t x domain pattern based ground roll removal
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(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

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

Morgan P. Brown* and Robert G. Clapp

Stanford Exploration Project

Stanford University

ground roll what is it
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.
talk outline
Talk Outline
  • Motivation for advanced separation techniques.
  • Model-based signal/noise separation.
  • Non-stationary (t,x) PEF.
  • Least squares signal estimation.
  • Real Data results.
advanced separation techniques why bother
Advanced Separation techniques…why bother?
  • Imaging/velocity estimation for deep targets.
  • Rock property inversion (AVO, impedance).
  • Single-sensor configurations.
signal noise separation an algorithm wish list
Signal/Noise Separation: an Algorithm wish-list
  • Amplitude-preservation.
  • Robustness to signal/noise overlap.
  • Robustness to spatially aliased noise.
talk outline1
Talk Outline
  • Motivation for advanced separation techniques.
  • Model-based signal/noise separation.
  • Non-stationary (t,x) PEF.
  • Least squares signal estimation.
  • Real Data results.
coherent noise separation a model based approach

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

coherent noise subtraction
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.
wiener optimal estimation
Assume:

data = signal + noise

signal, noise uncorrelated

signal, noise spectra known.

Optimal Reconstruction filter

Wiener Optimal Estimation
spectral estimation
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.

spectral estimation1
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.

talk outline2
Talk Outline
  • Motivation for advanced separation techniques.
  • Model-based signal/noise separation.
  • Non-stationary (t,x) PEF.
  • Least squares signal estimation.
  • Real Data results.
helix transform and multidimensional filtering

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

helix transform and multidimensional filtering1

...

trace 1

trace 2

trace Nx

*

*

...

a2

1

a1

a2

a3

a4

1

a3

a1

a4

Helix Transform and multidimensional filtering
why use the helix transform

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.

convolution with stationary pef
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

convolution with smoothly non stationary pef
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

smoothly non stationary t x pef pro and con
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.
estimating the noise pef
Small phase errors.

Amplitude difference OK.

Estimating the Noise PEF

Noise model = training data

Noise model requirements:

Noise model = Lowpass filter( data )

estimating the noise pef1

Via CG iteration

Noise model:

Unknown PEF:

“Fitting goal” notation:

Estimating the Noise PEF
estimating the noise pef2
Estimating the Noise PEF
  • Problem often underdetermined.
  • Apply regularization.
estimating the noise pef3
Estimating the Noise PEF
  • Problem often underdetermined.
  • Apply regularization.
estimating the signal pef

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

talk outline3
Talk Outline
  • Motivation for advanced separation techniques.
  • Model-based signal/noise separation.
  • Non-stationary (t,x) PEF.
  • Least squares signal estimation.
  • Real Data results.
estimating the unknown signal

Apply constraint to eliminate n.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal
estimating the unknown signal1

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

In this form, equivalent to Wiener.

slide28

Apply Spitz’ choice of Signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

slide29

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Apply Spitz’ choice of Signal PEF.

slide30

Precondition with inverse of signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

slide31

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Precondition with inverse of signal PEF.

slide32

Estimating the Unknown Signal

  • e too small = leftover noise.
  • e too large = signal removed.
  • Ideally, should pick e = f(t,x).
talk outline4
Talk Outline
  • Motivation for advanced separation techniques.
  • Model-based signal/noise separation.
  • Non-stationary (t,x) PEF.
  • Least squares signal estimation.
  • Real Data results.
data specs
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.
conclusions
Conclusions
  • (t,x) domain, pattern-based coherent noise removal
  • Amplitude-preserving.
  • Robust to signal/noise overlap.
  • Robust to spatial aliasing.
  • Parameter-intensive.
acknowledgements
Acknowledgements
  • Saudi Aramco
  • SEP Sponsors
  • Antoine Guitton
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