Method of seismic attribute generation and seismic exploration

• US 5,940,778 A
• Filed: 07/31/1997
• Issued: 08/17/1999
• Est. Priority Date: 07/31/1997
• Status: Expired due to Term

• Current Assignee: BP Amoco (BP PLC)
• Original Assignee: BP Amoco (BP PLC)
• Inventors: Marfurt, Kurt, Gersztenkorn, Adam, Kirlin, R. Lynn
• Primary Examiner(s): McElheny, Jr., Donald E.
• Application Number:
  US08/904,040
• Time in Patent Office: 747 Days
• Field of Search: 702/16, 702/13, 702/12, 367/73
• US Class Current: 702/16
• CPC Class Codes: G01V 1/28 Processing seismic data, e.g. for interpretation or for event detection G01V1/48 takes precedence
• CPC Class Codes: G01V 2210/51 Migration
• CPC Class Codes: G01V 2210/56 De-ghosting; Reverberation compensation

Abstract

The present invention relates generally to the field of seismic exploration and, in more particular, to methods of quantifying and visualizing structural and stratigraphic features in three dimensions through the use of eigenvector and eigenvalue analyses of a similarity matrix. This invention also relates to the field of seismic attribute generation and the use of seismic attributes derived from similarity matrices to detect the conditions favorable for the origination, migration, accumulation, and presence of hydrocarbons in the subsurface. Additionally, the methods disclosed herein provide a new means for analyzing unstacked seismic data to uncover AVO effects. The invention disclosed herein will be most fully appreciated by those in the seismic interpretation and seismic processing arts.

Claims

1. A method for the exploration of hydrocarbons, wherein a predetermined volume of the earth containing structural and stratigraphic features has been specified, comprising:

(a) obtaining a representation of a set of spatially related seismic traces distributed over said pre-determined volume of the earth, said spatially related seismic traces containing signals representative of at least a portion of said structural and stratigraphic features, and each of said spatially related seismic traces being associated with a location on a surface of the earth;

(b) selecting a target location on the surface of the earth, said target location having at least three spatially related seismic traces proximate thereto;

(c) selecting at least three traces from said at least three spatially related seismic traces proximate to said target location;

(d) calculating a complex similarity matrix from said selected traces;

(e) calculating a seismic attribute from said complex similarity matrix;

(f) storing said seismic attribute at a position representative of said target location; and

,

(g) repeating steps (b) through (f) for at least two additional target locations, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify subsurface structural and stratigraphic features that are conducive to the migration, accumulation, or presence of hydrocarbons.

2. A method for the exploration of hydrocarbons according to claim 1 comprising the additional step of

(h) displaying at least a portion of said stored plane of seismic attributes.

3. A method according to claim 2, wherein the step of displaying at least a portion of said plane of seismic attributes includes the further step of recording visually perceptible images representative of said plane of seismic attributes on a generally flat medium.

4. A method according to claim 3, wherein said generally flat medium includes a computer monitor.

5. A method according to claim 1, wherein the complex similarity matrix of step (d) has a plurality of eigenvalues, and where the step of calculating a seismic attribute in step (e) comprises the steps of:

(1e) calculating at least one eigenvalue of said complex similarity matrix,

(2e) calculating a seismic attribute from any eigenvalues so calculated.

6. A method according to claim 5, wherein the complex similarity matrix has a largest eigenvalue, wherein the eigenvalue calculated in step (1e) is said largest eigenvalue, and wherein the seismic attribute calculated in step (2e) is said largest eigenvalue.

7. A method according to claim 1, wherein the complex similarity matrix of step (d) has a plurality of eigenvectors, and where the step of calculating a seismic attribute in step (e) comprises the steps of:

(1e) calculating at least one eigenvector of said complex similarity matrix, and,

(2e) calculating a seismic attribute from any eigenvectors so calculated.

8. A method according to claim 7, wherein the step of calculating a seismic attribute in step (2e) comprises the steps of:

(i) choosing an eigenvector from among those so calculated, said chosen eigenvector containing eigenvector elements,

(ii) associating each eigenvector element with an eigenvector element surface location, said eigenvector element surface location consisting of an X coordinate and a Y coordinate,

(iii) numerically fitting a function characterized by constant coefficients to said eigenvector elements and said eigenvector element surface locations, thereby obtaining one or more constant coefficient estimates, and

(iv) calculating a seismic attribute from any of said constant coefficient estimates so obtained.

