how low can you go? finding low frequencies in various ... · how low can you go? finding low...

1

How low can you go?Finding low frequencies in variousFinding low frequencies in various places – Hussar exampleHeather Lloyd & Gary Margrave

Outline

2

Outline• Why do we need low-frequencies and where did they

go?• How do we get low-frequencies back?▫ Borrow them▫ Predict them

R d th▫ Record them• Low-frequency conclusions

Full Spectrum & Band-Limited Reflectivity

3

Full Spectrum & Band-Limited Reflectivity

Full Spectrum Reflectivity

0 4

0.6

0.8

tude

Full Spectrum Reflectivity

500 400 300 200 100 0 100 200 300 400 5000

0.2

0.4

Am

pli

-500 -400 -300 -200 -100 0 100 200 300 400 500Frequency (Hz)

0.8Bandlimited Reflectivity

0.2

0.4

0.6

Am

plitu

de

-500 -400 -300 -200 -100 0 100 200 300 400 5000Frequency (Hz)

Recursion Formula

4

Recursion Formula

j=k kr

II 0keII j0

0 eII j 0(Oldenburg et al., 1983).

Full Spectrum Inversion/model

5

Full Spectrum Inversion/model

Reflectivity

0.1

tude

Reflectivity

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 20

0.05

Am

pli

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Time (s)

4000Impedance

2000

3000

Impe

danc

e(k

g/(m

2 *s))

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2000

Time (s)

Band-Limited Inversion

6

Band-Limited Inversion

Reflectivity

0.02

0.04

itude

Reflectivity

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2-0.02

0Am

pli

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Time (s)

2000

e

Impedance

1500

Impe

danc

e(k

g/(m

2 *s))

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000Time (s)

Real Well Log Example

7

Real Well Log Example

10x 106

nce

*s)) 0-5 Hz Filtered Impedance

0 0.2 0.4 0.6 0.8 1 1.2 1.405

10

Time (s)

Impe

dan

(kg/

(m2 *

Time (s)

510

x 106

danc

em

2 *s)) Impedance

0 0.2 0.4 0.6 0.8 1 1.2 1.405

Time (s)

Impe

(kg/

(m

6 5-500 Hz Filtered Impedance

05

10x 106

mpe

danc

ekg

/(m2 *s

)) 5 500 Hz Filtered Impedance

0 0.2 0.4 0.6 0.8 1 1.2 1.4Time (s)

Im (k

(From Lindseth 1979).

8

M d l h•Model them•Borrow themP di t th•Predict them

•Record them

Borrow low-frequencies using BLIMP

10

Borrow low-frequencies using BLIMP

Impedance Log

10

20

edan

ce*m

/(m3 *s

))

0 0.2 0.4 0.6 0.8 10Time (s)

Imp

106 *(

kg

( )

0.02Synthetic Trace

tude

0 0.2 0.4 0.6 0.8 1-0.02

0

Am

plit

0 0.2 0.4 0.6 0.8 1Time (s)

BLIMP Steps 1 & 2

11

BLIMP Steps 1 & 2

20Step 1: Remove the linear trend from the impedance log

10

15

20

edan

ce*m

/(m3 *s

))

Impedance LogLinear Trend

0 0.2 0.4 0.6 0.8 10

5Impe

106 *(

kg*

Time (s)

4x 10-4 Step 2: Apply the recursion formula to the trace using Io=1

nce

0

2

eudo

Impe

dan

0 0.2 0.4 0.6 0.8 1-2Time (s)

Pse

BLIMP Steps 3 & 4

12

BLIMP Steps 3 & 4

5

10x 108 Step 3: Compute the Fourier transform of the impedances

litud

e

Impedance Log SpectraInverted Reflectivity Spectra

0 5 10 15 20 25 30 35 40 45 500

5

Frequency (Hz)

Am

p

q y ( )

10x 108Step 4: Determine a scalar using the mean power

of the impedance log spectra and apply it

ude

0 5 10 15 20 25 30 35 40 45 500

5

Am

plitu

0 5 0 5 0 5 30 35 0 5 50Frequency (Hz)

BLIMP Steps 5 & 6

13

BLIMP Steps 5 & 6

108 Step 5: Apply filters to the impedance log and inverted reflectivity spectra

5

10x 10 Step 5: Apply filters to the impedance log and inverted reflectivity spectra

plitu

de

Impedance LogBLIMP inversion

0 5 10 15 20 25 30 35 40 45 500Frequency (Hz)

Am

p

q y ( )

