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

Talk OutlineTalk Outline

Morgan P. Brown* and Robert G. Clapp

Stanford Exploration Project

Stanford University

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

- 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?

- Imaging/velocity estimation for deep targets.
- Rock property inversion (AVO, impedance).
- Single-sensor configurations.

Signal/Noise Separation: an Algorithm wish-list

- Amplitude-preservation.
- Robustness to signal/noise overlap.
- Robustness to spatially aliased noise.

Talk Outline

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

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” approachdata = signal + noise

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.

Assume:

data = signal + noise

signal, noise uncorrelated

signal, noise spectra known.

Optimal Reconstruction filter

Wiener Optimal EstimationSpectral 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 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 Outline

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

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 filteringHelix 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

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

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

- Robust for spatially aliased data.
- Handles missing/corrupt data.
- No explicit patches (gates).
- Stability not guaranteed.

Small phase errors.

Amplitude difference OK.

Estimating the Noise PEFNoise model = training data

Noise model requirements:

Noise model = Lowpass filter( data )

Estimating the Noise PEF

- Problem often underdetermined.
- Apply regularization.

Estimating the Noise PEF

- Problem often underdetermined.
- Apply regularization.

Obtain Signal PEF:

Noise PEF:

Data PEF:

by deconvolution

Estimating the Signal PEFUse Spitz approach, only in (t,x)

Reference: 1/99 TLE, 99/00 SEG

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

Apply constraint to eliminate n.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown SignalNoise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown SignalIn this form, equivalent to Wiener.

Apply Spitz’ choice of Signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Apply Spitz’ choice of Signal PEF.

Precondition with inverse of signal PEF.

Noise: Signal: Data:

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Noise PEF: Signal PEF: Data PEF:

Regularization parameter:

Estimating the Unknown Signal

Precondition with inverse of signal PEF.

- e too small = leftover noise.
- e too large = signal removed.
- Ideally, should pick e = f(t,x).

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

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

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

Acknowledgements

- Saudi Aramco
- SEP Sponsors
- Antoine Guitton

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