1. Responding to pressing seismic E&P challenges
Arthur B. Weglein
M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007
M-OSRP report pages: 1-11

4. Seismic E&P challenges
Methods make assumptions; when they are satisfied the methods are effective and when they are not satisfied the methods have difficulty and/or fail – challenges arise from that breakdown or failure.

5. Seismic E&P challenges
Among assumptions:
acquisition
compute power
innate algorithmic shortcomings

6. Seismic E&P challenges
There are simple 2D acoustic examples where either:
The velocity cannot be accurately determined,
or,
The imaging algorithm breaks down with a
perfect velocity and more complete acquisition
or faster computers are not the solution.

7. How to address challenges?
Two ways:
Remove the assumption violation by satisfying the assumptions; or
Avoid the assumption violation by deriving methods that do not make those assumptions.
Either of these are reasonable and indicated
under different circumstances.

8. Cataloging seismic events
Reference wave field:
These two events have not reflected from the earth.

9. Cataloging seismic events
Ghosts:

10. Cataloging seismic events
Seismic reflection data:
After we remove/separate the reference wave
and ghosts, all remaining events are classified
as primaries or multiples.
free-surface
multiple
primary
internal multiple

11. Cataloging seismic events
Primary: the energy arriving at the receiver has
experienced one upward reflection.
Multiple: the energy arriving at the receiver has
experienced more than one upward reflection.
Free-surface multiples:
Multiples that have experienced at least one downward
reflection at the air–water or air–land surface ( free
surface ).
internal multiples:
Multiples that have all of their downward reflections below
the free surface.

12. The M-OSRP role and strategy
M-OSRP has a history of addressing (and
continues to address) innate algorithmic
assumption violations in the area of
multiples, wavelet estimation and
deghosting.

13. The M-OSRP role and strategy
The inverse scattering series has the potential
and promise of providing a superceding vision
and capability in the area of seismic imaging
and inversion.
The goal is to provide accurate seismic images
at depth where current imaging methods
either produce an inaccurately located image
or no image at all.

14. The M-OSRP role and strategy
There are different types and degrees and
categories of issues that arise as you:
move from one to higher dimensions; and,
move from a one parameter to a two parameter
acoustic, to a three parameter elastic or anelastic
earth.

15. Issues Issues in traditional velocity analysis & imaging:
There are imaging challenges that arise when you are trying
to determine the velocity; and other issues that arise when
you are trying to image through a known velocity.
Our Issues:
are issues that arise; and, the inverse series addresses,
when you set about to correctly and directly depth image
without the velocity.

16. 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.

17. Stages Recognize the potential Locate the potential
Gather-up the potential
Test and evaluate
Apply and determine the place in the
imaging toolbox

18. How hard does the series have to work to achieve a certain goal?
-- The answer depends upon several factors. Among
them are:
Is the goal time to time or time to depth?
Do you have reliable a-priori information
(e.g., that there is a free surface between
water and air.)
What is the extent and magnitude of the
issue that needs to be addressed?

19. 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 )

20. Data requirements Imaging subseries appreciates low in the data.
The lower you can go in , 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.
You are trading information about the subsurface
for a more complete and better defined acquisition.

21. Data requirements Recent advances on generating data with specific-
ally lower frequency content ( for mainly Basalt
imaging application ) and the advances in being
able to record those lower frequencies represent
an important contemporaneous development and
opportunity.

22. Imaging Status To-date, the M-OSRP imaging effort has collected
terms ( that address certain issues ) for a multi-
dimensional velocity only varying acoustic medium.
There are more imaging issues to address within the
latter acoustic model. But the partial imaging capture
is a cascaded infinite series of terms that sum to a
closed form which computes in essentially the time
of a single pre-stack FK migration, at water speed.

23. Our Strategy Our strategy is several fold:
Extend that current acoustic capture to elastic
media;
Broaden the net of captured imaging issues and ability within the acoustic model.
When the former is achieved, we are heading to field data
testing and evaluation;
Why do you need to extend to elastic first – before you go
to field data?
Among other advances and highlights in this technical
review we will describe how we are approaching the latter
problem.

