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SPECTRAL DECOMPOSITION AND HARMONIC BANDWIDTH
EXTRAPOLATION: A CASE STUDY OF A CHANNEL SYSTEM
ON A 3D MULTICOMPONENT SURVEY IN SOUTHERN
ALBERTA, CANADA
A Thesis Presented to
the Faculty of the Department of Earth and Atmospheric
Sciences University of Houston
In Partial Fulfillment
of the Requirements for the
Degree Master of Science
By Yang Mu
May 2017
SPECTRAL DECOMPOSITION AND HARMONIC BANDWIDTH
EXTRAPOLATION: A CASE STUDY OF A CHANNEL SYSTEM
ON A 3D MULTICOMPONENT SURVEY IN SOUTHERN
ALBERTA, CANADA
ii
Yang Mu APPROVED:
Dr. John P. Castagna, Committee Supervisor
Department of Earth and Atmospheric Sciences
Dr. Evgeni Chesnokov, Committee member
Department of Earth and Atmospheric Sciences
Dr. Heather Bedle, Committee member
Department of Earth and Atmospheric Sciences
Dr. Bruce Shang, Committee member
Sinopec Tech Houston
Dean, College of Natural Sciences and Mathematics
iii
ACKNOWLEDGEMENTS
I dedicate my Master’s thesis to my grandmother: I owe you my entire world.
I would like to thank Dr. John Castagna and Dr. Heather Bedle for their tremendous
help and support in this thesis process. I would also like to thank Dr. Evgeni Chesnokov
and Dr. Bruce Shang for their service in my committee and Mr. Gabriel Gil, Mr. Anthony
Torlucci, Mr. Firas Jarrah, Dr. Eshetu Gebretsadik, Dr. Arnold Oyem, and Dr. Azie Aziz
in Lumina Geophysical LLC for their help. At last, I would like to thank AGL and CGG
for sponsoring the Blackfoot 3C-3D dataset and Hampson-Russell software.
My special thank goes to my dear parents who love and support me unconditionally.
SPECTRAL DECOMPOSITION AND HARMONIC BANDWIDTH
EXTRAPOLATION: A CASE STUDY OF A CHANNEL SYSTEM
ON A 3D MULTICOMPONENT SURVEY IN SOUTHERN
ALBERTA, CANADA
iv
An Abstract of a Thesis
Presented to
the Faculty of the Department of Earth and Atmospheric
Sciences University of Houston
In Partial Fulfillment
of the Requirements for the
Degree Master of Science
By Yang Mu
May 2017
v
ABSTRACT
Conventional seismic attribute analysis, spectral decomposition, and harmonic-
bandwidth extrapolation are performed on the 3D multi-component seismic data from
southern Alberta, Canada to map the occurrence and distinguish the sand-filled segment
from the shale-plugged section of the glauconitic channel.
In conventional multi-component seismic-attribute analysis, the interval Vp/Vs ratio can
provide more distinctive and definitive interpretation of the glauconitic channel than can
isochron and amplitude attributes independently extracted from P-P and P-S data.
P-P and P-S amplitude maps and vertical sections from the analyzed spectral
decomposition methods show the superiority of Constrained Least-Square Spectral
Analysis (CLSSA) over the Short-Time Fourier Transform (STFT) and Continuous
Wavelet Transform (CWT) in delineating the glauconitic channel. The frequency-derived
Vp/Vs ratio fails to distinguish the lithology variation within the channel as does the Vp/Vs
ratio extracted from the conventional P-P and P-S data.