9. A method according to claim 8 wherein the function of step (iii) is a trend surface function.

10. A method according to claim 9 wherein the trend surface function is a second order trend surface function.

11. A method according to claim 8

wherein the complex similarity matrix has a plurality of eigenvalues,

wherein there is a largest eigenvalue among said plurality of eigenvalues,

wherein said largest eigenvalue corresponds to an eigenvector of said complex similarity matrix, and

wherein the eigenvector chosen in step (i) is said eigenvector that corresponds to said largest eigenvalue.

12. The process of claim 1, wherein at least steps (b) through (g) are digitally encoded as a set of instructions for programming a computer and further including the step of loading said instructions on said computer before performing steps (b) through (g).

13. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 12 are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

14. The device of claim 13, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

15. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 1, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

16. A method according to claim 1

wherein a zone of interest has been specified,

wherein an analysis window within said zone of interest has been specified,

wherein said selected traces contain digital samples, said digital samples being characterized by at least a time, a location, and an amplitude,

and wherein step (d) comprises the steps of:

(1d) identifying for each selected trace the digital samples falling within said analysis window, and,

(2d) calculating a complex similarity matrix from said digital samples so identified.

17. A method according to claim 16, wherein steps (b) through (g) are performed for at least two different specified analysis windows within said zone of interest, thereby producing at least two stored planes of seismic attributes.

18. A method of geophysical exploration for subsurface structural and stratigraphic features within seismic data that may be associated with the migration, accumulation, or presence of hydrocarbons according to claim 17, wherein said stored seismic attribute planes are formed into a stored seismic attribute cube.

19. A method of geophysical exploration according to claim 18, comprising the additional step of:

(g) displaying at least a portion of said stored seismic attribute cube.

20. A method according to claim 1 wherein the step of storing said seismic attribute at a position representative of the surface location of the target trace comprises the step of storing in computer RAM said seismic attribute at a position representative of the surface location of the target trace.

73. A method according to claim 1, wherein step (d) further includes the steps of:

(d1) calculating an analytic seismic trace from one of said selected at least three traces;

(d2) repeating step (d1) until at least three analytic seismic traces have been computed from at least three of said selected at least three traces; and

,

(d3) calculating a complex similarity matrix from any analytic seismic traces so calculated.

21. A seismic map for use in geophysical exploration prepared by a process, comprising the steps of:

(a) accessing, by means of a computer, a data set comprising seismic traces distributed over a pre-determined volume of the earth;

(b) selecting a target seismic trace having a surface location and at least two other seismic traces having surface locations from said set of seismic traces;

(c) calculating a complex similarity matrix from said selected seismic traces;

(d) calculating a seismic attribute from said complex similarity matrix;

(e) storing said seismic attribute at a position representative of the surface location of the target trace; and

,

(f) repeating steps (b) through (e) for at least two additional target traces, thereby creating a stored plane of seismic attributes; and

,

(g) converting said stored plane of seismic attributes into a printed display for use in the identification and detection of subsurface features that are conducive to hydrocarbon formation, migration, or occurrence.

22. In a digital computer wherein a data set of spatially related seismic traces obtained over a pre-determined volume of the earth are read into memory, wherein said spatially related seismic traces contain signals representative of at least a portion of said volume, and wherein said digital computer is used to form an attribute display for use in seismic exploration, a digital computer programmed to perform a process comprising the steps of:

(a) selecting at least three seismic traces from said spatially related seismic traces, each of said selected seismic traces being characterized by at least a surface location;

(b) calculating a complex similarity matrix from said selected seismic traces;

(c) calculating a seismic attribute from said complex similarity matrix;

(d) storing said seismic attribute at a position representative of the surface location of one of said selected seismic traces; and

,

(e) repeating steps (a) through (d) for at least two additional target traces, thereby forming a stored attribute display which can be used to detect subsurface features that are conducive to hydrocarbon formation, migration, or occurrence.

23. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 22, are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

24. The device of claim 23, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

25. A method of seismic attribute generation for use in geophysical exploration for hydrocarbons, wherein a reference frequency and a plurality of specified auxiliary frequencies have been provided, comprising the steps of:

(a) obtaining a set of spatially related seismic traces distributed over a 3-D volume of the earth, said spatially related seismic traces containing signals representative of at least a portion of said volume, and each spatially related seismic trace in said set being associated with a surface location;

(b) selecting a target seismic trace and at least two other seismic traces from said set of seismic traces, said target trace having a surface location;

(c) calculating a reference frequency complex similarity matrix at said reference frequency from said selected seismic traces;

(d) choosing an auxiliary frequency from among said specified auxiliary frequencies;

(e) calculating a single frequency phase-corrected complex similarity matrix at said chosen auxiliary frequency from said selected seismic traces;

(f) performing steps (d) and (e) as required until a predetermined number of the specified auxiliary frequencies have been chosen;

(g) combining any phase-corrected single frequency complex similarity matrices calculated in steps (e) and (f) with said reference frequency complex similarity matrix to form a composite complex similarity matrix;

(h) calculating a seismic attribute from said composite complex similarity matrix;

(i) storing said seismic attribute at a position representative of the surface location of said target trace; and

,

(j) repeating steps (b) through (i) for at least two other target traces, thereby creating a stored plane of seismic attributes which can be used to detect subsurface features that are conducive to hydrocarbon formation, migration, or occurrence.

26. A method according to claim 25 wherein said predetermined number of the specified auxiliary frequencies is numerically equal to unity.

27. A method according to claim 25 wherein step (e) comprises the steps of:

(1e) calculating from each selected seismic trace a Fourier transform at said chosen auxiliary frequency, said Fourier transform producing an auxiliary frequency Fourier transform coefficient for each selected seismic trace,

(2e) calculating phase-corrected Fourier transform coefficients from said auxiliary frequency Fourier transform coefficients, and

(3e) forming a phase-corrected single frequency similarity matrix at said chosen auxiliary frequency from said phase-corrected Fourier transform coefficients.

28. A method according to claim 25 wherein step (g) comprises the step of summing together any phase-corrected single frequency complex similarity matrices calculated in step (e) with said reference frequency complex similarity matrix to form a composite complex similarity matrix.

29. A method according to claim 25 wherein step (c) comprises the steps of:

(1c) calculating from each selected seismic trace a Fourier transform at said reference frequency, said Fourier transform producing a reference frequency Fourier transform coefficient for each selected seismic trace, and

(2c) calculating a reference frequency complex similarity matrix at said reference frequency from said seismic traces by way of the following equation;

space="preserve" listing-type="equation">S.sub.R =d.sub.R d.sub.R.sup.H,

where S_R is said reference frequency complex similarity matrix at said reference frequency, and d_R is a vector containing said reference frequency Fourier transform coefficients of step (1c).

30. A method according to claim 25 wherein the step of storing said seismic attribute at a position representative of the surface location of the target trace comprises the step of storing in computer RAM said seismic attribute at a position representative of the surface location of the target trace.

31. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 25, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

32. A method for the exploration of hydrocarbons according to claim 25 comprising the additional step of:

(k) displaying at least a portion of said stored seismic attribute plane.

33. A method according to claim 32 wherein the step of displaying at least a portion of said stored seismic attribute plane includes the step of displaying at least a portion of said stored seismic attribute plane on a computer monitor.

34. In the exploration for hydrocarbons, a seismic attribute map for use by an explorationist in identifying potential drilling sites, wherein subsurface features associated with the migration, accumulation or presence of hydrocarbons have been accentuated, said map being prepared by a process, said process comprising the steps of:

(a) accessing by means of a computer, a data set comprising spatially related seismic signal traces distributed over a pre-determined volume of the earth, said seismic signal traces being characterized by at least a surface location;

(b) selecting a target location, said target location having at least three seismic signal traces proximate thereto;

(c) selecting at least three seismic traces from said seismic signal traces proximate to said target location;

(d) calculating a complex similarity matrix from said selected seismic traces;

(e) calculating a seismic attribute from said complex similarity matrix;

(f) storing said seismic attribute at a position representative of the surface location of one of the selected seismic traces;

(g) repeating steps (b) through (f) for at least two additional target locations, thereby creating a stored plane of seismic attributes; and

,

(h) displaying said stored plane of seismic attributes on a generally flat medium for recording visually perceptible images thereon.

