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Attribute-Assisted Seismic Processing and Interpretation
http://geology.ou.edu/aaspi/
Attribute-Assisted Seismic Processing and Interpretation
http://geology.ou.edu/aaspi/
Brazilian carbonate reservoir study using the Wavelet Transform Teager-Kaiser Energy
Attribute-Assisted Seismic Processing and Interpretation
http://geology.ou.edu/aaspi/
Marcílio Castro de Matos [email protected] or www.matos.eng.br
Kurt J. Marfurt [email protected]
Oklahoma University
Paulo Roberto Schroeder Johann [email protected]
João Adolfo Rosseto [email protected]
Petrobras
AASPI
Motivation
Seismic attributes applied to carbonate reservoirs examples: Masaferro et al. (2004) state that the combined effects of variation in
depositional facies and diagenetic alteration play a key role in controlling variations in sonic velocities and thus is acoustic impedance in carbonate systems.
Pearson and Hart (2004) showed that spectral components can be used in carbonate reservoir characterization. Specifically, they predicted the porosity of a carbonate reservoir from a linear combination of the slope from peak to maximum spectral frequency and the ratio of the number of positive samples over the number of negative samples within a time interval.
Chopra and Marfurt (2007) show how the shape or geomorphology of reflection patterns, coupled with appropriate models deposition and diagenesis, further aid the mapping of carbonate facies. Thus, both geometric (measuring lateral changes) and trace shape (measuring vertical seismic waveform) seismic attributes can be a great aid in the characterization of carbonate reservoirs.
Now, carbonates are very important to Brazil !!!
Objectives
To show how the seismic density energy can be related to the Wavelet Transform Teager-Kaiser Energy
To show that this nonlinear energy-tracking algorithm allows us to differentiate high amplitude reservoir from other high amplitude reflections
To show how we applied this technique to a Brazilian carbonate reservoir
Summary
• Introduction: Seismic x Teager-Kaiser Wave Energy
• The Wavelet Transform TK Energy - WaveTeKE
• WaveTeKE applied to a Brazilian carbonate reservoir
• Conclusions
Seismic Wave Energy Density (Sheriff and Geldart, 1995)
Simple Harmonic Motion Energy (Kaiser, 1990)
22222 22
1 f 22
2
1 m
22
Newton’s law of motion of a mass m suspended by a spring of force constant k:
02
2
xm
k
dt
xd tAtx cos
Total Energy E of the system:
22
2
1
2
1xmkx
Total energy is equal to the maximum value of the kinetic energy
X
Mass-spring system
F=-kx
Animation courtesy of Dr. Dan Russell, Kettering University http://www.kettering.edu/~drussell/demos.html
http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm
Teager-Kaiser Energy(Kaiser, 1990)
11sin 222 nxnxnxA
nEnxnxnxAA 11sin 22222
tAtx cos A/D conversion
Oscillatory Phenomena
sin0when
sampling period: ts sampling frequency: fs
4 ms 250 Hz 31.25 Hz
2 ms 500 Hz 62.5 Hz
22
ss fff 2
Teager-Kaiser Energy
TK energy estimation error < 11 %8
.,.,7854.04
sffeiwhen
nAnx cos
Teager-Kaiser Energy: examples and drawbacks
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Am
plitu
de
10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
TK
Ene
rgy
Sample number n
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
Am
plitu
de10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5
TK
Ene
rgy
Sample number n
Ex: Signal consisting on two sinusoids
sin(pi/6*n)+sin(pi/4*n)sin(pi/6*n) sin(pi/4*n)
TK Energy crossterms
It is essential to separate the components of the signal by some form of band-pass filtering before applying the algorithm.
22AE
drawback
Summary
• Introduction: Seismic x Teager-Kaiser Wave Energy
• The Wavelet Transform TK Energy - WaveTeKE
• WaveTeKE applied to a Brazilian carbonate reservoir
• Conclusions
Continuous Wavelet Transform
0 1 2 3 4 5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
tempo
Am
plitu
de
0.02 0.04 0.06 0.08 0.1 0.12 0.14
0
2
4
6
8
10
12
14
16
18
frequencia normalizada (x )
Am
plit
ude
Cdd0 2
0
2 ˆˆ
0
dtt
s
ut
stsu 1
, 00ˆ
dtt
-5 -4 -3 -2 -1 0 1 2 3 4 5-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Wavelet Chapeu Mexicano
tempo
Am
plitu
de
(x) L2() is called a wavelet
100 200 300 400 500 600 700 800 900 1000
-0.2
0
0.2
0.4
Amostras
Am
plitu
de
Amostras
Esc
ala
100 200 300 400 500 600 700 800 900 1000
10
20
30
40
50
60
Continuous Wavelet Transform (CWT)
time
Amplitude
( ),
1( , ) ( , ) , ( )x u s
t uCWT u s Wf u s f f t dt
ss
1
( , ) ( ) s
t uWf u s f t dt f u
ss
s
t
sts 1
ˆ ˆs s s The CWT can be interpreted
as a band pass filter response at each scale s
Sca
les
Time (ms)
Time (ms)
f t t
WaveTeKEDescription
Band pass filter 1
Band pass filter 2
Band pass filter n
...
Teager-Kaiser Energy
Teager-Kaiser Energy
Teager-Kaiser Energy...
