NMR log processing using wavelet filter and iterative inversion

• US 6,225,803 B1
• Filed: 10/29/1998
• Issued: 05/01/2001
• Est. Priority Date: 10/29/1998
• Status: Expired due to Fees

• Current Assignee: Baker Hughes Incorporated (Baker Hughes Company)
• Original Assignee: Baker Hughes Incorporated (Baker Hughes Company)
• Inventors: Chen, Songhua
• Primary Examiner(s): Patidar, Jay
• Assistant Examiner(s): SHRIVASTAV, BRIJ B
• Application Number:
  US09/182,624
• Time in Patent Office: 915 Days
• Field of Search: 324/303, 324/300, 324/322, 348/397
• US Class Current: 324/303
• CPC Class Codes: G01N 24/081 Making measurements of geologic samples, e.g. measurements of moisture, pH, porosity, permeability, tortuosity or viscosity
• CPC Class Codes: G01R 33/4625 Processing of acquired signals, e.g. elimination of phase errors, baseline fitting, chemometric analysis
• CPC Class Codes: G01V 3/32 operating with electron or nuclear magnetic resonance

Abstract

A method of nuclear magnetic resonance (NMR) well log processing. A wavelet decomposition of an NMR echo train is preformed. The resulting small scale coefficients, which may be discretely or continuously indexed by scale, in alternative embodiments, are windowed, and a first reconstruction generated therefrom by inverse wavelet transformation. The reconstructed signal is inverted and fit to a multiexponential model. Further refinements may be generated by iteratively decomposing the fitted signal at a preselected maximum scale, increasing at each iteration, generating a new coefficient by replacing the corresponding portion of the previous coefficient with the coefficient at the current scale, reconstructing the signal with the new coefficient, and fitting the signal so reconstructed to the relaxation time distribution.

Claims

1. A method of nuclear magnetic resonance (NMR) well log processing comprising the steps of:

forming a wavelet decomposition of an NMR data signal, thereby obtaining a set of first coefficient values having a preselected first maximum scale and a preselected first minimum scale;

windowing a preselected subset of said set of first coefficient values, thereby forming a windowed set of coefficient values; and

generating an inverse wavelet transform of said windowed set of coefficient values, to form a first reconstruction of said NMR signal.

2. The method of claim 1 further comprising the step of inverting said first reconstruction to form a relaxation spectrum signal.

3. The method of claim 1 wherein said windowing step comprises the steps of:

applying a windowing function to each member of said preselected subset of first coefficient values; and

substituting each member of said subset by a corresponding windowed coefficient formed in said applying step.

4. The method of claim 3 wherein said preselected subset comprises a discrete subset and wherein said step of applying a windowing function comprises the step of applying a discretely indexed windowing function to said preselected subset.

5. The method of claim 4 wherein said step of applying a windowing function comprises the step of generating windowed coefficients defined by:

6. The method of claim 3 wherein said preselected subset comprises a continuous subset and wherein said step of applying a windowing function comprises the step of applying a continuously indexed windowing function to said subset.

7. The method of claim 6 wherein said step of applying a windowing function comprises the step of generating windowed coefficients defined by:

8. The method of claim 1 further comprising the step of fitting said first reconstruction to a preselected model signal to form a first fitted NMR signal.

9. The method of claim 8 wherein said step of fitting said first reconstruction includes the step of determining a set of parameter values according to a fitting algorithm.

10. The method of claim 8 further comprising the steps of:

forming a wavelet decomposition of said first fitted NMR signal, thereby obtaining a set of second coefficient values having a preselected next maximum and next minimum scale, wherein said next maximum scale is less than a previous maximum scale and said next minimum scale is not less than a previous minimum scale;

replacing a corresponding subset of said set of windowed first coefficient values by said set of second coefficient values; and

forming an inverse wavelet transformation of a set of coefficients formed in said replacing step, to form a second reconstruction of said NMR signal.

11. The method of claim 10 further comprising the step of fitting said second reconstruction to said preselected model signal to form a second fitted NMR signal.

12. The method of claim 11 further comprising the step of, for a preselected number, M-2, of iterations, repeating said steps of forming said wavelet transform, replacing a corresponding subset, forming an inverse wavelet transform, and fitting to form an “

Mth”

fitted NMR signal.

13. The method of claim 12 further comprising the step of, for each iteration, inverting a corresponding reconstruction to form a corresponding relaxation spectrum, thereby forming an “

Mth”

relaxation spectrum at a last iteration.

