AVO, migration apertures Fresnel zones, stacking, Q, anisotropy, and fast inversions

1
AVO, migration apertures Fresnel zones, stacking,
Q, anisotropy, and fast inversions

• John C. Bancroft and grad students
• University of Calgary
• CREWES 2003

NSERC
2
Grad students

• Shuang Sun
• Pavan Elapavuluri
• Kun Liu (and Hugh Geiger)
• John Millar
• Xiang Du
• Zhihong (Nancy) Cao
• Chunyan (Mary) Xiao

3
Outline

• Differentiators
• Fresnel zones AVO migration apertures
• Q
• Wavefield extrapolators
• Multiples and radon transforms
• Inversion

4
Digital differentiator

• Accuracy
• Speed
• Beauty
• (1, -1)
• 1, 0, -1) better
• Theoretical shape?

5
Inverse FFT of (j?)
6
Derivative assumes

• Maximum bandwidth
• Ideal interpolator
• Sinx/x operator
• Derivative of sinx/x

SincFn.m
7
Shuang Sun

• Stacking specula energy
• Fresnel zone for offset and dipping reflectors
• Balanced AVO in areas of poor geometry
• Caution model based migration

One hoarsepower
What is the basic unit of laryngitis?
8
What size hole can we see with seismic?
9
What happens at the edge of a reflector?
10
Fresnel zone

• Fresnel Size
• frequency
• depth
• velocity

Claerbout
11
Depends on the size of the Fresnel radius
Only for stacked data!!!
12
Analytic function for zero-offset case(no
wavelet)
Solution to the acoustic wave equation for
zero-offset, the diffraction response can be
written as
Diffraction operator D0
te minimum two-way travel time to the
edge of the reflector tt-te time measured
after onset time te ?e angle between the
normal to the reflector and raypath of the
minimum travel time to the edge of the
reflector.

Berryhill, 1977
13
Diffraction amplitude
Amplitude
Time
Angle
14
Diffraction amplitude
15
Scaled amplitude (evaluate phase)
16
Fresnel zone with Ricker wavelet source
Source signature with dominant frequency 50hz
Reflected signal amplitude
17
Fresnel zone with fixed bandwidth
Frequency from 0-120 hz
Frequency from 0-150 hz
18
Reflector smaller than Fresnel zone width 50m
19
Reflector width 1000m
20
Amplitude (no wavelet)
21
Diffraction modelling
22
Valid area for AVO
23
Comments

• Locations for AVO analysis before migration
  should be at least a Fresnel radius away from the
  target edge.
• The amplitudes will be in error if the target
  size is smaller than or equal to the Fresnel
  zone.
• Wavelet will contribute to the size of
  contamination area.
• Only zero offset was considered
• Should consider a prestack migration to perform
  AVO analysis.

24
Offset traveltime
2h
DSR eqn.
25
Cheops pyramid - DSR eqn.
Hyperbola CMP at T0 Zero off.
DSR eqn. Const. Off CMP gath.
26
Prestack data, flat 7 Cheops .
Specula energy
27
Reflections from dipping event
Reflecting element
28
Prestack data, dipping... Cheops p.
29
Cheops summation specula energy
Fresnel zones
30
Prestack Fresnel zone horizontal layers
31
P. S. Fresnel zone for dipping event
32
Contours equal angle of incidence
Angle 2
Offset increases with x
Angle 1
33
Constant offset migration
34
What about dipping specula energy?
Smear of dips
Still OK ???
35
CMP gather
36
Limited aperture EO gather
37
Comments

• Prestack specula energy can be identified,
• horizontal and dipping
• Limited aperture
• faster, better SNR, may preserve amplitudes
• Optimum size of a super-CMP gather can be defined
  using Fresnel zones
• Should use prestack migration gathers for AVO
• Use model based migration with caution

38
Comments

• Constant offset migration
• smears AVO energy (OK)
• requires velocity information
• EOM
• also smears AVO energy (OK)
• Stacking within the Fresnel zone may reduce
  acquisition geometry artifacts

39
Pavan Elapavuluri

• Q

One microscope
What is one millionth of a mouth wash?
40
Wavelets with varying Q and Time

• Build Q wavelet table Q, time
• Q 30, 50, 70, 90, 110,
• T 0 to 6.0 sec
• Cross-correlate (coherence) trace with all
  wavelets
• At a given time, peak corresponds to Q

41
9 wavelets
T1000
T5000
T3000
Q90
Q70
Q50
42
3 Spikes on trace Q 70
43
Noise on trace Q 70
44
Kun Liu (and Hugh Geiger)

• Wavefield extrapolation

What is 2000 pounds of Chinese soup?
Won ton
45
Input
46
200m depth extrapolation with adaptive taper
47
Xiang Du

• Finite element method integrated with
• Finite difference migration

A semicolon
What is half a large intestine?
48
Comparison FE-FDM with FX-FDM
Result of FE-FDM
Result of FX-FDM (SU)
49
Trace comparisons
50
Steep oblique model
Velocity model
Seismic section
51
Comparison of methods
Result of FE-FDM
Result of FX-FDM (SU)
52
Runtime and memory requirements

• FE-FD 26 secs 2.2 meg
• FK-FD 31 secs 1.3 meg.

53
Chunyan (Mary) Xiao
Zhihong (Nancy) Cao

• Tutorials
• Review of Multiple suppression techniques
• Multiple attenuation using the Radon transform

A kilohurtz
What is one thousand aches?
54
after Kabir and Marfurt, 1999
55
Semblance plot is a Radon transform
56
Lorraine Bloom
David Henley
Larry Lines
The model and inverse
57
Modelling process
Inversion expert
58
The Model (Not the inverse)
59
The Inverse
60
The artifacts (of inversion)
After inversion
Before modelling
61
Of course, some things are easier to model
and invert.
62
Inversion

• Mathematical process
• Used in many geophysical applications
• decon., statics, tomography, tau-p,
• Geophysical terminology
• Estimation of rock properties
• Modelling lt-gt Inversion

63
Millar time

• Multigrid inversion
• Borrowed from fluid dynamics
• Recursive
• Variable grid size
• Solutions are frequency dependent
• Fast

Eskimo pi
What is the ratio of an igloos circumference to
its diameter?
64
(No Transcript)
65
Iterative solution
66
Laplaces equation
67
Variable grid size
68
Analogous to FFT ???
69
Sorting a 2-D array into a vector
70
(No Transcript)
71
Extractions, smoothings and interpolations
S Solution with one iterative step
33x33
17x17
Pass defects down and errors up
72
Performance
73
Conclusions

• Migration apertures speed, SNR, balanced
  amplitudes
• CMP AVO consider Fresnel zones
• Finite element / Finite difference migration
• Multiples and Radon transforms
• Q and differential operators
• Multi grid inversions

74
The end
75
(No Transcript)