35. A method according to claim 34, wherein said generally flat medium includes a computer monitor.

36. A method for the exploration of hydrocarbons, wherein a predetermined volume of the earth containing structural and stratigraphic features has been specified, comprising:

(a) obtaining a representation of a set of spatially related seismic traces distributed over said pre-determined volume of the earth, said spatially related seismic traces containing signals representative of at least a portion of said structural and stratigraphic features, and each of said spatially related seismic traces being characterized by at least a location on a surface of the earth;

(b) selecting a target location on the surface of the earth, said target location having at least three seismic traces proximate thereto;

(c) selecting at least three traces from said at least three seismic traces proximate to said target location;

(d) calculating a similarity matrix from said selected traces, said similarity matrix having a plurality of eigenvectors;

(e) calculating a particular eigenvector of said similarity matrix, said particular eigenvector containing eigenvector elements;

(f) associating each of said eigenvector elements with an eigenvector element surface location;

(g) fitting a function characterized by constant coefficients to said eigenvector elements and said eigenvector element surface locations, thereby obtaining one or more constant coefficient estimates;

(h) calculating a seismic attribute from any of said constant coefficient estimates so obtained;

(i) storing said seismic attribute at a position representative of said target location; and

,

(j) repeating steps (b) through (i) for at least two additional target locations, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify subsurface structural and stratigraphic features that are conducive to the migration, accumulation, or presence of hydrocarbons, conducive to the migration, accumulation, or presence of hydrocarbons.

37. A method for the exploration of hydrocarbons according to claim 36 comprising the additional step of

(k) displaying at least a portion of said stored plane of seismic attributes.

38. A method according to claim 37, wherein the step of displaying at least a portion of said plane of seismic attributes includes the further step of recording visually perceptible images representative of said plane of seismic attributes cube on a generally flat medium.

39. A method according to claim 38, wherein said generally flat medium includes a computer monitor.

40. A method according to claim 36,

wherein said similarity matrix of step (d) has plurality of eigenvalues,

wherein there is a largest eigenvalue among said plurality of eigenvalues, said largest eigenvalue being associated with at least one of said plurality of eigenvectors, and

wherein said particular eigenvector calculated in step (e) is an eigenvector associated with said largest eigenvalue of said similarity matrix.

41. A method according to claim 36 wherein the step of storing said seismic attribute at a position representative of the surface location of the target trace comprises the step of storing in computer RAM said seismic attribute at a position representative of the surface location of the target trace.

42. A method according to claim 36 wherein the function of step (g) is a trend surface function.

43. A method according to claim 42 wherein the trend surface function is a second order trend surface function.

44. The process of claim 36, wherein at least steps (b) through (j) are digitally encoded as a set of instructions for programming a computer and further including the step of loading said instructions on said computer before performing steps (b) through (j).

45. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 44 are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

46. The device of claim 45, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

47. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 36, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

48. A method according to claim 36

wherein a zone of interest has been specified,

wherein an analysis window within said zone of interest has been specified,

wherein said selected traces contain digital samples, said digital samples being characterize by at least a time, a location, and an amplitude,

and wherein step (d) comprises the steps of:

(1d) identifying for each selected trace the digital samples falling within said analysis window, and,

(2d) calculating a complex similarity matrix from said digital samples so identified.

49. A method according to claim 48, wherein steps (b) through (j) are repeated for at least two different specified analysis windows within said zone of interest, thereby producing at least two stored planes of seismic attributes.

50. A method of geophysical exploration for subsurface structural and stratigraphic features within seismic data that may be associated with the migration, accumulation, or presence of hydrocarbons according to claim 49, wherein said stored seismic attribute planes are formed into a stored seismic attribute cube.

51. A method of geophysical exploration according to claim 50, comprising the additional step of:

(k) displaying at least a portion of said stored seismic attribute cube.

52. A seismic map for use in geophysical exploration, said map prepared by a process comprising the steps of:

(a) accessing, by means of a computer, a data set comprising seismic traces distributed over a pre-determined volume of the earth;

(b) selecting a target seismic trace having a surface location and at least two other seismic traces having surface locations from said set of seismic traces;

(c) calculating a similarity matrix from said selected seismic traces, said similarity matrix having a plurality of eigenvectors;

(d) calculating a particular eigenvector of said similarity matrix, said particular eigenvector having eigenvector elements;

(e) associating each of said eigenvector elements with a surface location;

(f) fitting a function characterized by constant coefficients to said eigenvector elements and said surface locations, thereby obtaining one or more constant coefficient estimates;

(g) calculating a seismic attribute from any of said constant coefficient estimates so obtained;

(h) storing said seismic attribute at a position representative of the surface location of the target trace; and

,

(i) repeating steps (b) through (h) for at least two additional target traces, thereby creating a stored plane of seismic attributes; and

,

(j) converting said stored plane of seismic attributes into a printed display for use in the identification and detection of subsurface features that are conducive to hydrocarbon formation, migration, or occurrence.

