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(t,x) domain, pattern-based ground roll removal

(t,x) domain, pattern-based ground roll removal. Morgan P. Brown* and Robert G. Clapp Stanford Exploration Project Stanford University. Receiver lines from 3-D cross-spread Shot Gather. Ground Roll - what is it?. To first order: Rayleigh (SV) wave. Dispersive, often high-amplitude

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(t,x) domain, pattern-based ground roll removal

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  1. (t,x) domain, pattern-based ground roll removal Morgan P. Brown* and Robert G. Clapp Stanford Exploration Project Stanford University

  2. Receiver lines from 3-D cross-spread Shot Gather

  3. Ground Roll - what is it? • To first order: Rayleigh (SV) wave. • Dispersive, often high-amplitude • In (t,x,y), ground roll = cone. • Usually spatially aliased. • In practice, “ground roll cone” muted.

  4. Talk Outline • Motivation for advanced separation techniques. • Model-based signal/noise separation. • Non-stationary (t,x) PEF. • Least squares signal estimation. • Real Data results.

  5. Advanced Separation techniques…why bother? • Imaging/velocity estimation for deep targets. • Rock property inversion (AVO, impedance). • Single-sensor configurations.

  6. Signal/Noise Separation: an Algorithm wish-list • Amplitude-preservation. • Robustness to signal/noise overlap. • Robustness to spatially aliased noise.

  7. Talk Outline • Motivation for advanced separation techniques. • Model-based signal/noise separation. • Non-stationary (t,x) PEF. • Least squares signal estimation. • Real Data results.

  8. Noise Subtraction simple subtraction adaptive subtraction pattern-based subtraction Noise Modeling moveout-based frequency-based “Physics” step “Signal Processing” step Wiener Optimal Estimation Coherent Noise Separation - a “model-based” approach data = signal + noise

  9. Coherent Noise Subtraction • The Noise model: kinematics usually OK, amplitudes distorted. • Simple subtraction inferior. • Adaptive subtraction: mishandles crossing events, requires unknown source wavelet. • Wiener optimal signal estimation.

  10. Assume: data = signal + noise signal, noise uncorrelated signal, noise spectra known. Optimal Reconstruction filter Wiener Optimal Estimation

  11. Spectral Estimation Question: How to estimate the non-stationary spectra of unknown signal and noise? • Answer: Smoothly non-stationary (t,x) Prediction Error Filter (PEF). PEF, data have inverse spectra.

  12. Spectral Estimation Question: How to estimate the non-stationary spectra of unknown signal and noise? • Answer: Smoothly non-stationary (t,x) Prediction Error Filter (PEF). Wiener technique requires signal PEF and noise PEF.

  13. Talk Outline • Motivation for advanced separation techniques. • Model-based signal/noise separation. • Non-stationary (t,x) PEF. • Least squares signal estimation. • Real Data results.

  14. Nt x ... 1 a1 a2 a3 a4 t Data = Ntx Nx x ... trace 1 trace 2 trace Nx a2 t PEF = 1 a3 a1 a4 Helix Transform and multidimensional filtering Helix Transform

  15. ... trace 1 trace 2 trace Nx * * ... a2 1 a1 a2 a3 a4 1 a3 a1 a4 Helix Transform and multidimensional filtering

  16. Helix Transform 1-D PEF Stable Inverse PEF 1-D Decon (Backsubstitution) Why use the Helix Transform? 2-D PEF 1-D filtering toolbox directly applicable to multi-dimensional problems.

  17. Convolution with stationary PEF trace 1 Ntx Nx 1 a1 … a2 a3 a4 1 a1 … a2 a3 a4 trace 2 x Ntx Nx 1 a1 … a2 a3 a4 1 a1 … a2 a3 a4 ... Convolution Matrix trace Nx

  18. Convolution with smoothly non-stationary PEF Up to m = Ntx Nx separate filters. trace 1 Ntx Nx 1 a1,1 … a1,2 a1,3 a1,4 1 a2,1 … a2,2 a2,3 a2,4 trace 2 x Ntx Nx 1 am-1,1 … am-1,2 am-1,3 am-1,4 1 am,1 … am,1 am,3 am,4 ... Convolution Matrix trace Nx

  19. Smoothly Non-Stationary (t,x) PEF - Pro and Con • Robust for spatially aliased data. • Handles missing/corrupt data. • No explicit patches (gates). • Stability not guaranteed.

  20. Small phase errors. Amplitude difference OK. Estimating the Noise PEF Noise model = training data Noise model requirements: Noise model = Lowpass filter( data )

  21. Via CG iteration Noise model: Unknown PEF: “Fitting goal” notation: Estimating the Noise PEF

  22. Estimating the Noise PEF • Problem often underdetermined. • Apply regularization.

  23. Estimating the Noise PEF • Problem often underdetermined. • Apply regularization.

  24. Given Obtain Signal PEF: Noise PEF: Data PEF: by deconvolution Estimating the Signal PEF Use Spitz approach, only in (t,x) Reference: 1/99 TLE, 99/00 SEG

  25. Talk Outline • Motivation for advanced separation techniques. • Model-based signal/noise separation. • Non-stationary (t,x) PEF. • Least squares signal estimation. • Real Data results.

  26. Apply constraint to eliminate n. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal

  27. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal In this form, equivalent to Wiener.

  28. Apply Spitz’ choice of Signal PEF. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal

  29. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal Apply Spitz’ choice of Signal PEF.

  30. Precondition with inverse of signal PEF. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal

  31. Noise: Signal: Data: Noise PEF: Signal PEF: Data PEF: Regularization parameter: Estimating the Unknown Signal Precondition with inverse of signal PEF.

  32. Estimating the Unknown Signal • e too small = leftover noise. • e too large = signal removed. • Ideally, should pick e = f(t,x).

  33. Talk Outline • Motivation for advanced separation techniques. • Model-based signal/noise separation. • Non-stationary (t,x) PEF. • Least squares signal estimation. • Real Data results.

  34. Data Specs • Saudi Arabian 3-D shot gather - cross-spread acquisition. • Test on three 2-D receiver lines. • Strong, hyperbolic ground roll. • Good separation in frequency. • Noise model = 15 Hz Lowpass.

  35. Data Results - Gather #1

  36. Data Results - Gather #1

  37. Data Results - Gather #1

  38. Data Results - Gather #2

  39. Data Results - Gather #2

  40. Data Results - Gather #3

  41. Data Results - Gather #3

  42. Conclusions • (t,x) domain, pattern-based coherent noise removal • Amplitude-preserving. • Robust to signal/noise overlap. • Robust to spatial aliasing. • Parameter-intensive.

  43. Acknowledgements • Saudi Aramco • SEP Sponsors • Antoine Guitton

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