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.


T x domain pattern based ground roll removal

Apply Spitz’ choice of Signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal


T x domain pattern based ground roll removal

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Apply Spitz’ choice of Signal PEF.


T x domain pattern based ground roll removal

Precondition with inverse of signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal


T x domain pattern based ground roll removal

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Precondition with inverse of signal PEF.


T x domain pattern based ground roll removal

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