Transcript Document

Illumination, resolution, and
incidence-angle in PSDM:
A tutorial
Isabelle Lecomte
NORSAR, R&D Seismic Modelling, P.O.Box 53, 2027 Kjeller, Norway
[email protected]
?
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
1
Hubble telescope: space-variant PSF*
*Point-Spread Functions
Space-variant PSF!
http://huey.jpl.nasa.gov/mprl
2006 SEG
76th
Annual Meeting – 10/5/2006 – SPMI6-6
2
Point-Spread Functions in Marmousi*
Seismics: PSF may be very space-variant!
*Marmousi model courtesy of IFP
2006 SEG
76th
Annual Meeting – 10/5/2006 – SPMI6-6
3
Resolution, illumination, …etc!
*
**
Acoustic/elastic impedance
Reflection ~ contrasts!
PSDM … at best!
Not 1D convolution!
!
*http://www.lenna.org , **Liner (2000), and Monk (2002)
2006 SEG
76th
Annual Meeting – 10/5/2006 – SPMI6-6
4
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
5
Imaging in PSDM: K is the key!
Getting data
Migration
(*)GF:
Waves!
Waves!
Green’s Function
Key information:
Back propagation
Scattering Wavenumber!
GF(*)
G,G:
●: GF-node
1
Incident wave
Wave propagation corrections
Waves!
?
2
Scattering
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Imaging
Focusing
6
Imaging
Scattering isochrones
Common shot
(x = 0)
■
Model: constant velocity
Data: point scatterer
Common
(0 m)
data
■
offset
data
■
● point scatterer
PSDM
ellipse
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
PSDM
7
circle
PSDM and point scatterer
Common offset (0 m)
■■■■■■■■■■■■■■■■
●●●●●●●●●●●●●●●●
∑ traces Same point scatterer…
1 trace
Common shot (x = 0)
■
●■■■■■■■■■■■■■■■
∑ traces …different PSDM images!
1 trace
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
8
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?
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
9
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
10
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
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
11
Scattering Wavenumber K
Definition at a local “Scattering Object” (diffraction, reflection, ..)
Easy to calculate with ray tracing
and similar
Incident wavenumber
scattered wavenumber
Calculation performed in the
PSDM velocity model
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
12
K: which parameters?
geophone g
source s
- Vs: incident wave velocity
- Vg: scattered wave velocity
- ŝ and ĝ: unit vectors
-  frequency
K
ŝ
- VP: P-velocity
- VS: S-velocity
If Vs = Vg (no wave conversion)
ŝ
ĝ
● ●
●
”incidence” angle = 0
║ĝ – ŝ║ = 2
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K
ĝ
”incidence” angle ≠ 0
║ĝ – ŝ║ < 2
13
From K to PSF using FFT
X
-Kx max.
+Kx max.
-Kz max.
PSF
max./2
2D FFT-1
module
Green’s Functions
at one GF-node
no data!
●
Z
0
●
0.
●
Marmousi
●
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
14
2D FFT
K and scattering isochrones
K is perpendicular to the
scattering isochrone
║K ║ = f() : pulse effect
K corresponds to a local
plane wavefront
approximation of the
scattering isochrone
[K]
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
PSF
15
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
16
Resolution of an inverse problem!
Your model!
1 d
obs.
 G.m
Generalized Inverse
true
m
est .
Direct problem
 G .d
obs.
Inverse problem
d: data
m: parameters
obs.: observed
est.: estimated
1+2 m
g
Resolution!
est .
g
 (G G).m
true
g
RG G
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
17
 R.m
true
Data independent!
2
K and resolution: wavenumber coverage
[K] for [5-60] Hz
Marmousi model
Courtesy of IFP
qs = [0-10] º
DKZ
DKx
1
Lateral resolution ~ 2 / DKX
Vertical resolution ~ 2 / DKZ
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
18
PSDM of point scatterer and PSF
K
Kmean
low R
Common offset (0 m)
PSF
PSDM – data from point scatterer
high R
K and PSF: no data!
K
Kmean
high R
low R
Common shot (x = 0)
PSF
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
19
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
20
K and reflection
”P-to-P” reflection
From source
”P-to-S” reflection
From source
To geophone
qs
qg
incident ray
To geophone
qs
qg
reflected ray
qs incidence angle
qg scattering angle
Reflector
Reflector
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.
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
21
K and illumination: dip
[K] for [5-60] Hz
Marmousi model
Courtesy of IFP
qs = [0-10] º
Marmousi Model
Courtesy of IFP
2
~ 45 º
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
22
Illuminated dips
~ 25 º
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
23
Playing with the pulse
[K]
Target model (Vp)
120 Hz
Reflectivity
0 Hz
Spectrum
10 Hz
SimPLI
20 Hz
30 Hz
SimPLI
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
SimPLI
24
40 Hz
SimPLI
Illumination and resolution: illustration
FFT+1
Fault
“Green’s Functions”
Reflectivity = 1
[K] incl. 20 Hz pulse
FFT-1
FFT-1
Fault
Fault
SimPLI – 0 km offset
PSF
0 km offset
FFT-1
FFT-1
Fault
Fault
SimPLI – 4 km offset
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
4 km offset
25
PSF
Incidence-angle in PSDM
Reflectivity
Reflectivity:
Reflectivity:: 35°-45°
25°-35°
00°-05°
05°-15°
15°-25°
[K]
[K] Filter
Filter:: 35°-45°
00°-05°
05°-15°
15°-25°
25°-35°
Σ
Final SimPLI Image – 20 Hz
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
SimPLI Image: 25°-35°
15°-25°
00°-05°
05°-15°
35°-45°
26
Overburden effects
A●
B●
Not illuminated!
Good resolution
Good illumination
K
Poor resolution
Bad illumination
PSF
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
K
27
PSF
PSDM images: not a simple 1D convolution!
This is PSDM effects!
No illumination effects!
Elastic impedance (x,z)
“1D” PSDM
2D Filter: 0 km offset
KX
KX
KZ
KZ
!
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
2D Filter: 4 km offset
KX
KZ
Function of survey,
overburden, pulse, wavephases, local velocity.
28
Content
• Introduction
• Image formation in PSDM
• Scattering wavenumber: the key!
• Resolution
• Illumination
• Examples
• Controlling imaging
• Conclusions
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
29
Image and survey sampling
Dshot: 12.5 m
K
Dshot: 125 m
K
Dshot: 625 m
K
PSF
PSF
PSF
SimPLI
SimPLI
SimPLI
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
30
Controlling imaging: check local K!
”blind!”
automatic corrections
Irregular
Sampling!
Blind!
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
Controlled!
31
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
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
32
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 
2006 SEG 76th Annual Meeting – 10/5/2006 – SPMI6-6
33