1. Annual Meeting and Technical Review
Mission-Oriented Seismic Research Program:
Annual Meeting and Technical Review
M-OSRP Annual Meeting
20-21 April, 2005
University of Houston

2. Introduction
1. Welcome
2. Program objectives, projects and
progress

3. Program Objectives seismic E&P challenges
To address and solve prioritized
seismic E&P challenges

4. Seismic E&P
The objective is to use reflected seismic data to make useful inferences about the subsurface; in particular, to locate and delineate hydrocarbon targets

5. Free-surface multiple
Categories of Events
Primary
Free-surface multiple
Internal multiple

6. Let’s discuss the meaning and relevance of a word that you will hear during these presentations:
Non-linear

7. A method (or seismic objective) is non-linear in a processing sense if a multiplication of data by data (and, in general, sums of such products) is required to achieve a given goal.

8. There are two kinds of non-linearity:
(1) Intrinsic
(2) Circumstantial
Intrinsic non-linearity is always
present while circumstantial depends
on your ability to bring accurate and
adequate information to a given
problem.

9. These two types can occur simultaneously.
The inverse scattering series is a
multidimensional direct inversion method that
addresses both types of non-linearity.

10. --It provides the only direct inversion
method for the intrinsic non-linearity
(e.g., non-linear AVO) with a known
overburden

11. --It provides the only direct method where only the situational non-linearity is the issue (e.g., migration without the correct velocity ) and internal multiple elimination with absolutely no subsurface information, whatsoever.

12. --It provides the only direct multidimensional
method where both types of non-linear
issues are present (e.g., non-linear AVO in
the presence of an unknown overburden)

13. In each of these cases it is unique in its ability,
and there is no other candidate method able
to achieve one of those isolated objectives,
let alone those in combination.

14. Although powerful and impressive, it has
prerequisites for useful, impactful application.
Among them:
The source signature in water;
Deghosted data;
Wave theory data collection
The inverse scattering series doesn’t directly
provide its own prerequisites.
The extinction theorem provides that
opportunity for (1) and (2).

15. Marine events didn’t experience the earth experienced the earthFS
no ghost
ghost
primaries + internal multiples
free surface multiples
primaries
internal multiples
locate
invert

16. Marine events Tools experienced the earth didn’t experience the earth
Green’s theorem
Scattering Series
experienced the earth
didn’t experience the earth FS
no ghost
ghost
primaries + internal multiples
free surface multiples
primaries
internal multiples
locate
invert

17. Before we go to the ISS, let’s take a look at
a few simple examples of these non-linear
ideas.

18. Consider the simplest seismic problem1 R
The reflection coefficient, R, is given in terms
of C0 and C1 as

19. Let

20. Hence C1-C0 is non-linear in R and no a priori
information circumstance about the target can
change that fact.
It is convenient in scattering theory to
characterize the difference between C0
and C1 as

21. Where for the one reflector problem the
relationship becomes
and is a number.
Given C0 and we can find C1, just as before
given C0 and we find C1.

22. The inverse problem (in this representation)
is to find (given C0) from R

23. Similarly equation (1) can be solved for
in terms of R and a Taylor series for R in
terms of results in
Hence, the simplest inverse problem to
imagine is non-linear.

24. Other issues and conditions that determine
form of linear or non-linearity in inverse
scattering processing
1. Type and extent of a-priori information
2. Whether the processing objective is output as data in time or as a function of space, x, y and z.

25. Consider multiples, ocean bottom multiples in particular
To illustrate issue 1
Consider multiples, ocean bottom multiples in particular
If you provide source character and location,
ocean bottom and ocean top properties, and
receiver properties and location, you can
predict the multiple and subtract it from your
data.
Ocean top S R
Ocean bottom

26. The method is linear in the data
Data without = data – predicted multiple
And a priori information is complete
In the free-surface multiple removal
method only a single piece of a priori
information is provided, the free surface,
and the algorithm is non-linear in the data

27. D = Df + Df2 + Df3 +∙∙∙ ∙∙∙ ∙∙∙
Where Df and D correspond to data with and without free surface multiple, respectively.
One term Df2 added to Df eliminates every multiple reflector at the free surface

28. The inverse scattering internal multiple removal method operates with absolutely no a priori information, whatsoever.
To eliminate one order of internal multiples (from all interfaces at once) requires an infinite series -- and the first term of that elimination series is an attenuator that has a specific cubic multiplicative communication of the entire data without free surface multiples.

29. That first term attenuator presents the exact time of every first order internal multiple (including converted waves) using only water speed of all primaries and internal multiples.
We can summarize the multiples, a priori information, and non-linearity relationship.