14. The method of claim 12 wherein said wavelet transform is a discrete wavelet transform (DWT).

15. The method of claim 12 wherein said wavelet transform is a continuous wavelet transform (CWT).

16. The method of claim 10 wherein said set of second coefficient values comprises a continuously indexed set, said wavelet transform comprising a continuous wavelet transform.

17. The method of claim 10 further comprising the step of inverting said second reconstruction to form a second relaxation spectrum.

18. The method of claim 10 wherein said set of second coefficient values comprise a set of detail coefficients and wherein said wavelet decomposition of said fitted NMR signal further an approximation coefficient, said wavelet decomposition comprising a discrete wavelet transform.

19. The method of claim 1 wherein said step of forming a wavelet decomposition comprises the step of forming a discrete wavelet transform, said discrete wavelet transform further including an approximation coefficient, and wherein said set of first coefficient values includes a discrete, preselected, number of members.

20. The method of claim 19 wherein said set of first coefficients comprises a set of detail coefficients and said second coefficient comprises an approximation coefficient.

21. A computer program product operable for storage on machine readable media, the program product for nuclear magnetic resonance (NMR) well logging comprising:

programming for forming a wavelet decomposition of an NMR data signal, thereby obtaining a set of first coefficients;

programming for windowing a preselected subset of said set of first coefficient values, thereby forming a windowed set of coefficient values; and

programming for generating an inverse wavelet transform of said windowed set of coefficient values, to form a first reconstruction of said NMR signal.

22. The computer program product of claim 21 further comprising programming for inverting said first reconstruction to form a relaxation spectrum signal.

23. The computer program product of claim 21 wherein said programming for windowing comprises:

programming for applying a windowing function to each member of said preselected subset of first coefficients; and

substituting each member of said subset by a corresponding windowed coefficient formed in said applying step.

24. The computer program product of claim 23 wherein said preselected subset comprises a discrete subset and wherein said programming for applying a windowing function comprises programming for applying a discretely indexed windowing function to said preselected subset.

25. The method of claim 24 wherein said programming for applying a windowing function comprises programming for generating windowed coefficients defined by:

26. The computer program product of claim 23 wherein said preselected subset comprises a continuous subset and wherein said programming for applying a windowing function comprises the programming for applying a continuously indexed windowing function to said subset.

27. The computer program product of claim 26 wherein said programming for applying a windowing function comprises programming for generating windowed coefficients defined by:

28. The computer program product of claim 21 further comprising programming for fitting said first reconstruction to a preselected model signal to form a first fitted NMR signal.

29. The computer program product of claim 28 wherein said programming for fitting said first reconstruction includes programming for determining a set of parameter values according to a fitting algorithm.

30. The computer program product of claim 29 further comprising:

programming for forming a wavelet decomposition of said first fitted NMR signal, thereby obtaining a set of second coefficient values having a next maximum and next minimum scale;

programming for replacing a corresponding subset of said set of windowed first coefficient values by said set of second coefficient values; and

programming for forming an inverse wavelet transformation of a set of coefficients formed in said replacing step, to form a second reconstruction of said NMR signal.

31. The computer program product of claim 30 further comprising programming for fitting said second reconstruction to said preselected model signal to form a second fitted NMR signal.

32. The computer program product of claim 31 further comprising programming for, for a preselected number, M-2, of iterations, repeating said programming for forming said wavelet transform, replacing a corresponding subset, forming an inverse wavelet transform, and fitting to form an “

Mth”

fitted NMR signal.

33. The computer program product of claim 32 further comprising programming for, for each iteration, inverting a corresponding reconstruction to form a corresponding relaxation spectrum, thereby forming an “

Mth”

relaxation spectrum at a last iteration.

34. The computer program product of claim 32 wherein said wavelet transform is a continuous wavelet transform (CWT).

35. The computer program product of claim 32 wherein said wavelet transform is a discrete wavelet transform (DWT).

36. The computer program product of claim 30 further comprising programming for inverting said second reconstruction to form a second relaxation spectrum.

37. The computer program product of claim 30 wherein said set of second coefficient values comprise a set of detail coefficients and wherein said wavelet decomposition of said fitted NMR signal further an approximation coefficient, said wavelet decomposition comprising a discrete wavelet transform.

38. The computer program product of claim 30 wherein said set of second coefficient values comprises a continuously indexed set, said wavelet transform comprising a continuous wavelet transform.

39. The computer program product of claim 21 wherein said programming for forming a wavelet decomposition comprises programming for forming a discrete wavelet transform, said discrete wavelet transform further including an approximation coefficient, and wherein said set of first coefficient values includes a discrete, preselected, number of members.

40. The computer program product of claim 39 wherein said set of first coefficients comprises a set of detail coefficients and said second coefficient comprises an approximation coefficient.