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12006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Illumination, resolution, and incidence-angle in PSDM:A tutorial
Isabelle LecomteNORSAR, R&D Seismic Modelling, P.O.Box 53, 2027 Kjeller, Norway
?
22006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Hubble telescope: space-variant PSF*
http://huey.jpl.nasa.gov/mprl
*Point-Spread Functions
Space-variant PSF!
32006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Point-Spread Functions in Marmousi*
*Marmousi model courtesy of IFP
Seismics: PSF may be very space-variant!
42006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Resolution, illumination, …etc!
*http://www.lenna.org , **Liner (2000), and Monk (2002)
*
Acoustic/elastic impedance Reflection ~ contrasts!
**
PSDM … at best!
!
Not 1D convolution!
52006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
62006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Waves!
Scattering
Imaging in PSDM: K is the key!
Getting data
Incident wave
Waves!
Imaging
Key information:
Scattering Wavenumber!
Imaging2Focusing
?
Back propagation
Waves!
1Wave propagation corrections
G,G: GF(*)
●: GF-node
(*)GF: Green’s FunctionMigration
72006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Scattering isochrones
Common shot(x = 0)
■Common offset(0 m)
■Model: constant velocityData: point scatterer
data data
ellipse circle
■
● point scatterer
PSDMPSDM
82006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
PSDM and point scatterer
■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
●■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■●
Common offset (0 m)
Common shot (x = 0)
1 trace
1 trace
∑ traces
∑ traces
Same point scatterer…
…different PSDM images!
92006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
PSF and PSDM: why?
• scattering structures = set of point scatterers(e.g., exploding reflector concept, etc)
• PSDM(point scatterer) = Point-Spread Function
• If PSF known: PSDM image = Reflectivity * PSF
• Question 1: how to get PSF without generating synthetic point scatterers at each image point?
• Question 2: how to use PSF to understand and improve PSDM?
102006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
112006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Methods: ”ray-tracing” based
• Green’s functions– Paraxial ray tracing
– Wavefront Construction
– Eikonal solver
• PSDM (~Kirchhoff)– Diffraction Stack (DS)
– Local Imaging (LI)
• 1 GF-node only!
• ”SimPLI” (*)
– Simulated Prestack Local Imaging
• No seismic records needed!(*) patent pending
●
122006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Scattering Wavenumber K
Incident wavenumber
Definition at a local “Scattering Object” (diffraction, reflection, ..)
scattered wavenumber
Easy to calculate with ray tracingand similar
Calculation performed in thePSDM velocity model
132006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K: which parameters?
g sK k k
ˆ ˆ2
g s
g sK
V V
s sP SV V orV V 2
ˆs
sk sV
source s
g gP SV V orV V 2
ˆg
gk gV
geophone g
- Vs: incident wave velocity- Vg: scattered wave velocity- ŝ and ĝ: unit vectors- frequency
- VP: P-velocity- VS: S-velocity
If Vs = Vg (no wave conversion)
2ˆ ˆ( )K g s
V
”incidence” angle = 0║ĝ – ŝ║ = 2
●●ŝ ĝ
K
●ŝ ĝ
K
”incidence” angle ≠ 0║ĝ – ŝ║ < 2
142006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
From K to PSF using FFT
2D FFT-1
PSF
Z
X
Green’s Functionsat one GF-node
●
Marmousi
●
-Kx max. +Kx max.-Kz max.
0.
max./2
0m
odu
le
no data!
●
2D FFT
●
152006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K and scattering isochrones
K corresponds to a localplane wavefront
approximation of thescattering isochrone
K is perpendicular to thescattering isochrone
║K ║ = f() : pulse effect
[K] PSF
162006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
172006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
truetruegest mRmGGm .).(. 1+2
.. . obsgest dGm Inverse problem
2trueobs mGd .. Direct problem
1
Resolution of an inverse problem!
GGR g
1 !!!gG G
Your model! Generalized Inverse
d: datam: parametersobs.: observedest.: estimated
Data independent!