30. Multiples a priori information and the inverse scattering series
ocean bottom
complete
linear FS
partial
one non-linear term eliminates one order
internal multiple
none
non-linear series eliminate one order; first non-linear cubic term attenuates all first order; predicts correct time and approximate amplitude

31. The issue for multiple prediction is time and amplitude.
Primaries
The ultimate objective for imaging primaries in depth is a spatial map of reflectors where (at each point on the interface) a function is provided that provides either an image dependent reflection coefficient with respect to the normal to the reflector or, in general, a scattering operator, when the interface is, e.g., undulating or diffracting.

32. Given perfect overburden information this objective is achievable in a linear manner. Green’s theorem, Fourier methods and finite difference wave migration are among the linear imaging algorithms that can achieve that objective, with perfect overburden information.

33. The output for primaries requires a correctly located image in space and an exact amplitude function (of angle) at each point on the reflector.
In addition to imaging, the inversion objective for primaries is to determine medium property changes across the reflectors.
The fact that the input to inverse methods is data in time, makes the output in space of structure and parameter estimation more daunting than operations like multiple removal in time

34. Given perfect overburden information, the linear migration and/or migration – inversion will not correctly predict changes in material properties across the reflector
With an inadequate velocity model the output of linear migration –inversion will image at the wrong spatial location and will have overburden transmission errors added to the linear approximate value of the earth property changes
The first term in the inverse series is migration –inversion with the reference medium velocity.

35. The terms in the inverse series addressing intrinsic non-linearity are always turned on and ready to go.
In contrast, the terms in the series addressing circumstantial non-linearity decide whether their services are needed/required and only light up and go into action when the data decides an issue warrants an intervention.
The latter properties represent the epitome of purposeful perturbation.

36. In the case of lack of a priori information internal multiple require an infinite series to predict the correct amplitude, the first term has the correct time and the approximate amplitude.
In contrast, the first term in the imaging series for primaries produces the conventional migration, with the wrong depth and the wrong amplitude. A cascaded series is required to achieve the exact depth; useful results are obtained using a leading order uncascaded portion of that imaging subseries.
Let’s take a look at the inverse-series now.

37. Scattering Theory Scattering theory is perturbation theory
Relates differences in media to differences in wavefield

38. Scattering Theory (cont’d.)
Inverse Series, V as power series in data, (fs)m

39. Four Tasks of Direct Inversion
(1) Free surface demultiple
(2) Internal demultiple
(3) Image reflectors at depth
(4) Determine medium properties

40. Concepts developed (1) Tasks within inversion (2) Subseries
(3) Purposeful perturbation

41. Intervention and the ISS for practical objectives
Isolated tasks (restatement of the problem).
Definition of events.
Time output --- G0 sandwich.
Extension to new definitions of primaries and multiples.

42. Intrinsic and circumstantial non-linearity
Intrinsic non-linearity and circumstantial non-linearity involve very different actions within the series
Circumstantial non-linearity to achieve a task without adequate a-priori information immediately triggers a call for a more inclusive and extensive data involvement in the non-linear communication than the corresponding task requires in the case of adequate a-priori information and linear processing. Furthermore, the same absence of a-priori information requires a different type of communication with the more inclusive data, depending upon whether you are addressing, e.g., a depth imaging or a target identification (AVO) problem.

43. A purely intrinsic non-linearity doesn’t require a more inclusive or extensive data set to achieve its task (in comparison to the corresponding linear case). It requires specific non-linear communication between the same data that produces the linear approximate
The first term in the inverse series is linear in the data (by definition). Hence, it is assuming that overburden a-priori information is adequate and that the intrinsic non-linear is replaceable by the linear approximate

44. The second term in the inverse series deals with both types of non-linearity, to quadratic order – the intrinsic is always on – and the circumstantial determines if the situation warrants its intervention, for both imaging and inversion

45. Is it a Primary or multiple?
Given an event
event t
Is it a Primary or multiple?

46. Given that the event is a primary
Depth image?
Non-linear AVO?
When the overburden is unknown

47. Model type Another expression you will encounter here is model type
Model type connotes the number and set of physical properties and their dimension of spatial variability, required to define your model
Our objective is to provide algorithms for field data application
Inverse-scattering multiple removal methods are independent of assumed earth model type
As we develop new methods for imaging and inverting primaries we examine the model type issue and progress the development and evaluation of concepts through a set of ever more complex and realistic models

48. Program agenda

49. Program agenda

50. Marine events didn’t experience the earth experienced the earthFS
no ghost
ghost
primaries + internal multiples
free surface multiples
primaries
internal multiples
locate
invert

51. Marine events Tools experienced the earth didn’t experience the earth
Green’s theorem
Scattering Series
experienced the earth
didn’t experience the earth FS
no ghost
ghost
primaries + internal multiples
free surface multiples
primaries
internal multiples
locate
invert