Method for 2D or 3D modelling of a heterogeneous medium such as the subsoil described by one or more physical parameters

• US 6,522,973 B1
• Filed: 10/30/2000
• Issued: 02/18/2003
• Est. Priority Date: 10/29/1999
• Status: Active Grant

• Current Assignee: Institut Francais Du Petrole
• Original Assignee: Institut Francais Du Petrole
• Inventors: Richard, Vincent, Mace-Prieur, Daniéle, Cuer, Michel, Tonellot, Thierry
• Primary Examiner(s): Lefkowitz, Edward
• Assistant Examiner(s): Gutierrez, Anthony
• Application Number:
  US09/698,164
• Time in Patent Office: 841 Days
• Field of Search: 702/16, 367/73
• US Class Current: 702/16
• CPC Class Codes: G01V 1/306 for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
• CPC Class Codes: G01V 11/00 Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00

Abstract

A method of obtaining a representative 2D or 3D model of a heterogeneous medium described by multiple physical parameters (such as the impedances of the subsoil in relation to P or S type waves, its density, etc.) from various data. An a priori model with multiple parameters formed from known or estimated isolated values of the physical parameters and the initial model is improved by minimizing a global cost function representative, on the one hand, of the differences between synthetic records giving the response of the current model and the seismic records obtained, and on the other hand of the differences between the current model and the a priori model. These differences are measured in the sense of norms deduced from the a priori information on the uncertainties relative to the data and to the model, and the information can vary from one point of the model to another. The invention has an application for characterization of hydrocarbon reservoirs.

Claims

1. A method of obtaining a 2D or 3D representative optimized model of a heterogeneous medium described by physical parameters or quantities, from recorded data corresponding to waves reflected by the medium and picked up by receivers coupled with the medium, in response to waves transmitted therein from a source, and from a priori information including data measured in situ, the method comprising:

constructing a 2D or 3D geometric model describing correlation lines or surfaces;

constructing a 2D or 3D multi-parameter a priori model described by the physical parameters, from the 2D or 3D geometric model and from data measured in situ for the physical parameters, at points of the medium;

modeling any uncertainty of the parameters and correlations thereof in the a priori model by a covariance operator which takes into account a degree of confidence variable at any point for all parameters of the a priori model; and

forming an optimum multi-parameter model by inversion of the recorded data which takes into account all the a priori information.

2. A method as claimed in claim 1, wherein:

the operator for modeling the uncertainties is a multi-parameter exponential covariance operator.

3. A method as claimed in claim 2, wherein:

the multi-parameter exponential covariance operator is variable according to location in the medium.

4. A method as claimed in claim 3, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 2D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected in a relation onto a tangent to a local correlation line.

5. A method as claimed in claim 3, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

6. A method as claimed in claim 5, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

7. A method as claimed in claim 5, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

8. A method as claimed in claim 3, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for one of a 2D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto the tangent to the local correlation line.

9. A method as claimed in claim 3, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

10. A method as claimed in claim 9, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

11. A method as claimed in claim 9, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to a priori model.

12. A method as claimed in claim 2, wherein:

the covariance model is a one of 1D model, 1D model along correlation lines, a 2D model, 2D model along correlation surfaces, or a 3D model.

13. A method as claimed in claim 2, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 2D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a tangent to a local correlation line.

14. A method as claimed in claim 2, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

15. A method as claimed in claim 14, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

16. A method as claimed in claim 14 wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm. L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

17. A method as claimed in claim 2, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for one of a 2D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto the tangent to the local correlation line.

18. A method as claimed in claim 2, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

19. A method as claimed in claim 18, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

20. A method as claimed in claim 18, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

21. A method as claimed in claim 2, wherein:

the medium is a subsoil zone and in situ measurements are obtained at depths of the subsoil in at least one well through the zone.

22. A method as claimed in claim 2, wherein:

the waves transmitted in the medium are elastic waves.

23. A method as claimed in claim 2, wherein:

the waves transmitted in the medium are electromagnetic waves.

24. A method as claimed in claim 1, wherein:

the covariance model is a one of 1D model, 1D model along correlation lines, a 2D model, 2D model along correlation surfaces, or a 3D model.

25. A method as claimed in claim 24, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 2D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a tangent to a local correlation line.

26. A method as claimed in claim 24, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

27. A method as claimed in claim 26, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

28. A method as claimed in claim 26, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

29. A method as claimed in claim 24, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for one of a 2D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto the tangent to the local correlation line.

30. A method as claimed in claim 24, wherein:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

31. A method as claimed in claim 30, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

32. A method as claimed in claim 30, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

33. A method as claimed in claim 1, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium.

34. A method as claimed in claim 33, wherein:

the medium is a subsoil zone and in situ measurements are obtained at depths of the subsoil in at least one well through the zone.

35. A method as claimed in claim 33, wherein:

the waves transmitted in the medium are elastic waves.

36. A method as claimed in claim 33, wherein:

the waves transmitted in the medium are electromagnetic waves.

37. A method as claimed in claim 15, wherein:

the covariance operator is anisotropic with different correlation lengths in different directions in the medium.

38. A method as claimed in claim 37, wherein:

the medium is a subsoil zone and in situ measurements are obtained at depths of the subsoil in at least one well through the zone.

39. A method as claimed in claim 37, wherein:

the waves transmitted in the medium are elastic waves.

40. A method as claimed in claim 37, wherein:

the waves transmitted in the medium are electromagnetic waves.

41. A method as claimed in claim 1, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 2D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected in a relation onto a tangent to a local correlation line.

42. A method as claimed in claim 41, wherein:

the medium is a subsoil zone and in situ measurements are obtained at depths of the subsoil in at least one well through the zone.

43. A method as claimed in claim 41, wherein:

the waves transmitted in the medium are elastic waves.

44. A method as claimed in claim 41, wherein:

the waves transmitted in the medium are electromagnetic waves.

45. A method as claimed in claim 1, wherein:

formation of the optimum multi-parameter model is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to a square of the norm L² of the difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand of the square of the norm L² of the difference in relation to the a priori model and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

46. A method as claimed in claim 45, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

47. A method as claimed in claim 45, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

48. A method as claimed in claim 1, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for one of a 2D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto the tangent to the local correlation line.

49. A method as claimed in claim 1, comprising:

modifying the covariance operator to define differences in relation to the a priori model for other physical parameters, so that the differences are independent at any point of the medium, the formation of the optimum model with parameters being obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of a norm L² of a difference between synthetic data and the recorded data, and a term relative to the medium, for a 3D model, on one hand, of the square of the norm L² of the difference in relation to the a priori model expressed by the other physical parameters and, on another hand, of the square of the norm L² of a gradient of the difference in relation to the a priori model, projected onto a plane tangent to a local correlation surface.

50. A method as claimed in claim 49, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model, a norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

51. A method as claimed in claim 49, wherein:

for a 3D a priori model, a term relative to the medium is proportional to the square of the norm L² of the difference in relation to the a priori model measured in relation to other physical parameters, the norm L² of the gradient of the difference in relation to the a priori model and the square of a Laplacian operator of the difference in relation to the a priori model.

52. A method as claimed in claim 1, wherein:

the medium is a subsoil zone and in situ measurements are obtained at depths of the subsoil in at least one well through the zone.

53. A method as claimed in claim 1, wherein:

the waves transmitted in the medium are elastic waves.

54. A method as claimed in claim 1, wherein:

the waves transmitted in the medium are electromagnetic waves.