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PhD Final Presentation by Marcelo Guarido
- 1. Supervisors: Dr. Larry Lines Dr. Robert Ferguson Convergence of a full waveform inversion scheme based on PSPI migration and forward modeling-free approximation: procedure and validation Presenter: Marcelo Guarido de Andrade
- 5. Reduce the cost of a gradient descent FWI routine preserving its resolution at most Replacing the RTM by a PSPI migration Reducing cost to estimate the step length Re-interpretation of the gradient Objective 5
- 6. Introduction Steepest-descent (gradient) method Trial-and-error line search vs. Pica et al. (1990) approximation Monochromatic averaged gradient Initial model Conjugate gradient Impedance inversion of the gradient Forward modeling-free gradient Pre-stack Post-stack Well calibration of the gradient Same initial model Conclusions Future work Outline 6
- 8. Introduction C 𝑚 ≡ ∆𝑑 𝑚 2Minimize Least Squares 𝒅 𝒐𝒃𝒔 − 𝒅 𝒔𝒚𝒏 8
- 9. 𝒎(𝒏+𝟏) = 𝒎(𝒏) − 𝜶(𝒏) 𝒈(𝒏) m0 ∆dm g0 m1 α0 9
- 12. Steepest-descent (gradient) method 96 simulated shots (“real model”) Initial model (smoothed velocity) Synthetic Data Residuals PSPI Migration (Deconvolution Imaging Condition) Step length (linear search and quadratic fit) Update ModelConvergence? Final Model Yes No Mute and Stack 12
- 13. Steepest-descent (gradient) method Acquisition Type Marine Number of shots 96 Shot spacing 100m Shot depth 30m # of receivers 401 Receiver spacing 10m Receiver depth 0m Frequency 10Hz Processing Starting frequency 1-6Hz Iterations per frequency < 16Hz 10 Iterations per frequency > 15Hz 5 Frequency increment < 25Hz 1Hz Frequency increment > 24Hz 5Hz Mute Yes Water bottom mute Yes Scale factor tests 21 13
- 14. Steepest-descent (gradient) method Model Depth 3km Width 10km Resolution 10m Min. velocity 1500m/s Max. velocity 3900m/s Velocity(m/s) 14
- 27. Trial-and-error Try several step lengths Update the model Synthetic shot L2-norm Quadratic fit (3 points) Lowest error Expensive Steepest-descent (gradient) method 27
- 28. Steepest-descent (gradient) method Least Squares: Step length: 28
- 29. Steepest-descent (gradient) method Velocity(m/s) Velocity(m/s) Initial Model CorrectModel 29
- 30. Steepest-descent (gradient) method Trial-and-error line search 30
- 31. Steepest-descent (gradient) method Pica et al. (1990) approximation 31
- 33. Steepest-descent (gradient) method Acquisition Model Marmousi Number of shots 101 Shot spacing 100m Shot depth 0m # of receivers 401 Receiver spacing 10m Receiver depth 0m Frequency 10Hz Processing Starting frequency 1-4Hz Iterations per frequency < 13Hz 5 Iterations per frequency > 12Hz 2 Frequency increment < 13Hz 1Hz Frequency increment > 12Hz 5Hz Mute Yes Smooth Yes Scale factor tests 21 33
- 39. Monochromatic PSPI migration of the residuals Gradient for each frequency One step for each gradient Average scaled monochromatic gradients Monochromatic averaged gradient 39
- 40. Starting: low frequency Increase frequency band Convergence By 2Hz Maximum: 60Hz More migrations as frequency band gets larger Monochromatic averaged gradient 40
- 58. Impedance inversion of the gradient 58
- 59. Gradient -> reflection coefficients or impedance? Impedance inversion FWI as seismic processing tools I – impedance inversion S – stacking M – migration Impedance inversion of the gradient 59
- 60. Band-Limited Impedance Inversion (BLIMP) Depth-to-time and time-to-depth conversions Initial model as pilot impedance One migration step per iteration Impedance inversion of the gradient 60
- 61. Impedance inversion of the gradient 61
- 62. Impedance inversion of the gradient 62
- 63. Impedance inversion of the gradient 63
- 64. Impedance inversion of the gradient 64
- 65. Impedance inversion of the gradient 65
- 67. Forward modeling-free gradient And: Step length requires 2 forward modeling Linear operators 67
- 73. Commuting the Migration and Stacking operators Forward modeling-free gradient 73
- 74. Invert frequencies > 4Hz Step length: biased by position Select random shot Can’t control objective function Forward modeling-free gradient 74
- 84. Well calibration of the gradient 84
- 85. Sonic log Storage difference of sonic log and current model (what the gradient should be) Compute gradient Compute matching filter between gradient and stored difference of sonic log and current model Convolve matching filter with the whole gradient Inverting frequencies > 4Hz Well calibration of the gradient 85
- 86. Well calibration of the gradient 86
- 87. Well calibration of the gradient 87
- 88. Well calibration of the gradient 88
- 89. Well calibration of the gradient 89
- 90. Well calibration of the gradient 90
- 91. Well calibration of the gradient 91
- 92. Well calibration of the gradient 92
- 93. Advantages of a forward modeling-free inversion: No source (wavelet) estimation No need to for any forward modeling Cheaper More robust to work on real data? Well calibration of the gradient 93
- 95. Simulation of a velocity analysis Divide Marmousi in 5 horizontal areas Pick one random position inside each area Linear interpolation Repeat for all columns Smooth Same initial model 95
- 96. Same initial model 96 Repeat for all columns
- 103. Conclusions 103
- 104. Steepest-descent: works well on simple models Least squares step length: cheaper and good Monochromatic averaged gradient: higher resolution with high cost Conjugate gradient: improved resolution Impedance inversion of the gradient: great resolution reducing costs Forward modeling-free gradient: pre and post-stack approximations, cheaper with good resolution Well calibration of the gradient: 100% forward modelling-free FWI, lowest cost with improved resolution Conclusions 104
- 105. Reverse time migration (RTM) Multi-parameter (if possible) Extend to 3D Real data Deep learning (Neural Networks?) Future work 105
- 106. Dr. Larry Lines Dr. Rob Ferguson NSERC CREWES Sponsors Students and staff Dr. Kris Innanen Dr. Daniel Trad Dr. Gary Margrave Dr. Babatunde Arenrin Dr. Raul Cova Dr. Wenyong Pan FWI group Laura Baird Soane Mota dos Santos Acknowledgments 106
- 107. 107