Synthetic P-P and P-S wedge models indicate the improvement in P-P and P-S seismic
resolution after harmonic-bandwidth extrapolation. However, the limited improvement in
P-P and P-S seismic resolution is not sufficient to map the occurrence of the glauconitic
channel.
vi
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................................................................................... iii
ABSTRACT ........................................................................................................................ v
CHAPTER ONE Introduction .......................................................................................... 1
1.1 Motivation .............................................................................................................................. 1
1.2 Geology Background ............................................................................................................. 3
1.3 Blackfoot 3C-3D Dataset Review .......................................................................................... 4
CHAPTER TWO Conventional Joint P-P and P-S Interpretation .................................. 10
2.1 Introduction .......................................................................................................................... 10
2.2 Sensitivity Analysis ............................................................................................................. 11
2.3 Phase Confirmation .............................................................................................................. 18
2.4 P-P and P-S Horizon Attributes. .......................................................................................... 24
2.5 Chapter Summary ................................................................................................................ 33
CHAPTER THREE P-P and P-S Spectral Decomposition ............................................. 34
3.1 Introduction .......................................................................................................................... 34
3.2 Theory .................................................................................................................................. 36
3.3 Quality Control .................................................................................................................... 41
3.4 Multi-Component Frequency Attributes Analysis. .............................................................. 45
3.5 Frequency-Derived Vp/Vs Ratio Analysis. ........................................................................... 62
3.6 Chapter Summary. ............................................................................................................... 68
CHAPTER FOUR P-P and P-S Harmonic-Bandwidth Extrapolation ............................ 70
4.1 Introduction .......................................................................................................................... 70
4.2 Theory .................................................................................................................................. 71
4.3 P-P and P-S Harmonic-Bandwidth Extrapolation ................................................................ 74
4.4 Chapter Summary ................................................................................................................ 91
CHAPTER FIVE Conclusions ........................................................................................ 92
REFERENCES ................................................................................................................. 94
vii
LIST OF FIGURES
Figure 1.2.1: The stratigraphic column of the Blackfoot field (Miller et al., 1995). .......... 3
Figure1.3.1: The base map of the Blackfoot field and glauconitic channel incision isopach
(Larsen, 1999). .................................................................................................................... 5
Figure 1.3.5: Base map of the migrated vertical component and radial component. The
blue line indicates the orientation of inlines, while the red line indicates the orientation of
crosslines............................................................................................................................. 8
Figure 2.2.7: Gamma-ray values versus sonic-log S-wave velocity in the glauconitic
channel for well 8-8, 4-16 and 12-16................................................................................ 16
Figure 2.2.8: Gamma-ray values versus Vp/Vs ratio in the glauconitic channel in well 8-8,
4-16 and 12-16 (Potter et al., 1996). ................................................................................ 17
Figure 2.3.1: (a) Time response of the P-P full wavelet extracted at nine well locations;
(b) Amplitude and phase spectra of the P-P full wavelet extracted at nine well locations.
The black dashed line indicates the phase response at each frequency component. The red
line shows that the average phase is 118◦. ........................................................................ 20
Figure 2.3.2: (a) Time response of the P-S full wavelet extracted at nine well locations; (b)
Amplitude and phase spectra of the P-P full wavelet extracted at nine well locations. The
black dashed line indicates the phase response at each frequency component. The red line
shows that the average phase is 39◦. ................................................................................. 20
Figure 2.3.3: (a) Vertical display of inline 88 of P-P data before conditioning. The red
arrow indicates the post-stack migration artifacts; (b) Vertical display of inline 88 of P-P
data after conditioning. ..................................................................................................... 21
Figure 2.3.4: (a) Vertical display of inline 88 of P-S data before conditioning; (b) Vertical
display of inline 88 of P-S data after conditioning. .......................................................... 22
Figure 2.3.5: Seismic-well tie between synthetic trace from well 8-8 and P-P data. From
left to right the curves are P-wave velocity, S-wave velocity, and density, synthetic trace
(blue), extracted composite trace at the well location (red), and traces along the well path
(black). The correlation coefficient is 0.731 over a window from 800 ms to 1065 ms. .... 23
Figure 2.3.6: Seismic-well tie between synthetic trace from well 4-16 and P-S data. From
left to right the curves are P-wave velocity, S-wave velocity, density, synthetic trace (blue),
extracted composite trace at the well location (red), and traces along the well path (black).