WaveTeKE
Reservoir
Wavelet Transform
Case 01: Carbonate Oil Well
Time-frequency attributes
Frequency
Amplitude
Peak Frequency
Peak Amplitude Highest Frequency Peak Amplitude
Highest Frequency Peak
Mean
Highest Frequency Peak Amplitude over mean
Peak Amplitude over mean
Difference between PF and HFP
Difference between PA and HFPA
WaveTeKE Applied to wedge model
(b)
Tra
vel t
ime
(ms)
(a)
5 10 15 20 25 30 35 40 45 50
50100150200250
-200
0
200
(c)
Tra
vel t
ime
(ms)
5 10 15 20 25 30 35 40 45 50
50100150200250
20
40
Temporal thickness (ms)
Tra
vel t
ime
(ms)
5 10 15 20 25 30 35 40 45 50
50100150200250
0.511.52x 10
4
0 5 10 15 20 25 30 35 40 45 500
1
2
3x 10
4
Am
plitu
de o
f th
e M
axim
um F
requ
ency
Temporal thickness (ms)0 5 10 15 20 25 30 35 40 45 50
20
30
40
50
Max
imum
Fre
quen
cy
(d)
Amp Max Freq
Max Freq
Amplitude of the maximum
instantaneous frequency
Maximum instantaneous
frequency
Instantaneous seismic attributes generated from the time-frequency
analysis
Time interval seismic attributes generated from the time-frequency
analysis
0 5 10 15 20 25 30 35 40 45 50
0
0.05
0.1
0.15
0.2
0.25
Temporal Thickness (ms)
Travel tim
e (m
s)
Temporal Thickness (ms)
Travel tim
e (m
s)
5 10 15 20 25 30 35 40 45 50
50
100
150
200
250-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a)
b)
Thin bed model
CWT with real Morlet
WaveTeKE with real Morlet
Seismic trace
WaveTeKE with complex
Morlet
CWT with complex Morlet
The same dominant frequency and instant time
-200 0 200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Amplitude
tim
e
20 40 60 80 100 120
50
100
150
200
250
20
40
60
80
100
120
140
20 40 60 80 100 120
50
100
150
200
250
20
40
60
80
100
120
140
20 40 60 80 100 120
50
100
150
200
250
10
20
30
40
50
60
70
80
90
-200 0 200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Amplitude
time
20 40 60 80 100 120
50
100
150
200
250
10
20
30
40
50
60
70
80
90
20 40 60 80 100 120
50
100
150
200
250
10
20
30
40
50
60
70
80
90
20 40 60 80 100 120
50
100
150
200
250
10
20
30
40
50
60
70
80
90
-200 0 200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Amplitude
tim
e
time
5 10 15 20 25 30 35 40 45 50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20 ms
30 ms
35 ms
Peak Amplitude
Highest Frequency Peak Amplitude
Peak Amplitude
Highest Frequency Peak Amplitude
20 40 60 80 100 120
50
100
150
200
250
20
40
60
80
100
120
140
Amplitude
High
Low
Freq
Time
Freq
Time
Freq
Time
Freq
Time
Freq
Time
Freq
Time
Summary
• Introduction: Seismic x Teager-Kaiser Wave Energy
• The Wavelet Transform TK Energy - WaveTeKE
• WaveTeKE applied to a Brazilian carbonate reservoir
• Conclusions
80 ms below the negative peak horizon
2 km
AA’
400 ms
B B’
dry
ho
le
pro
du
ce
r
B
B’
A’
A
1.2 km
A’
400 ms
pro
du
ce
r
BB’A
Negative
Positive
Amplitude
Reservoir Base Map AmplitudeSeismic Sections (dip/strike) of a Carbonate
Oil Field - Campos Basin
Reservoir Base Maps
Reservoir topStructural Time
Semblance
Time (s)
1.4
1.5
1.6
1.7
(a)
Low
High
Semblance
Reservoir Base Maps
Most negative curvature
Sobel filter
(d)
(b)
B
B’
A’
A Sobel FilterLow
High
Most Neg Curv
Pos
Neg
0
AA’
400 ms
B B’
dry
ho
le
pro
du
ce
r
A’
400 ms
pro
du
ce
r
BB’A
1.2 km
Zero
Positive
2 km
B
B’
A’
A
TE energy absolute sum value between the top Horizon and 80 ms bellow it
WaveTeKEPeak amplitude
Carbonate Oil Field - Campos Basin
low highPeak energy
50
10
Pe
ak
fre
qu
en
cy
(H
z)
++ ++
Minimum amplitude
Max
Min
Minimum amplitude bellow the reservoir top
80 ms Time interval seismic attributes
Peak WaveTeKE frequency and its associated amplitude plotted together using a 2D color bar bellow the reservoir top
RGB display of spectrum attributes
Frequency
Peak Frequency
Mean
Peak Amplitude over mean
Difference between PF and HFP
Red
Green
Blue
RGB display of spectrum attributes
Frequency
Highest Frequency Peak
Mean
Highest Frequency Peak Amplitude over mean
Difference between PF and HFP
Red
Green
Blue
RGB display of spectrum attributes
Frequency
Highest Frequency Peak
Mean
Difference between PF and HFP
Green
Blue
Peak Frequency
Red
RGB display of spectrum attributes
Frequency
Mean
Peak Amplitude over mean
Difference between PF and HFP
Red
Green
Highest Frequency Peak Amplitude over mean
Blue
Summary
• Introduction: Seismic x Teager-Kaiser Wave Energy
• The Wavelet Transform TK Energy - WaveTeKE
• WaveTeKE applied to a Brazilian carbonate reservoir
• Conclusions
Conclusions
We show that the Teager-Kaiser energy can be computed for seismic data through the joint time-frequency representation.
The TK energy appears to be quite effective in delineating strong amplitude, high frequency events associated with a producing areas of a carbonate reservoir.
The results obtained with real seismic data show the WaveTeKE potential use as an exploratory tool to detect energy associated with important geological marks and potential exploratory leads.
Acknowledgements
We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.
Attribute-Assisted Seismic Processing and Interpretation
http://geology.ou.edu/aaspi/
The first two authors would like to thank the support from the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation Consortium and its sponsors.