5

10x 108Step 6: Combine the filtered impedance log and inverted reflectivity spectra

tude

0 5 10 15 20 25 30 35 40 45 500

5

Am

plit

Frequency (Hz)

BLIMP Step 7

14

BLIMP Step 7

20Step 7: Inverse Fourier transform the solution and add the linear trend

16

18

Impedance LogBLIMP inversion

12

14

nce

(m3 *s

))

8

10

Impe

dan

106 *(

kg*m

/(

4

6

0 0.2 0.4 0.6 0.8 12Time (s)

BLIMP Inversion Problems

15

BLIMP Inversion Problems

• Sensitive to low-frequency cut-off• Best applied to one trace or a model withoutBest applied to one trace or a model without

structure• Relies heavily on log informationy g

Prediction Filters

17

Prediction Filters

One-Lag Prediction Filter Multi-Lag Prediction Filter

⋅⋅ 100 00 dad

⋅⋅ +lagdad 00 100

=

×

⋅⋅∴⋅⋅ 2101

::0::0

d

d

a

a

ddd

dd

=

×

⋅⋅∴⋅⋅ +lag

d

d

a

a

ddd

dd::0::

0 2101

⋅⋅ +− 101 mnmm daddd ⋅⋅ +− mlagnmm daddd 01

Prediction Filters18

0.8

Frequencies Predictedfrom Positive Spectra

0.8

Frequencies Predictedfrom Negative Spectra

Prediction Filters

0.4

0.6

Am

plitu

de

0.4

0.6

Am

plitu

de

-500 0 5000

0.2

Frequency (Hz)

A

-500 0 5000

0.2

Frequency (Hz)

A

0.6

0.8Average of Positive and Negative Spectra

e

0.2

0.4

Am

plitu

de

-500 -400 -300 -200 -100 0 100 200 300 400 5000Frequency (Hz)

12 Layer Model

19

12 Layer Model

4000

5000

e ))

Impedance For 12 Layer Model 0

Reflectivity

Full Spectrum

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 21000

2000

3000

4000Im

peda

nce

(kg/

(m2 *s

)

0.2

0.4

Bandlimited

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

3000

4000

5000

danc

em

2 *s))

One-lag Predicted Impedance0.6

0.8

1e (s

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000

3000

Impe

d(k

g/(m

Multi-lag Predicted Impedance

1

1.2

1.4

Tim

e

2000

3000

4000

5000

mpe

danc

ekg

/(m2 *s

))1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000Im (k

Time (s)-0.2 0 0.22

Amplitude

12 Layer Model with Noise

20

12 Layer Model with Noise

4000

5000

e ))

Impedance For Noisy 12 Layer Model 0

Reflectivity

Full Spectrum

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 21000

2000

3000

4000Im

peda

nce

(kg/

(m2 *s

)

0.2

0.4

Bandlimited

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

3000

4000

5000

danc

em

2 *s))


0.8

1e (s

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000

3000

Impe

d(k

g/(m


1

1.2

1.4

Tim

e

2000

3000

4000

5000

mpe

danc

ekg

/(m2 *s

))1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000Im (k

Time (s)-0.2 0 0.22

Amplitude

12 Layer Model with Ricker Wavelet

21

12 Layer Model with Ricker Wavelet

4000

5000

e )

Impedance For 12 Layer Model with Ricker Wavelet 0

Reflectivity

Full Spectrum

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 21000

2000

3000

4000

Impe

danc

e(k

g/(m

2 *s)

0.2

0.4

Bandlimited

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2000

3000

4000

5000

danc

em

2 *s))


0.8

1e (s

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000

3000

Impe

d(k

g/(m


1

1.2

1.4

Tim

e

2000

3000

4000

5000

mpe

danc

ekg

/(m2 *s

))1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21000

2000Im (k

Time (s)-0.2 0 0.22

Amplitude

Well 12-27

22

Well 12-27

Impedance For Well 12-27Reflectivity

10

20

Impe

danc

e*(

kg*m

/(m3 *s

)) 0

0.2

Full SpectrumBandlimited

0 0.2 0.4 0.6 0.8 1 1.20

I10

6 *

20

nce

m3 *s

))


s)

0 0.2 0.4 0.6 0.8 1 1.20

10

Impe

dan

106 *(

kg*m

/(m

Multi lag Predicted Impedance

0.6

0.8

Tim

e (s

10

20

mpe

danc

ekg

*m/(m

3 *s))


