Innovative Solutions for Seismic Challenges

1. Mission-Oriented Seismic Research Program Annual Meeting & Technical Review May 10, 11 and 12 th, 2006 University of Houston

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

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

4. 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.

5. 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

6. 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

7. 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.

8. 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.

9. 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

10. 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

11. 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.

12. 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.

13. 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.

14. 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

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

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

17. 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

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

19. Two parameter 2D acoustic inversion 1D acoustictwo parameterearth model (bulk modulus and density or velocity and density)

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

21. Derivation of the inverse series In actual medium: In reference medium: Perturbation: L-S equation: Forward scattering (Born) Series:

22. Inverse Scattering Series Linear Non-linear

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

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

25. Two parameter 2D acoustic inversion x 0 One interface model a Fig. 2 z

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

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

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

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

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

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

32. One parameter 2D acoustic inversion (velocity) Solution for second order (first term beyond linear)

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

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

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

36. Imaging and inversion of primaries 1-D Normal Incidence Example Choose c0(z)= constant and A()=1 here.

37. 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

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

39. a1 c0 c1 c0 c0 <c1

40. One Layer Example (cont’d.) a2 The second term in the inverse series, 2 , is given by (in general) And for the specific one-layer case

41. a2 d (z - b ) c0 >c1

42. One Layer Example (cont’d.) a1 Substitute ysin the equation fora1

43. The boxes serve two functions: (1) Eliminate internal multiples (2)Correct the amplitude of thea1+a2+... towardsa But they don’t correct the depth of the deeper reflector from b to b. This depth correction is carried out by the terms

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

46. 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.

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

48. 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

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

50. 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