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

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

Morgan P. Brown* and Robert G. Clapp

Stanford Exploration ProjectStanford 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

• In (t,x,y), ground roll = cone.

• Usually spatially aliased.

• In practice, “ground roll cone” muted.

• Motivation for advanced separation techniques.

• Model-based signal/noise separation.

• Non-stationary (t,x) PEF.

• Least squares signal estimation.

• Real Data results.

Talk Outline

Advanced Separation techniques…why bother?

• Imaging/velocity estimation for deep targets.

• Rock property inversion (AVO, impedance).

• Single-sensor configurations.

• Amplitude-preservation.

• Robustness to signal/noise overlap.

• Robustness to spatially aliased noise.

Signal/Noise Separation: an Algorithm wish-list






Talk Outline

Coherent Noise Separation - a “model-based” approach

Noise Subtractionsimple subtraction

adaptive subtractionpattern-based subtraction

“Signal Processing” step

data = signal + noise

Noise Modelingmoveout-based

frequency-based

“Physics” stepWiener Optimal Estimation

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.

),(),(

),(),( k

kkk

ωn

ωnωs

P

PPωH

Optimal Reconstruction filter

• Question: How to estimate the non-stationary spectra of unknown signal and noise?

PEF, data have inverse spectra.

Spectral Estimation

• Answer: Smoothly non-stationary (t,x) Prediction Error Filter (PEF).

• Question: How to estimate the non-stationary spectra of unknown signal and noise?

Wiener technique requires signal PEF and noise PEF.

Spectral Estimation

• Answer: Smoothly non-stationary (t,x) Prediction Error Filter (PEF).






Talk Outline

Helix Transform and multidimensional filtering

x

t

Data =

Helix Transform

1 a4a1 a3a2...

Nt

Nt x Nx

trace 1 trace 2 trace Nx...

x

1 a3

a1 a4

a2

PEF =t

Helix Transform and multidimensional filtering

1 a3

a1 a4

a2

*1 a4a1 a3a2...

trace 1 trace 2 trace Nx...

*

Why use the Helix Transform?

2-D PEFHelix

Transform1-D PEF

1-D Decon(Backsubstitution)

Stable Inverse PEF

1-D filtering toolbox directly applicable to multi-dimensional problems.

Convolution with stationary PEF

1 a1 … a2 a3 a4

1 a1 … a2 a3 a4

1 a1 … a2 a3 a4

1 a1 … a2 a3 a4

Nt x Nx

trace 1trace 2

trace Nx

...

Nt x N

x

x

Convolution Matrix

Convolution with smoothly non-stationary PEF

1 a1,1 … a1,2 a1,3 a1,4

1 a2,1 … a2,2 a2,3 a2,4

1 am-1,1 … am-1,2 am-1,3 am-1,4

1 am,1 … am,1 am,3 am,4

Nt x Nx

trace 1trace 2

trace Nx

...

Nt x N

x

x

Convolution Matrix

Up to m = Nt x Nx separate filters.

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.

Noise model requirements:

Noise model = Lowpass filter( data )

Noise model = training data


Noise model:

Unknown PEF:

0n

na

Via CG iteration

20 min n

aan

n

0 0 nan“Fitting goal” notation:


• Problem often underdetermined.

• Apply regularization.

0 0 nan


0

00

n

n

aRan

• Problem often underdetermined.

• Apply regularization.

Estimating the Signal PEF

GivenNoise PEF:

Data PEF: na

da 1

nds aaa Obtain Signal PEF:

by deconvolution

Use Spitz approach, only in (t,x)

Reference: 1/99 TLE, 99/00 SEG






Talk Outline

0 0

sana

s

n

Estimating the Unknown Signal

Noise: Signal: Data:Noise PEF: Signal PEF: Data PEF: Regularization parameter:

na dasan ds

sdn

Apply constraint to eliminate n.

0

sadasa

s

nn



na dasan ds

sdn

In this form, equivalent to Wiener.

0

sadasa

s

nn


na dasan ds


1 nds aaa

Apply Spitz’ choice of Signal PEF.

0

saa

dasa

nd

nn1


na dasan ds


1 nds aaa

Apply Spitz’ choice of Signal PEF.

0

saa

dasa

nd

nn1


na dasan ds


Precondition with inverse of signal PEF.

psaa nd 1

0

pdapaaa ndnn 1


na dasan ds


Precondition with inverse of signal PEF.

psaa nd 1

• too small = leftover noise.

• too large = signal removed.

• Ideally, should pick = f(t,x).







Talk Outline

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.

Data Results - Gather #1







• (t,x) domain, pattern-based coherent noise removal

• Amplitude-preserving.

• Robust to signal/noise overlap.

• Robust to spatial aliasing.

• Parameter-intensive.

Conclusions

• Saudi Aramco

• SEP Sponsors

• Antoine Guitton

Acknowledgements

Documents

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