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Gabor Deconvolution

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Gabor Deconvolution

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    1. Gabor Deconvolution

    2. This is about

    3. Limerick

    4. Limerick

    5. Limerick

    6. Limerick

    7. So Who were these guys? What was on the other side of the door? Why was the door locked? How did the window help? What does this have to do with deconvolution?

    8. Joseph Fourier (1768-1830)

    9. Example of Fourier Analysis

    10. Example of Fourier Analysis

    11. Fourier Analysis

    12. Dennis Gabor (1900-1971)

    13. Gabors Door

    14. Gabors Door

    15. Fouriers Window

    16. Fouriers Window

    17. Fouriers Window

    18. Problem: Physical interpretation of Fourier Spectra

    19. The Gabor Idea

    20. A Partition of Unity

    21. The Gabor Idea

    22. The Gabor Idea

    23. The Gabor Idea

    24. Time-Frequency Analysis

    25. The Utility of the Gabor Transform

    26. Norbert Wiener (1894-1964)

    27. Enders Robinson (1930-)

    28. Stationary seismic trace model

    29. Stationary seismic trace model

    30. Wiener deconvolution

    31. Wiener deconvolution

    32. Stationarity A stationary physical process can be characterized by convolution. We do not try to characterize a time series as stationary or not.

    33. Nonstationary A nonstationary stationary physical process is characterized by a superposition process whose spectral content evolves. Attenuation processes are nonstationary and characterized by Q

    34. Q

    35. Q

    36. Attenuation and minimum phase

    37. Attenuation Simulation

    38. Attenuation Simulation

    39. Attenuation and nonstationarity

    40. Haiku

    41. Real Seismic (200 traces) after gain for spherical spreading

    42. Gabor spectrum of trace 100 after gain

    43. Stationary seismic trace model

    44. Nonstationary seismic trace model

    45. Gabor Factorizes Nonstationary Trace Model

    46. Gabor Deconvolution

    47. Comparison on Synthetic

    48. Comparison on Synthetic

    49. Real Data Comparison

    50. Real Data Comparison

    56. Real Data Comparison

    57. Validation of Gabor wavelets with a VSP

    58. Comparison of wavelets

    59. Summary

    60. Research Goals Incorporate well information as a constraint Better phase estimation (remove more delay) Develop theory on nonstationary minimum phase filters Extend to multiple attenuation

    61. Acknowledgements

    62. Haiku2

    63. What about the Wavelet Transform?

    64. Gabor transform via a partition of unity

    65. Gabor transform via a partition of unity

    66. Gabor transform via a partition of unity

    67. Time-Frequency Analysis

    68. Early Pioneers in Time-Frequency

    69. Advancements in Gabor Theory

    70. Norbert Wiener

    71. Dennis Gabor

    72. Joseph Fourier

    73. Gabors Door

    74. Gabors Door

    75. Compatible windows

    76. Compatible windows

    77. Compatible windows

    78. Limerick

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