24. Agenda (Tuesday, June 5th)
8:30 A.M. Continental Breakfast
9:00 A.M. Opening remarks: Welcome
Arthur B. Weglein
9:05 A.M. Overview: Exploration goals and types of challenges, M-OSRP Program goals; M-OSRP Annual Technical Review and Meeting progress, status, plans and open issues
Tutorial: a tutorial on wave theory and integral equation formulations
10:30 A.M. Coffee Break
10:40 A.M. Review of Green's theorem deghosting algorithm:
Jingfeng Zhang and Arthur B. Weglein
11:40 A.M. Lunch
12:40 P.M. Remarks on Green’s theorem for seismic interferometry.
Adriana C. Ramírez and Arthur B. Weglein
Data-driven regularization/extrapolation using interferometry with the direct wave.
Adriana C. Ramírez, Ketil Hokstad (Statoil) and Einar Otnes (Statoil).
2:20 P.M. Coffee Break
2:35 P.M. Developing an effective response to seismic E&P challenges: isolated task sub series, intrinsic and circumstantial nonlinearity, and purposeful perturbation
(Please note that the originally scheduled presentation by A.C. Ramirez, K.H. Matson (BP) and R. Johnson (BP) was withdrawn since the permission to show BP field data did not arrive by the meeting date.)

25. Agenda (Wednesday, June 6th)
8:30 A.M. Continental Breakfast
9:00 A.M. Relationship between ISS free surface multiple removal and wave-field deconvolution,
Adriana C. Ramírez and Arthur B. Weglein
9:30 A.M. ICA and adaptive subtraction of free surface multiples: Sam Kaplan
10:10A.M. Coffee Break
10:20 A.M. 3D free surface multiple elimination and summation in the cross- line conjugate domain: Kristopher Innanen, Sam Kaplan, and Arthur B. Weglein
11:00 A.M. Progressing the development of inverse scattering series direct, non-linear Q compensation and estimation procedures: extending linear inversion to multidimensional media: Kristopher Innanen, Jose Eduardo Lira, and Arthur B. Weglein
11:40 A.M. Lunch
12:30 P.M. Inverse scattering internal multiple elimination
Adriana C. Ramírez, Simon A. Shaw (ConocoPhillips) and Arthur B. Weglein
1:10 P.M. Inverse Scattering Series and Q: Response of the Internal Multiple Attenuation Algorithm to Absorption and an Application to Bulk Q-estimation:
Jose Eduardo Lira, K. Innanen and Adriana C. Ramirez
2:30 P.M. A comparison of run times for the 2D M-OSRP inverse scattering internal multiple code, and for FFTs on a set of different traditional industry architectures and newer architectures, including Cell: M Perrone (IBM)
3:15 P.M. Coffee Break
3:25 P.M. What does linear in the data mean? It’s necessary to take a closer look?
Arthur B. Weglein
4:25 P.M. How to accurately prepare the linear term?
Fang Liu
5:00 P.M. BBQ and beer at HSC 102

26. Agenda (Thursday, June 7th)
8:00 A.M. Continental Breakfast
8:30 A.M. Analysis of the imaging closed forms
Jingfeng Zhang, Fang Liu, Kristopher Innanen, and Arthur B. Weglein
9:20 A.M. Inverse Scattering imaging algorithms directly producing flat amplitude undamaged common image gathers at the right depth without the velocity: Fang Liu
10:20 A.M. Steps towards increased imaging capability and field data application
Arthur B. Weglein, Kristopher Innanen, Bogdan Nita, Adriana C. Ramirez, Jingfeng Zhang, Fang Liu, Shansong Jiang, and Einar Otnes
11:10 A.M. Coffee Break
11:20 A.M. Model type independent contributions in the inverse scattering series for processing primaries: Adriana C. Ramírez, Bogdan G. Nita, Arthur B. Weglein and Einar Otnes
11:50 A.M. Imaging the wave-field at depth without the velocity…forward and inverse diagrams point the way: Bogdan G. Nita, Adriana C. Ramírez, Arthur B. Weglein and Einar Otnes
12:30 P.M. Lunch
1:20 P.M. Progressing 1D elastic media imaging by using inverse scattering series: analytical PP-data preparation and constant velocity migration
Shansong Jiang, Fang Liu, Jingfeng Zhang, Arthur B. Weglein
3:00 P.M. Coffee Break
3:15 P.M. Towards velocity independent collapsing of diffractions: early stage concepts and approximations: Kristopher Innanen
4:00 P.M. Summary and Plan; Meeting Adjournment: Arthur B. Weglein
4:20 P.M. Advisory Board Meeting
7:00PM Fogo de Chao Dinner

