How low can you go? Finding low frequencies in various ... · How low can you go? Finding low...
Transcript of How low can you go? Finding low frequencies in various ... · How low can you go? Finding low...
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How low can you go?Finding low frequencies in variousFinding low frequencies in various places – Hussar exampleHeather Lloyd & Gary Margrave
Outline
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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
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Recursion Formula
j=k kr
II 0keII j0
0 eII j 0(Oldenburg et al., 1983).
Full Spectrum Inversion/model
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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
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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
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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).
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M d l h•Model them•Borrow themP di t th•Predict them
•Record them
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Borrow low-frequencies using BLIMP
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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
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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
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Prediction Filters
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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))
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 Ricker Wavelet
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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))
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
Well 12-27
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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
))
One-lag Predicted Impedance0.4
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))
Multi-lag Predicted Impedance
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
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Prediction Filter Problems
• Sensitive to spectra curvature• Sensitive to NoiseSensitive to Noise• Sensitive to prediction filter length• Sensitive to complicated modelsSensitive to complicated models
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Accelerometer CMP Stacks
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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
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10Hz Geophone CMP Stacks
Processed 10Hz Geophone 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
4 5Hz Geophone CMP Stacks
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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
CMP Gather Number50 100 150 200 250 300 350 400
4
Creating the Stacked Traces
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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
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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))
Impedance106*(kg*m/(m3*s))
Well Impedance Blimp Inversion Impedance Trend
BLIMP – 5Hz cut-off
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BLIMP – 5Hz cut-offAccelerometer BLIMP Inversion
F =5 E=4010Hz Geophone BLIMP Inversion
F =5 E=384.5Hz Geophone 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
ImpedanceImpedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Well Impedance Blimp Inversion Impedance Trend
34
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=4110Hz Geophone BLIMP Inversion
F =1 E=394.5Hz Geophone 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
ImpedanceImpedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Well Impedance Blimp Inversion Impedance Trend
BLIMP 5Hz cut-off
38
BLIMP 5Hz cut-offAccelerometer BLIMP Inversion
F =5 E=3710Hz Geophone BLIMP Inversion
F =5 E=354.5Hz Geophone 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))
Well Impedance Blimp Inversion Impedance Trend
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
Impedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Impedance106*(kg*m/(m3*s))
Well Impedance Blimp Inversion Impedance Trend
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