Resolution!
182006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
[K] for [5-60] Hz
s = [0-10] º
K and resolution: wavenumber coverage
Kx
KZ
Lateral resolution ~ 2 / KX
Vertical resolution ~ 2 / KZ
1
Marmousi modelCourtesy of IFP
192006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K and PSF: no data!
PSF
PSF
K
K
PSDM of point scatterer and PSF
PSDM – data from point scatterer
Common offset (0 m)
Common shot (x = 0)
high R
high Rlow R
low R
Kmean
Kmean
202006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
212006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K and reflection”P-to-S” reflection”P-to-P” reflection
ReflectorReflector
From sourceFrom source
incident ray
In the PSDM velocity model:
- A given couple (ks,kg) may correspond to an actual reflection.
- it is the case IF there is a reflector perpendicular to K at the GF-node.
s incidence angle
s s
To geophoneTo geophone
reflected ray
g scattering angle
g g
222006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
[K] for [5-60] Hz
s = [0-10] º
Illuminated dips2
~ 45 º ~ 25 º
K and illumination: dip
Marmousi ModelCourtesy of IFP
Marmousi modelCourtesy of IFP
232006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
242006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
0 Hz
120 Hz
[K]
Playing with the pulse
Spectrum
Target model (Vp) Reflectivity
10 Hz
SimPLI
20 Hz
SimPLI
30 Hz
SimPLI
40 Hz
SimPLI
252006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Fault
4 km offset
Reflectivity = 1
FFT+1
“Green’s Functions”
Illumination and resolution: illustration
Fault
[K] incl. 20 Hz pulse
0 km offset
Fault
Fault
PSF
FFT-1
PSF
FFT-1
FFT-1
SimPLI – 0 km offset
FFT-1
SimPLI – 4 km offset
Fault
262006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Incidence-angle in PSDM
SimPLI Image: 00°-05°SimPLI Image: 05°-15°SimPLI Image: 15°-25°SimPLI Image: 25°-35°SimPLI Image: 35°-45°
[K] Filter : 00°-05°[K] Filter : 05°-15°[K] Filter : 15°-25°[K] Filter : 25°-35°[K] Filter: 35°-45°Reflectivity : 00°-05°Reflectivity : 05°-15°Reflectivity : 15°-25°Reflectivity: 25°-35°Reflectivity: 35°-45°
Final SimPLI Image – 20 Hz
Σ
272006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Overburden effects
●A
K PSF
Good resolutionGood illumination
●B
K PSF
Poor resolutionBad illumination
Not illuminated!
282006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
PSDM images: not a simple 1D convolution!
Elastic impedance (x,z)
KX
KZ
“1D” PSDM
!
No illumination effects!
KX
KZ
2D Filter: 0 km offset
KX
KZ
2D Filter: 4 km offset
This is PSDM effects!
Function of survey, overburden, pulse, wave-
phases, local velocity.
292006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
302006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Image and survey sampling
K
PSF
SimPLI
shot: 12.5 m
K
PSF
SimPLI
shot: 125 m
K
PSF
SimPLI
shot: 625 m
312006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
”blind!”
automatic corrections
Controlling imaging: check local K!
IrregularSampling!
Blind! Controlled!
322006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Conclusions
• Define your PSDM velocity model…– Should be smooth in the imaging zone…– … but can have layers with contrast outside!
• …then use the scattering wavenumbers!– Prior or after imaging– Survey planning mode– Resolution/illumination analyses– Controlling and improving imaging– Understanding image formation– Testing the validity of interpretation results
• Flexible and fast!– Ray tracing based– FFT
332006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Acknowledgements
• Research Council of Norway (projects 131341/420, 128440/43, and 153889/420)
• Statoil (Gullfaks), IFP (Marmousi), Seismic Unix, and the “Svalex” project (www.svalex.net, Storvola)
• Håvar Gjøystdal, Åsmund Drottning and Ludovic Pochon-Guerin.
• Thanks