Application of surface-consistent matching filters(SCMF) to time-lapse data set

Mahdi Almutlaq and Gary F. Margrave

University of Calgary, Department of Geoscience, CREWES

December 02, 2011

What is the purpose of this study?

Our goal is to design matching filters thatscale data to same amplitude level

equalize phase and bandwidth

compensate for time-shifts

What is the purpose of this study?

Our goal is to design matching filters thatscale data to same amplitude level

equalize phase and bandwidth

compensate for time-shifts

What is the purpose of this study?

Our goal is to design matching filters thatscale data to same amplitude level

equalize phase and bandwidth

compensate for time-shifts

What is the purpose of this study?

Our goal is to design matching filters thatscale data to same amplitude level

equalize phase and bandwidth

compensate for time-shifts

Outline

1 Surface-consistent matching filtersSurface-consistent model

Matching filters

Surface-consistent matching filters

2 Constructing the matching filtersTime-lapse data set

How do we get the SCMF?

3 Examples2D example

4 Conclusions

5 Acknowledgements

Surface-consistent model

Surface-consistent model

The seismic trace can be modeled as

dij(t) = si (t) ∗ rj(t) ∗ hk(t) ∗ yl(t)

where

dij : seismic tracesi : source response at location irj : receiver response at location jhk : offset response at location k; k = |i − j |yl : subsurface response at l ; l = (i+j)

2

Matching filters

Time domain:m ∗ s1 = s2 (1)

Fourier domain:

M(ω) =S2(ω)

S1(ω). (2)

Important remarks:

a perfect matching filter is a spectral ratio; however

spectral ratio is unstable in presence of noise; and

What do we do?

We solve time-domain (equation 1) in LSQ sense and Fouriertransform the solution which is a good approximation to thespectral ratio method.

Matching filters

Time domain:m ∗ s1 = s2 (1)

Fourier domain:

M(ω) =S2(ω)

S1(ω). (2)

Important remarks:

a perfect matching filter is a spectral ratio; however

spectral ratio is unstable in presence of noise; and

What do we do?

We solve time-domain (equation 1) in LSQ sense and Fouriertransform the solution which is a good approximation to thespectral ratio method.

Matching filters

Time domain:m ∗ s1 = s2 (1)

Fourier domain:

M(ω) =S2(ω)

S1(ω). (2)

Important remarks:

a perfect matching filter is a spectral ratio; however

spectral ratio is unstable in presence of noise; and

What do we do?

We solve time-domain (equation 1) in LSQ sense and Fouriertransform the solution which is a good approximation to thespectral ratio method.

Matching filters

Matching filters

Matching filters

Matching filters

Matching filters

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

Surface-consistent modelMatching filtersSurface-consistent matching filters

In time-lapse we normally have 2 data sets:

Baseline survey; and

Monitoring survey

Their surface-consistent model is:

d1ij(t) = s1i (t) ∗ r1j(t) ∗ h1k(t) ∗ y1l(t)

d2ij(t) = s2i (t) ∗ r2j(t) ∗ h2k(t) ∗ y2l(t) (3)

Almutlaq and Margrave Surface-consistent matching filters

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

Surface-consistent matching filters

Several steps to obtain a SCMF:

design m such thatd1 = D2m, (4)

where D2 is the convolution matrix formed from d2

solve for m

m = (D2TD2 + α2I)−1D2Td1 (5)

FFT m

take the log of FFT(m)

The above are trace-by-trace process. Once that complete, we

decompose the log(FFT(m)) into four-components

1D example: variations in source

variation in input shot filters only

decomposed filters show variation in all components

comparing the input data with the decomposed data we seethe following:

1D example: variations in source

variation in input shot filters only

decomposed filters show variation in all components

comparing the input data with the decomposed data we seethe following:

1D example: variations in source

variation in input shot filters only

decomposed filters show variation in all components

comparing the input data with the decomposed data we seethe following:

1D example: variations in source

1D example: variations in source

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

Time-lapse data setHow do we get the SCMF?

Almutlaq and Margrave Surface-consistent matching filters

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

Time-lapse data setHow do we get the SCMF?

Zoom in:

Almutlaq and Margrave Surface-consistent matching filters

Data acquisition

shot spacing = 100mreceiver spacing = 10mtotal number of shots = 26101 receivers per shot

How do we get the SCMF?

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S_1

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R_1

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d 1,1

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d1.nr

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d2,nr

d_ns,nr

=

Sources Receivers Offsets Midpoints Unknowns Data

How do we construct the SCMF?

Gx = p, (6)

where G is the geometry matrix and x contains the unknownparameters. Recall that we have the log(FFT(m)), we denote it p,and the decomposition is:

x = (GTG + α2I)−1GTp, (7)

Constructing the SCMF

Constructing the SCMF

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

2D example

We will show two examples:

1 matching monitor # 1 survey to baseline survey

2 matching monitor # 2 survey to monitor # 1 survey

Almutlaq and Margrave Surface-consistent matching filters

2D example 1

2D example 1

2D example 1

What is NRMS?

Nrms is considered as the metric system that measures therepeatability between two traces at and bt in a time gate:

NRMS = 2RMS(at − bt)

RMS(at) + RMS(bt). (8)

2D example 1: NRMS

2D example 2

2D example 2

2D example 2

2D example 2: NRMS

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

Conclusions

We’ve deomonstrated the theory of surface-consistentmatching filters

It’s analogous to surface-consistent deconvolution except weconsider two data set

Synthetic time-lapse data sets: baseline, first monitor survey,second monitor survey

Constructed the 4-component surface-consistent matchingfilters

Applied the matching filters to two time-lapse examples

Balanced amplitudes, equalized phase and bandwidth andcompensated for time-shifts

Almutlaq and Margrave Surface-consistent matching filters

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

The authors thank the following:

The sponsors CREWES.

CREWES staff and students, in particular FaranakMahmoudian, Hassan Khaniani, Marcus Wilson, A.NaserYousef Zadeh, Rolf Maier, Kevin Hall, and David Henley.

Saudi Aramco for sponsoring Mahdi Almutlaq’s studyprogram.

Almutlaq and Margrave Surface-consistent matching filters

OutlineSurface-consistent matching filters

Constructing the matching filtersExamples

ConclusionsAcknowledgements

Thank you ...Questions?

Almutlaq and Margrave Surface-consistent matching filters