontal distanceD

epth

Resonant Multiple Migration Image

Horizontal distance

Dep

th

Work Flow

CMP

Moveout Correction for Non-zero Offset Traces

Stack into zero-offset

Migration of post-stack resonant multiples

t

x

ZOG

t

x

Post-stack ZOG

z

x

Image

t

offset

CMP

0

t

offset

CMP

0

Introduction and motivation

Theory

Numerical results

Conclusions and future work

Outline

Synthetic Result: Point Scatterers

Data generated by Kirchhoff modeling and migrated by Kirchhoff migration

Z (k

m)

x (km) x (km)

0.64

2.0811.6 12.4 11.6 12.4

Primary Image Resonance Image

Field Data Example

X (km)0 30

t (s)

1.5

6.0

COG = 107 m

Resonant multiple

Primary reflection

Zoom in

Field Data: Zoom-in of COG

X (km)0 30

t (s)

3.3

6.0

Dissimilar multiplesBefore After

h

1

CMP0.0

6.00.1 5.0

t (s)

5.0(km) h

2

0.0

6.00.1 h

t (s)

5.0 5.0(km)

h

CMP

3

0.0

6.00.1 h

t (s)

5.0 5.0(km) h

Top of Salt

Z (k

m)

X (km)2.0

0 30

Primary Reflection Image0.0

Multiple Image

X (km)0 30

Post-stack Multiple Image

Field Data: Migration Image

Higher-resolution top of the salt

False reflectors from dissimilar multiples

Field Data 2: Sonar Data

Processsed 120 kHz data

0

80

1600 370 x (m)

t (m

s)

Primary reflection

Resonant multiple

Processsed 200 kHz data

0 370 x (m)

Primary reflection

Migration Image of the Sea BottomImage from 120 kHz Primary Reflections

0

60

0 270 x (m)

Z (m

)

Image from 120 kHz Resonant Multiples0

60

Z (m

)

Image from 200 kHz Primary Reflections

Image from 120 kHz Resonant Multiples

Introduction and motivation

Theory

Numerical results

Conclusions and future work

Outline

Conclusions Resonant multiples give super-resolution

Pre-resonant multiples resonant multiples

Alignment and stacking improve SNR

0.0

6.00.1 5.0

t (s)

h (km)

CMP0.0

6.00.1 5.0

t (s)

h (km)

CMP

Limitations and Future Research

Multiples suffer more from attenuation than primaries

Inaccurate moveout correction blur the stacked resonant multiples

Multiples from dissimilar reflectors cause artifacts

Acknowledgement

We would like to thank King Abdullah University of Science and Technology for their support

Thank you for your attention