1. M-OSRP Objectives
To address and solve prioritized seismic E&P challenges
(isolated task sub-series, intrinsic and circumstantial nonlinearity, and purposeful perturbation)
Arthur B. Weglein
M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007

2. Seismic Challenges Why challenges?
Seismic goals are basically unchanged, therefore
Methods bumping into assumptions are the source of these challenges;
Deep water, complex media and boundaries.

3. Introduction
In this introduction we explain how the strategy/plan behind the M-OSRP program (and its projects) represents an effective response to a suite of pressing seismic challenges

4. A research strategy responding to pressing challenges requires:
Defining the challenges and their priority; and,
Developing methods that can
Address the pressing issues.
Avoid the pitfalls of previous approaches that failed

5. When assumptions are not satisfied methods can fail.
Two responses :
(1) develop new procedures to
improve the satisfaction of
assumptions, requirements
and prerequisites; and
(2) develop new methods that
totally avoid the assumptions
that impede current capability.

6. We recognize the value in each type of response and adopt distinctly different attitudes for different issues:
1. Help improve requirements
e.g., recorded data collection/extrapolation.
- we cannot (yet) develop a method that avoids this requirement for seismic data.
- hence, we seek to help satisfy that requirement.

7. 2. For subsurface information, e.g. velocity,
-We recognize that it is:
Difficult to progress that requirement for level of detail and accuracy required under complex conditions.
There is a comprehensive framework with the potential to avoid that prerequisite

8. The inverse scattering series represents a
set of unique opportunities and properties:
1. Multi-D
2. Direct inverse – neither optimization nor objective functions
3. Comprehensive – inputs primaries and multiples
4. Transparency
5. Can accommodate any form or type of a priori information and/or absence of a priori information

9. The inverse scattering series represents a
set of unique opportunities and properties:
1. Multi-D
2. Direct inverse – neither optimization nor objective functions
3. Comprehensive – inputs primaries and multiples
4. Transparency
5. Can accommodate any form or type of a priori information and/or absence of a priori information
Impressive, but taken on its own, will not be an effective response to the challenge.

10. To recognize and avoid the pitfalls of previous attempts to respond to these challenges requires the introduction of a set of additional concepts:
Tasks within the series
Isolated task specific subseries
Purposeful perturbation
Model-type independent subseries
A specific order to the achievement of these tasks
The inverse scattering series plus these five concepts represent an effective response.

11. This strategy avoids the need for subsurface information but heightens the need for the completeness and definition of the seismic experiment.
Requires:
Data
Source signature in water and
Deghosted data
Hence, the latter represent critical projects in our program and strategy.

12. M-OSRP Projects Data interpolation/extrapolation
Deghosting and wavelet estimation
Beyond attenuation: internal multiple elimination
Depth imaging without the velocity model
Direct improved estimation of changes in elastic properties and
density
Implementation of the inverse scattering
series internal multiple attenuation and free surface multiple
elimination algorithms: code development project
Towards Q compensation without an adequate Q estimate:
the inverse scattering series in an anelastic world

13. The inverse scattering series
…direct inversion based on scattering theory

14. The inverse scattering series
…direct inversion based on scattering theory

15. Seismic data and processing objectives
Intrinsic and circumstantial non-linearity
The inverse scattering series is the only direct multidimensional method which deals with either intrinsic or circumstantial non-linearity separately or in combination
The ability to achieve processing objectives without knowing or determining propagation properties of the earth

16. Non-linear inversion for a single reflector
1-D Normal Incidence Example c0 c1

17. Two parameter 2D acoustic inversion
1D acoustic two parameter earth model
(bulk modulus and density or velocity and density)

18. Two parameter 2D acoustic inversion
The 3D differential equations:
Then
Where

19. Inverse Scattering Series
Linear
Non-linear

20. Two parameter 2D acoustic inversion For 1D acoustic earth model
Solution for first order (linear)

21. Two parameter 2D acoustic inversion
Relationship of is shown in the fig.1. z
Fig.1

22. Two parameter 2D acoustic inversionx
One interface model a z
Fig. 2

23. Two parameter 2D acoustic inversion
“Linear migration-inversion”

24. Two parameter 2D acoustic inversion
Solution for second order (first term beyond linear)

25. Two parameter 2D acoustic inversion
1. The first 2 parameter direct non-linear
inversion of 1D acoustic medium for a
2D experiment is obtained.

26. Two parameter 2D acoustic inversion
2. Tasks for the imaging-only and inversion-only within the series are isolated.

27. Two parameter 2D acoustic inversion
3. Purposeful perturbation.

28. Two parameter 2D acoustic inversion
4. Leakage.

29. Two parameter 2D acoustic inversion
(velocity and density)
Solution for second order (first term beyond linear)

30. Two parameter 2D acoustic inversion
1. Leakage and a special parameter

31. Two parameter 2D acoustic inversion
2. Purposeful perturbation

32. The pressing challenge of seismic E&P:
Imaging and target identification beneath complex, ill-defined media

33. The pressing challenge of seismic E&P:
Imaging challenges derive from assumptions behind velocity and imaging algorithms…
…inadequacies in either/both can cause failure or mislocated targets