27. Agenda (Tuesday, June 5th)
8:30 A.M. Continental Breakfast
9:00 A.M. Opening remarks: Welcome
Arthur B. Weglein
9:05 A.M. Overview: Exploration goals and types of challenges, M-OSRP Program goals; M-OSRP Annual Technical Review and Meeting progress, status, plans and open issues
Tutorial: a tutorial on wave theory and integral equation formulations
10:30 A.M. Coffee Break
10:40 A.M. Review of Green's theorem deghosting algorithm:
Jingfeng Zhang and Arthur B. Weglein
11:40 A.M. Lunch
12:40 P.M. Remarks on Green’s theorem for seismic interferometry.
Adriana C. Ramírez and Arthur B. Weglein
Data-driven regularization/extrapolation using interferometry with the direct wave.
Adriana C. Ramírez, Ketil Hokstad (Statoil) and Einar Otnes (Statoil).
2:20 P.M. Coffee Break
2:35 P.M. Developing an effective response to seismic E&P challenges: isolated task sub series, intrinsic and circumstantial nonlinearity, and purposeful perturbation
(Please note that the originally scheduled presentation by A.C. Ramirez, K.H. Matson (BP) and R. Johnson (BP) was withdrawn since the permission to show BP field data did not arrive by the meeting date.)

28. Tutorial: Wave theory and integral equations.
Arthur B. Weglein
M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007
M-OSRP report pages

29. Theory
Consider an acoustic homogeneous whole-space with a single point source at and
( , )
(1)
The causal solution to this equation is

30. Theory With causal (physical) solution
If we have several point sources at ( , ) (i=1,2…N) with weight , the d.e. is
With causal (physical) solution

31. For a continuous distribution of sources ,
The d.e. is
(2)
and the causal solution to this equation is
(3)

32. If you have (and include) all of the sources in space and time that produce a wavefield then equation (3) is the solution for all and .
In the frequency domain,
(4)
Right hand side integrates over all space, left hand side is valid in all space.

33. If you include all the sources in your problem, then equation (3) and (4) indicate that the physical solution requires neither boundary nor temporal (initial) conditions.
The latter is based on linear superposition and causality ( and will lead to the scattering equation ).
(3)
(4)

34. Key questions
What if you are not interested in the wavefield everywhere (but only in a given specific region of space)?
Can we work out some kind of deal or compromise on what is required?
Can we provide less if we are requesting less?

35. Answers?
Superposition and causality cannot reach a compromise… it is an inclusive view:
It includes all sources, and,
It provides the solution everywhere.
We need to start with Issac Newton and the Fundamental Theorem of the Integral Calculus to find an asking for less and providing less attitude.

36. Two principles: (5) Linear Superposition
Fundamental Theorem of the Integral Calculus
Newton Leibnitz
Gauss
Green
(5)

37. Green’s theorem In
(5) let and

38. Green’s theorem where and satisfy:
And (5) has a volume V bounded by a surface S.

39. If you choose in V, and , then (6) becomes
(7)
If and in the surface integral correspond to the
boundary conditions for a causal ,then the left hand side is in V.

40. The field at inside V is a physical quantity and
observable and cannot depend on the math you use to compute
Therefore, from equation (4) and (6)
anywhere
in V

41. all space = U = V + ( U - V )
U = universe, V= volume, U-V= outside V
Therefore, for in V, the surface integral will be

42. Therefore,
for in V represents the contribution to the field P inside
V due to the sources outside V.

43. If there are no sources outside V, then the surface integral will be zero for in V.
Spatial boundary conditions in a wave theory problem indicate that there are sources that generate the wave that haven’t been taken explicitly into account but will nevertheless influence the solution.
Sources everywhere, including those outside V, impact the field P at any point, including points inside V.

44. Since the surface integral depends on and from all the sources in U, another way of explaining the latter condition is the surface integral for in V eliminates the portion of the field due to sources in the volume V.
In the time domain,
for any and any t.

45. And from Green’s theorem in and t , for in V and t > 0
(8)
The same is true when both space and time are truncated or
limited in accounting for influences on the wavefield.

46. Equation (8) has three terms on the right-hand-side: (1) the
first term represents the explicit contribution due to sources
within V within the time interval 0 to ( );
(2) The second term represents the influence of sources
outside of V on the field inside of V, where those external
sources are only accounted for from 0 to ; and
(3) the third term represents the influence of all sources before time is 0 which contribute to the field inside the volume at time t. No sources which activate after t can influence the field at t.

47. If in equations (6) and (8), one choose , then
the surface term will be active and non-zero whether or not
there are external sources. The general purpose of surface
contributions is to fix what is missing or in error in the
volume integral.

48. These integral equations form the basis for all of the
methods we pursue within M-OSRP
Deghosting
Wavelet estimation
Direct wave elimination
Wavefield retrieval and interferometry
Inverse scattering series
-- multiple removal
-- depth imaging
-- non-linear direct AVO
-- Q compensation without Q