1

0 0.2 0.4 0.6 0.8 1 1.20

Im10

6 *(k

Time (s)-0.2 0 0.2

1.2

Amplitude

Prediction Filter Problems

23

Prediction Filter Problems

• Sensitive to spectra curvature• Sensitive to NoiseSensitive to Noise• Sensitive to prediction filter length• Sensitive to complicated modelsSensitive to complicated models

Accelerometer CMP Stacks

25

Accelerometer CMP Stacks

Processed Accelerometer Stacked Data0

0.5

1

1.5

Tim

e (s

)

2

2.5

3

3.5

CMP Gather Number100 200 300 400 500 600 700 800

4

10Hz Geophone CMP Stacks

26

10Hz Geophone CMP Stacks

Processed 10Hz Geophone Stacked Data0

0.5

1

1.5

Tim

e (s

)

2

2.5

3

3.5


4

4 5Hz Geophone CMP Stacks

27

4.5Hz Geophone CMP Stacks

Processed 4.5Hz Geophone Stacked Data0

0.5

1

1.5

Tim

e (s

)

2

2.5

3

3.5


4

Creating the Stacked Traces

28

Creating the Stacked Traces

29

10

0A) Well 1227 Reflectivity Amplitude Spectra

10

0B) Accelerometer Amplitude Spectra

40

-30

-20

-10

mpl

itude

(db)

40

-30

-20

-10

mpl

itude

(db)

0 50 100 150 200 250-60

-50

-40

Frequency (Hz)

Am

0 50 100 150 200 250-60

-50

-40

Frequency (Hz)

Am

q y ( ) q y ( )

-10

0

b)

C) 10Hz Geophone Amplitude Spectra

-10

0

b)

D) 4.5Hz Geophone Amplitude Spectra

50

-40

-30

-20

Am

plitu

de (d

b

50

-40

-30

-20A

mpl

itude

(db

0 50 100 150 200 250-60

-50

Frequency (Hz)0 50 100 150 200 250-60

-50

Frequency (Hz)

30

0.3

Processed AccelerometerStacked Trace

0.3

Processed 10HzStacked Trace

0.3

Processed 4.5HzStacked Trace

0.4

0.5

0.4

0.5

0.4

0.5

0.6

0 7e (s

)

0.6

0 7e (s

)0.6

0 7e (s

)

0.7

0.8

Tim

e 0.7

0.8

Tim

e 0.7

0.8

Tim

e

0.9

1

0.9

1

0.9

1

-0.06 -0.04 -0.02 0 0.021.1

Amplitude-0.06 -0.04 -0.02 0 0.021.1

Amplitude-0.06 -0.04 -0.02 0 0.021.1

Amplitude

31

Processed AccelerometerImpedance Inversion

Processed 10HzImpedance Inversion

Processed 4.5HzImpedance Inversion

0.3

0.4

0 50.5

0.6

0 7me

(s)

0.7

0.8

0 9

Tim

0.9

1

1.10 5 10 15

1.1

Impedance106(kg*m/(m3*s))

0 5 10 15Impedance

106(kg*m/(m3*s))

0 5 10 15Impedance

106(kg*m/(m3*s))

BLIMP – 1Hz cut-off

32

BLIMP – 1Hz cut-offAccelerometer BLIMP Inversion

F =1 E=4210Hz Geophone BLIMP Inversion

F =1 E=364.5Hz Geophone BLIMP Inversion

F =1 E=41

0.3

0.4

FCut-off=1, E=42

0.3

0.4

FCut-off=1, E=36

0.3

0.4

FCut-off=1, E=41

0.5

0.6

0 7

e (s

)

0.5

0.6

0 7

e (s

)0.5

0.6

0 7

e (s

)

0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim

0 10 20

1

1.1

Impedance0 10 20

1

1.1

Impedance

0 10 20

1

1.1

ImpedanceImpedance106*(kg*m/(m3*s))

Impedance106*(kg*m/(m3*s))


Well Impedance Blimp Inversion Impedance Trend

BLIMP – 5Hz cut-off

33

BLIMP – 5Hz cut-offAccelerometer BLIMP Inversion



F =5 E=39

0.3

0.4

FCut-off=5, E=40

0.3

0.4

FCut-off=5, E=38

0.3

0.4

FCut-off=5, E=39

0.5

0.6

e (s

)

0.5

0.6

e (s

)0.5

0.6

e (s

)

0.7

0.8

0.9

Tim

e

0.7

0.8

0.9

Tim

e

0.7

0.8

0.9

Tim

e

0 10 20

1

1.1

Impedance0 10 20

1

1.1

Impedance

0 10 20

1

1.1





35

0.3

Processed AccelerometerStacked Trace

0.3

Processed 10HzStacked Trace

0.3

Processed 4.5HzStacked Trace

0.4

0.5

0.4

0.5

0.4

0.5

0.6

0 7e (s

)