34. A model of the imaging challengeU D R
When the wave experiences a complex medium and/or a complex boundary the resulting wave response is complex.
Complex = D R U

35. A model of the imaging challenge
D and U under complex conditions are approximated by simple forms d and u
Complex = dR u
R = d-1 complex u-1
Therefore, R is complex and the image beneath the salt is a fog.
The removal of multiples is also a problem in complex and ill-defined media

36. Two approaches Avoid the assumptions behind current imaging algorithms
Improve current methods; satisfy prerequisites.
Indirect
-model matching
-CFP
-CRS
-optimal offset traj.
-flat common image
gathers
Avoid the assumptions behind current imaging algorithms
Direct
-M-OSRP/inverse
scattering series

37. …based on non-linear multiplication of events
Multiple removal
…based on non-linear multiplication of events FS WB
Salt
Target

38. Mississippi Canyon example
Input
Predicted
multiples (2D)
Output
Input
Predicted
multiples (2D)
Output
1.7
3.4
Seconds
Water
bottom
Top salt
Base salt
Internal
multiples
Common Offset Panel (1450 ft)
Common Offset Panel (2350 ft)

39. Imaging of primaries
…the deepest primary is imaged through non-linear multiplication of shallower primaries, without any subsurface information FS WB
Salt
Target

40. Let’s first examine the 1D normal incidence acoustic case to get a hint at how to go to more complex models.
where αn is nth order in the measured values of the data.

41. For an incident spike wave field,
The first equation is
and,
Non-linear AVO
Indication of mislocated reflector

42. For 1 reflector
Depth of water bottom

43. For 1 reflector (continued)
Water bottom is well-located

44. For 2 reflectors
Correct depth
Wrong depth

45. For 2 reflectors (continued)
Continue with the term with the integral in
Comes from integral

46. For 2 reflector (continued)
Relates to duration of velocity error problem
Relates to amplitude of the velocity error
Where the problem resides
From outside the integral

47. Imaging results of Shaw et al.
Vertically-varying models, 1 example at normal incidence and 1 example with offset

48. Normal incidence imaging results

49. Pre-stack imaging results

50. cascaded series in the data
Imaging Primaries:
cascaded series in the data
1-D Normal Incidence Example
Cascaded series means each term
in the imaging series is itself a series.
Choose c0(z)= constant and A(w)=1 here.

51. 1-D Normal Incidence Example
The inverse series:
Provides , order by order, in terms of the measured values of s
n is n-th order in the data, i.e., in the measured values of s

52. One Layer Example c0 c1 c0 xs xm a b
For a spike incident field

53. One Layer Example (cont’d.)
Substitute ys in the equation for a1

54. a1 c0 c1 c0
c0 < c1 a b’ b

55. One Layer Example (cont’d.)
The second term in the inverse series, 2 , is given by (in general)
And for the specific one-layer case

56. a2
d (z - b )
c0 > c1

57. The boxes serve two functions:
(1) Eliminate internal multiples
(2) Correct the amplitude of the a1+a2+... towards a
But they don’t correct the depth of the deeper reflector from b to b.
This depth correction is carried out by the terms

59. xs xm a b b b Forgetting about the issue of amplitude, we want
(c0<c1) xs xm a b b b

60. Therefore the shift is a power series in b-b’
Therefore the shift is a power series in b-b’. And b-b’ is a power series in R. Hence, imaging is a cascaded series in the data.

61. Extending the imaging algorithm
Fang Liu’s high-order imaging algorithm
Considering testing on field data need to extend to a model beyond a velocity-only varying acoustic model

62. where αn is nth order in the measured values of the data.

63. Fang Liu et.al.

64. Large contrast model with mild lateral variations

65. Salt model with rapid lateral variations

66. Imaging project Challenges derive from assumptions/limitations in:
Velocity determination
Imaging algorithms
-- two separate sets of challenges and how and where
within the series these two distinct, and sometimes coupled issues occur.

67. Stages: Recognize the potential Locate the potential
Gather-up the potential
Test and evaluate
Apply and determine place in the imaging toolbox
How hard does the series have to work to achieve
a certain goal?
The answer depends upon several factors. Among
them are:
Is the process time to time or time to depth?
Do you have reliable a-priori information (e.g., that there is a surface between water and air.)
what is the extent and magnitude of the issue being addressed.

68. Data and isolated task subseries
-- all wave theory methods want data collected on the measurement surface where wave theory predicts it has arrived.
-- frequency ( )
Free surface ( one at a time)
Internal multiple ( all frequencies of the data needed to predict one frequency of the internal multiple. However, that dependence is the same as needed for a FK migration with water speed.)
Pre-stack FK migration
surface data

69. Data requirements (For Imaging subseries )
Imaging appreciates low Kz in the data. The lower you can go in Kz, the greater the efficacy. The longer the offset and the lower the temporal frequency, the greater the derived benefit. (doesn’t require zero frequency data.)
As with FSMA, all inverse scattering series require the wavelet; the source wavelet … not the wavelet at depth.

70. Data requirements (For Imaging subseries )
You are trading information about the subsurface for a more complete and better defined acquisition.
Recent advances on generating data with specifically lower frequency content ( for mainly Basalt imaging Application ) and the advances in being better able to record those lower frequencies represent a contemporaneous development and opportunity