3D illumination analysis using wave equation based

propagator Xiao-Bi Xie

University of California, Santa Cruz Shengwen Jin

Screen Imaging Technology Inc. Ru-Shan Wu

University of California, Santa Cruz

October, 2003, Dallas, Texas

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

The seismic illumination analysis is a useful estimate that gives potential detecting power of a specific acquisition system for a given structure.

Ray tracing based techniqueProvides both the intensity and direction information High efficientLimited by the high frequency asymptotic approximation

Full-wave finite-difference method Usually provides only the total illuminationExpensive

One-way wave-equation based method Wave-equation basedLocal plane wave analysis to provide direction information3D full-volume capabilityConsistent with the wave equation based migration/imaging

Different methods for extracting localized angle information from migrated wavefields

Ray tracing/Gaussian beam based techniquegive the wave propagation direction from the ray diagram

Shot domain common image gatheraverage direction between the source and the target

Plane source directional source from the surface

Offset-domain one-way wave equation method Offset plane wave

Wavelet transform based method use wavelet transform to give information localized in both space and angle

Local plane wave analysisLocal plane wave analysis to provide directional information

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K T θ = ( θ , φ ) θ ( K T ) = s i n - 1 ( K T / k ) φ ( K T ) = t a n - 1 ( K Y / K X )

Angle domain analysis for extrapolated wavefields

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

Illumination analysis using ray based method (Muerdter 2001)

Illumination analysis using wave equation based method

A sketch showing (a) the directional illumination (DI) and (b) the acquisition dip-response (ADR).

Acquisition system

DI ADR

Favoritetarget dip

unfavoritetarget dip

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

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F o r a n a c q u i s i t i o n s y s t e m c o m p o s e d o f m u l t i p l e s o u r c e s ,

S

zIzI TSTr

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D I c a n b e f u r t h e r s o r t e d a c c o r d i n g t o d i f f e r e n t p u r p o s e s t o g i v e u s e f u l i n f o r m a t i o n .

D i r e c t i o n a l I l l u m i n a t i o n T h e i n t e n s i t y a n d d i r e c t i o n o f t h e i n c o m i n g e n e r g y

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F o r a n a c q u i s i t i o n s y s t e m c o m p o s e d o f m u l t i p l e s o u r c e s ,

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zIzI TSTr

θxrθx ),,,;(),,,( .

D I c a n b e f u r t h e r s o r t e d a c c o r d i n g t o d i f f e r e n t p u r p o s e s t o g i v e u s e f u l i n f o r m a t i o n .

Locations of surface sources used for DI calculation,3600 shots areused to simulate marine type acquisition

3D SEG/EAGE Salt Model

DI maps for 3DSEG/EAGE Salt Model V-model

45º left

Vertical

45º right

cross sections at y = 6100 m

Locations of surface sources.45 shots are used to simulate land type acquisition

3D SEG/EAGE Salt Model

3D SEG/EAGE Salt Model, 45 shot data set, comparisons between the model, total illumination, andPrestack depth image.

Velocitymodel

Totalillumination

MigrationImage(Luo & Wu2003)

cross sections at x = 6000 m

Velocitymodel

verticalillumination

MigrationImage(Luo & Wu2003)

3D SEG/EAGE Salt Model, 45 shot data set, comparisons between the model, vertical DI, andPrestack depth image.

cross sections at x = 8600 m

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

A c q u i s i t i o n D i p - R e s p o n s e ( A D R ) T h e s i m u l a t i o n o f t h e d e t e c t i n g p o w e r o f a s o u r c e - r e c e i v e r p a i r

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θ d i p p i n g a n g l e o f t h e f a v o r i t e r e f l e c t o r F o r a n a c q u i s i t i o n s y s t e m w i t h m u l t i p l e s o u r c e - r e c e i v e r p a i r s

S R

zRzR TRSTr r

θxrrθx ),,,;;(),,,( .

A c q u i s i t i o n D i p - R e s p o n s e ( A D R ) T h e s i m u l a t i o n o f t h e d e t e c t i n g p o w e r o f a s o u r c e - r e c e i v e r p a i r

2/1),,,;(),,,;(),,,;;( RTRSTSTRS zIzIzR θxrθxrθxrr r R r e c e i v e r l o c a t i o n I ( r S ) , I ( r R ) D I s f r o m t h e s o u r c e a n d r e c e i v e r θ S , θ R i l l u m i n a t i o n a n g l e s

θ d i p p i n g a n g l e o f t h e f a v o r i t e r e f l e c t o r F o r a n a c q u i s i t i o n s y s t e m w i t h m u l t i p l e s o u r c e - r e c e i v e r p a i r s

S R

zRzR TRSTr r

θxrrθx ),,,;;(),,,( .

30 degree ADRfor a single source-cable system (one shot plus three 3.2 km long cables)

Cross section alongthe sail direction

Depth slice at1000 m

Velocitymodel

VerticalADR

MigrationImage (Jin et al. 2002)

Vertical ADR overlay on the prestack image

Velocity model

Total ADR

Migration Image(Jin et al. 2002)

Calculate the illumination on a target zone

Depth = f(x,y)

Outline

O IntroductionO Illumination analysisO Directional illuminationO Acquisition dip-responseO 3D numerical examples using

SEG/EAGE salt modelO Summary

SummaryO A wave equation based method is developed for the illumination analysis. The GSP propagator and local plane wave analysis are used to extrapolate the wavefield and provide the directional information.

O The method provides a practical tool to conduct the 3D full-volume illumination analysis in complex structures. Both directional illumination (DI) and acquisition dip-response (ADR) can be generated. The method can be naturally teamed with the wave equation based migration method to provide illumination analysis.

O Angle domain information is very useful. It adds a new dimension for us to look at the illumination. To demonstrate the potential applications of this method, preliminary numerical examples are calculated using the 3D SEG/EAGE salt model.

For more information, please visit the Modeling and Imaging Lab booth at #2745.

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