Imaging of diffraction objects using post-stack

reverse-time migration

I. Silvestrov* (OPERA, IPGG SB RAS), R. Baina (OPERA)

and E. Landa (OPERA)

Outline

• Motivation• Description of the proposed algorithm • Synthetic example based on Sigsbee model• Real-data example

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Diffraction imaging algorithm in dip-angle domain

Landa, E., Fomel S., and Reshef M. 2008. Separation, imaging, and velocity analysis of seismic diffractions using migrated dip-angle gathers. 78th Annual International Meeting, SEG, Expanded Abstracts, 2176–2180

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Diffractions and reflections have different shapes in migrated dip-angle domain

Motivation

• Diffraction imaging in areas where Kirchhoff migration fails (e.g. subsalt)

• Numerical efficiency of the diffraction imaging algorithm

Our choice:

Post-stack Reverse-time migration (RTM)

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Post-stack reverse-time migration

5

0,/

2/

12

2

2

=tu=tz,x,u

T<t,zδξxδtξ,d=Δut

u

zx,V

TtTt

x

0

,t

tzx,u=zx,I

For given data d(x; t) we solve wave-equation with half-velocity V/2 in reverse-time:

Image is simply the wavefield at zero time:

(1)

Why we can not use previous approach for diffraction separation?

•Due to summation over receivers in (1) we do not have extra dimension for straightforward construction of CIGs

•Analyzing the wavefield at zero time is equivalent to analyzing the image itself. However, we want to analyze the data and not the image.

Common image gathers in surface dip-angle domain

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Model Zero-offset data

0p

Vp /)sin(2

Plane-wave components of ZO data

As an extra dimension in CIGs we propose to use dip of event in data domain (horizontal slowness):

msp /0012.0

Common image gathers in surface dip-angle domain

Migration of plane-wave data componentsCIGs with respect to

“surface” dip

Reflection is a focused event.Diffraction is a horizontal line at the correct diffraction position.

How to separate them?

1 2 1 2

p=-0.0012 s/m p=0 p=0.0012 s/m p p

Diffraction separation using Kurtosis measure

N

=ii

N

=ii xNx=K

1

4

2

1

21 /

Inverse Kurtosis measure:

The events above a predefined threshold level are considered as diffractions

Kurtosis is a measure of peakedness of a probability distribution. Inverse Kurtosis is low for focused events.

At the same time inverse Kurtosis is large for coherent events as a correlation of a squared signal with a constant.

Plane-wave decomposition using sparse local Radon transform

wxx

wxx0 xxp+τx,d=xp,τ,m

0

0

0

0

0

0

0

0

~ pp

pp

wxx

wxx0xp,,xxptm=x,td

22l

Lmd=mJ

.0

0

0

wxx

wxx0p xp,,xxptm=x,td

Wang, J., Ng, M., and Perz, M. 2010. Seismic data interpolation by greedy local Radon transform. Geophysics 75(6), WB225-WB234.

Giboli, M., Baina, R., and Landa, E., 2013. Depth migration in the offset-aperture domain: Optimal summation. SEG Technical Program Expanded Abstracts, 3866-3871

Local Radon transform is defined as:

And its adjoint as:

To find the model we use greedy approach to minimize the least-squares misfit:

),,( 0xpm

The plane-wave data section is obtained by summation over all local windows:

The proposed algorithm for diffraction separation based on post-stack RTM

1. Plane-wave decomposition of zero-offset stack• Sparse local Radon transform based on greedy

approach

2. Depth migration of each plane-wave seismogram• RTM with zero-time imaging condition

3. Resorting of images into CIGs with respect to dip in data domain

4. Diffraction/reflection separation based on defocusing criteria• Sparse local Radon transform based on greedy approach• Inverse kurtosis as a measure of defocusing

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Sigsbee model (post-stack RTM result)

11Two parts of the model will be considered in diffraction imaging

Simple part Complex part

Zero-offset section

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Plane-wave data component of zero-offset section

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Horizontal slowness p=-0.00014 s/m

Plane-wave data component of zero-offset section

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Horizontal slowness p=0

Common image gathers in simple part

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X=6000 X=6000

Before separation After separation

Diffraction separation result in simple part

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Before separation After separation

Diffraction separation result in complex part

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Before separation After separation CIG at 15200m before and after

separation

After separation

Snapshots for diffraction and reflection below salt body

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Exploding reflector modeling

Reflection Diffraction

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Snapshots for diffraction and reflection below salt body

Exploding reflector modeling

Reflection Diffraction

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Diffraction’s and reflection’s responses are similar at the surface

Snapshots for diffraction and reflection below salt body

Redatuming may be used to simplify the wavefield

Reflection Diffraction

Redatuming level

Reshef M., Lipzer N., Dafni R. and Landa E., 3D post-stack interval velocity analysis with effective use of datuming, Geophysical Prospecting 1(60), 18–28, January 2012

Zero-offset section after redatuming

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Diffraction separation result in complex part

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Initial image Diffraction imagefor initial data

Diffraction imagefor redatumed data

CIGs before and after redatuming

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X=15200

Before redatuming After redatuming

Real-data example. Oseberg oil field in the North Sea.

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Zero-offset stack obtained using path-integral summation approach

Common image gathers

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Diffraction image

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Diffraction wavefield

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Full wavefield

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Conclusion

• We propose a method for imaging small scale diffraction objects based on post-stack Reverse-time migration

• The method is based on separation between specular reflection and diffraction components of the total wavefield in the migrated domain. We used continuity of diffractions in the surface dip-angle CIGs as a criterion for separating reflections from diffractions

• Synthetic and real data examples illustrate efficient application of the method

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Acknowledgements

The authors thank TOTAL for supporting this research. OPERA is a private organization funded by TOTAL and supported by Pau University whose main objective is to carry out applied research in petroleum geophysics.

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