0.6

0 7e (s

)0.6

0 7e (s

)

0.7

0.8

Tim

e 0.7

0.8

Tim

e 0.7

0.8

Tim

e

0.9

1

0.9

1

0.9

1

-0.06 -0.04 -0.02 0 0.021.1

Amplitude-0.06 -0.04 -0.02 0 0.021.1

Amplitude-0.06 -0.04 -0.02 0 0.021.1

Amplitude

36

0 3

Processed AccelerometerImpedance Inversion

Processed 10HzImpedance Inversion

Processed 4.5HzImpedance Inversion

0.3

0.4

0 50.5

0.6

0 7e (s

)

0.7

0.8

0 9

Tim

e

0.9

1

1 10 5 10 15

1.1

Impedance106(kg*m/(m3*s))

0 5 10 15Impedance

106(kg*m/(m3*s))

0 5 10 15Impedance

106(kg*m/(m3*s))

BLIMP 1Hz cut-off

37

BLIMP 1Hz cut-offAccelerometer BLIMP Inversion



F =1 E=40

0.3

0.4

FCut-off=1, E=41

0.3

0.4

FCut-off=1, E=39

0.3

0.4

FCut-off=1, E=40

0.5

0.6

0 7me

(s)

0.5

0.6

0 7me

(s)

0.5

0.6

0 7me

(s)

0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim

0 10 20

1

1.1

Impedance0 10 20

1

1.1

Impedance

0 10 20

1

1.1





BLIMP 5Hz cut-off

38

BLIMP 5Hz cut-offAccelerometer BLIMP Inversion



F =5 E=36

0.3

0.4

FCut-off=5, E=37

0.3

0.4

FCut-off=5, E=35

0.3

0.4

FCut-off=5, E=36

0.5

0.6

0 7me

(s)

0.5

0.6

0 7me

(s)

0.5

0.6

0 7me

(s)

0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim 0.7

0.8

0.9

Tim

0 10 20

1

1.1

Impedance0 10 20

1

1.1

Impedance

0 10 20

1

1.1

Impedancep106*(kg*m/(m3*s))

p106*(kg*m/(m3*s))

p106*(kg*m/(m3*s))


BLIMP 3Hz cut-off

39

BLIMP 3Hz cut-off

Accelerometer BLIMP Inversion 10Hz Geophone BLIMP Inversion 4.5Hz Geophone BLIMP Inversion

0.3

0.4

cce e o ete e s oFCut-off=3, E=39

0.3

0.4

0 Geop o e e s oFCut-off=3, E=37

0.3

0.4

5 Geop o e e s oFCut-off=3, E=37

0.5

0.6

(s)

0.5

0.6

(s)

0.5

0.6

(s)

0.7

0.8

0.9

Tim

e 0.7

0.8

0.9

Tim

e 0.7

0.8

0.9

Tim

e 0 10 20

1

1.10 10 20

1

1.1

0 10 20

1

1.1





Conclusions

40

Conclusions• BLIMP inversion relies heavily on the low

frequencies of the well impedance and is very sensitive to the low frequency cut-off value.

• Prediction filter low frequency recovery methods are good for simple models with flat wavelets currently this method is not suitable for wells or real data.

Recording lo er freq encies in the field is possible• Recording lower frequencies in the field is possible even down to 1Hz but some well information is still required.q

References

41

References• Oldenburg, D. W., Scheuer, T., and Levy, S., 1983,

Recovery of the acoustic impedance from reflection seismograms: Geophysics, Vol. 48, No. 10.

• Lindseth, R. O., 1979, Synthetic sonic logs – a process for stratigraphic interpretation: Geophysics, V l 44 N 1Vol. 44, No. 1.

• Ferguson, R. J. and Margrave, G. F., 1996, A simple l ith f b dli it d i d i ialgorithm for bandlimited impedance inversion:

CREWES Research Report, Vol. 8, No. 21.

Acknowledgements

42

Acknowledgements• Helen Isaac• Kris Innanen• Husky Energy, INOVA and Geokinetics• Kevin Hall• Peter Gagliardi, Faranak Mahmoudian, Chris Bird,

i i iSteve Kim, Diane Lespinasse• Laura Baird

CREWES t d t t ff & f lt• CREWES students, staff & faculty• CREWES Sponsors

how low can you go? finding low frequencies in various ... · how low can you go? finding low...

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