53. In a digital computer wherein a data set of spatially related seismic traces obtained over a pre-determined volume of the earth are read into memory, and wherein said digital computer is used to form an attribute display for use in seismic exploration, a digital computer programmed to perform a process comprising the steps of:

(a) selecting a target seismic trace and at least two other seismic signal traces from said spatially related seismic traces;

(b) calculating a similarity matrix from said selected seismic traces, said similarity matrix having a plurality of eigenvectors;

(c) calculating a particular eigenvector of said similarity matrix, said eigenvector consisting of eigenvector elements;

(d) associating with each of said eigenvector elements a location;

(e) fitting a function characterized by constant coefficients to said eigenvector elements and said locations, thereby obtaining one or more constant coefficient estimates;

(f) calculating a seismic attribute from any of said constant coefficient estimates so obtained;

(g) storing said seismic attribute at a position representative of the surface location of the target trace; and

,

(h) repeating steps (b) through (g) for at least two additional target traces, thereby creating a stored attribute display, said stored attribute display being used to identify subsurface structural and stratigraphic features that are conducive to the migration, accumulation, or presence of hydrocarbons.

54. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 53, are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

55. The device of claim 54, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

56. In the exploration for hydrocarbons, a seismic attribute map for use by an explorationist in identifying subsurface features associated with the migration, accumulation or presence of hydrocarbons, said map being prepared by a process, said process comprising the steps of:

(a) accessing by means of a computer, a data set comprising spatially related seismic traces distributed over a pre-determined volume of the earth, said seismic traces containing digital information representative of subterranean structures and stratigraphy;

(b) selecting at least three seismic traces from said data set of spatially related seismic traces, said selected seismic traces each being characterized by at least a surface location;

(c) calculating a similarity matrix from said selected seismic traces, said similarity matrix having a plurality of eigenvectors;

(d) calculating a particular eigenvector of said similarity matrix, said eigenvector being characterized by a plurality of eigenvector elements;

(e) associating a surface location with each of said plurality of eigenvector elements;

(f) selecting a function characterized by at least one constant coefficient;

(g) fitting said function to said plurality of eigenvector elements and surface locations, thereby producing at least one constant coefficient estimate;

(h) calculating a seismic attribute from any of said constant coefficient estimates so produced;

(i) storing said seismic attribute at a position representative of the surface location of one of said selected seismic traces;

(j) repeating steps (b) through (i) for at least two additional target traces, thereby creating a stored plane of seismic attributes; and

,

(k) displaying said plane of seismic attributes on a generally flat medium for recording visually perceptible images thereon.

57. A method of geophysical exploration, wherein unstacked seismic traces are analyzed for variations in seismic reflector amplitude with changing offset distance from a CMP location, said method comprising the steps of:

(a) obtaining a representation of an unstacked seismic data set, said unstacked seismic data set being organized into a plurality of CMP gathers, each of said CMP gathers being associated with a location on the surface of the earth and each of said CMP gathers consisting of at least one unstacked seismic trace;

(b) selecting a CMP gather consisting of at least three unstacked seismic traces from said plurality of CMP gathers;

(c) selecting at least three traces from said unstacked seismic traces in said selected CMP gather, each of said selected traces being associated with a location on the surface of the earth;

(d) calculating a similarity matrix from said selected traces, said similarity matrix having a plurality of eigenvectors;

(e) calculating a particular eigenvector of said similarity matrix, said particular eigenvector having eigenvector elements;

(e) associating each of said eigenvector elements with a surface location;

(f) fitting a function characterized by constant coefficients to said eigenvector elements and said surface locations, thereby obtaining one or more constant coefficient estimates;

(g) calculating a seismic attribute from any of said constant coefficient estimates so obtained;

(h) storing said seismic attribute at a position representative of said surface location of said selected CMP gather; and

,

(i) repeating steps (b) through (h) for at least two additional CMP gathers, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify amplitude variations with offset that are indicative of subsurface features conducive to the accumulation or presence of hydrocarbons.

58. A method for the exploration of hydrocarbons according to claim 57 comprising the additional step of

(j) displaying at least a portion of said stored plane of seismic attributes.

59. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes representative of variations in seismic reflectivity with offset has been prepared by the method of claim 57, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

60. The process of claim 57, wherein at least steps (b) through (i) are digitally encoded as a set of instructions for programming a computer and further including the step of loading said instructions on said computer before performing steps (b) through (i).

61. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 60 are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

62. The device of claim 61, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

63. A method for the exploration of hydrocarbons, wherein unstacked seismic traces containing subsurface structural and stratigraphic information are analyzed for AVO effects, comprising the steps of:

(a) obtaining a representation of an unstacked seismic data set, said unstacked seismic data set being organized into a plurality of CMP gathers, each of said CMP gathers being associated with a location on the surface of the earth and each of said CMP gathers consisting of at least one unstacked seismic trace;

(b) selecting a CMP gather consisting of at least three unstacked seismic traces from said plurality of CMP gathers;

(c) selecting at least three traces from said unstacked seismic traces in said selected CMP gather, each of said selected traces being associated with a location on the surface of the earth;

(d) calculating a complex similarity matrix from said selected traces;

(e) calculating a seismic attribute from said complex similarity matrix;

(f) storing said seismic attribute at a position representative of said surface location of said selected CMP gather; and

,

(g) repeating steps (b) through (f) for at least two additional CMP gathers, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify amplitude variations with offset that are indicative of subsurface features conducive to the accumulation or presence of hydrocarbons.

64. A method for the exploration of hydrocarbons according to claim 63 comprising the additional step of

(h) displaying at least a portion of said stored plane of seismic attributes.

65. The process of claim 63, wherein at least steps (b) through (g) are digitally encoded as a set of instructions for programming a computer and further including the step of loading said instructions on said computer before performing steps (b) through (g).

66. A device adapted for use by a digital computer wherein a plurality of computer instructions defining the process of claim 65 are encoded, said device being readable by said digital computer, and said computer instructions programming said computer to perform said process.

67. The device of claim 66, wherein said device is selected from the group consisting of a magnetic tape, a magnetic disk, a magneto-optical disk, an optical disk and a CD-ROM.

68. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 63, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

69. A method for the exploration of hydrocarbons, comprising:

(a) obtaining a set of spatially related seismic traces distributed over a surface of the earth, said seismic traces containing signals representative of subterranean structures and stratigraphy;

(b) selecting a target seismic trace having a surface location and at least two other seismic traces having surface locations from said set of seismic traces;

(c) calculating a complex similarity matrix from said selected seismic traces;

(d) calculating a seismic attribute from said complex similarity matrix;

(e) storing said seismic attribute at a position representative of the surface location of the target trace; and

,

(f) repeating steps (b) through (e) for at least two additional target traces, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify subsurface structural and stratigraphic features that are conducive to the migration, accumulation, or presence of hydrocarbons.

70. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 69, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.

74. A method according to claim 69, wherein step (c) further includes the steps of:

(c1) calculating an analytic seismic trace from one of said selected at least three traces;

(c2) repeating step (c1) until at least three analytic seismic traces have been computed from at least three of said selected at least three traces; and

,

(c3) calculating a complex similarity matrix from any analytic seismic traces so calculated.

71. A method of geophysical exploration, comprising the steps of:

(a) obtaining a set of spatially related seismic traces distributed over a surface of the earth, said seismic traces containing signals representative of subterranean structures and stratigraphy;

(b) selecting a target seismic trace and at least two additional neighborhood seismic traces from said spatially related, said selected seismic traces being characterized by at least a surface location;

(c) calculating a similarity matrix from said selected seismic traces, said similarity matrix having a plurality of eigenvectors;

(d) calculating a particular eigenvector of said similarity matrix, said particular eigenvector containing eigenvector elements;

(e) associating each of said eigenvector elements with a surface location;

(f) fitting a function characterized by constant coefficients to said eigenvector elements and said surface locations, thereby obtaining one or more constant coefficient estimates;

(g) calculating a seismic attribute from any of said constant coefficient estimates so obtained;

(h) storing said seismic attribute at a position representative of the surface location of the target trace; and

,

(i) repeating steps (b) through (h) for at least two additional target traces, thereby creating a stored plane of seismic attributes, said stored plane of seismic attributes being used to identify subsurface structural and stratigraphic features that are conducive to the migration, accumulation, or presence of hydrocarbons.

72. A method for the exploration of hydrocarbons, wherein a stored plane of seismic attributes has been prepared by the method of claim 71, comprising:

(a) accessing said stored plane of seismic attributes; and

,

(b) displaying at least a portion of said stored plane of seismic attributes.