The correlation coefficient is 0.832 over a window from 1200 ms to 1705 ms. ............... 23
Figure 2.3.7: (a) The correlation profile between synthetic traces from nine wells and P-P
data. The total correlation coefficient is 0.642591 over a window from 800 ms to 1200 ms;
(b) The correlation profile between synthetic traces from nine wells and the P-S data. The
total correlation coefficient is 0.760342.over a window from 1200 ms to 1800 ms. Red
numbers are correation coefficients for each well. .......................................................... 24
Figure 2.4.2: P-P wedge model using rock parameters from Table 2.4.1. ...................... 25
viii
Figure 2.4.3: P-S wedge model using rock parameters from Table 2.4.1. ....................... 26
Figure 2.4.4: Tuning curves extracted from the P-P and P-S wedge models. The blue lines
represent the P-P tuning curve and the corresponding tuning thickness is 36m. The green
lines represent the P-S tuning curve and the corresponding tuning thickness is 27m. .... 26
Figure 2.4.6: Vertical display of crossline 129 of P-P data. VIKING, MANN, COAL1,
GLCTOP/OST, and WABAMUN represent the Viking Member, the Blairmore Member, the
first coal bed, the top of the glauconitic channel, and the Wabamun event on the P-P
domain respectively. The inserted curves are P-P synthetic traces.The color bar represents
reflection strength. ............................................................................................................ 27
Figure 2.4.7: Vertical display of crossline 129 of P-S data. VIKING_PS, MANN_PS,
COAL1_PS, GLCTOP/OST_PS, and WABAMUN_PS represent The Viking Member, the
Blairmore Member, the first coal bed, the top of the glauconitic channel, and the Wabamun
event on the P-S domain respectively. The inserted red curves are P-S synthetic traces. The
color bar represents reflection strength. .......................................................................... 28
Figure 2.4.8: (a) P-P isochron from the top of the glauconitic channel to the Wabamun
event; (b) P-S isochron from the top of the glauconitic channel to the Wabamun event. The
black arrows indicate the channel and the red arrows indicate the possible crevasse splays.
The color bars represents two-way time. .......................................................................... 29
Figure 2.4.9: (a) P-P amplitude map at the top of the glauconitic channel; (b) P-S
amplitude map at the top of the glauconitic channel. The black square shows the
discontinuity in the glauconitic channel. The color key represents amplitude. ................ 30
Figure 2.4.11: Interval Vp/Vs ratio extracted from the top of the glauconitic channel to the
Wabanum event. ................................................................................................................ 31
Figure 3.1.1: Principal of layer imaging (Partyka et al., 1999). ..................................... 35
Figure 3.2.1: Thin bed model (Marfurt and Kirlin, 2001)................................................ 40
Figure 3.3.1: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
100 ms STFT of P-P data; (b) Time-frequency panel of the trace at inline 72 and crossline
129 for the 100 ms STFT of P-S data; (c) Amplitude spectrum of the trace at inline 72 and
crossline 129 of P-P data; (d) Amplitude spectrum of the trace at inline 72 and crossline
129 of P-S data. The color bar indicates the spectral amplitude. .................................... 43
Figure 3.3.2: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
STFT of P-P data; (b) Time-frequency panel of the trace at inline 72 and crossline 129 of
The CWT of P-P data; (c) Time-frequency panel of the trace at inline 72 and crossline 129
for the CLSSA of P-P data. The color bar indicates spectral amplitude. ......................... 44
Figure 3.3.3: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
STFT of P-S data; (b) Time-frequency panel of the trace at inline 72 and crossline 129 of
The CWT of P-S data; (c) Time-frequency panel of the trace at inline 72 and crossline 129
for the CLSSA of P-S data. The color bar indicates spectral amplitude. ......................... 44
Figure 3.4.1: (a) 30 Hz discrete-frequency map at the top of the glauconitic channel for
the STFT of P-P data; (b) 30 Hz discrete-frequency map at the top of the glauconitic
ix
channel for the CWT of P-P data; (c) 30 Hz discrete-frequency map at the top of the
glauconitic channel for the CLSSA of P-P data. The color bar indicates spectral amplitude.
........................................................................................................................................... 46
Figure 3.4.2: (a) 60 Hz discrete-frequency map at the top of the glauconitic channel for
the STFT of P-P data; (b) 60 Hz discrete-frequency map at the top of the glauconitic
channel for the CWT of P-P data; (c) 60 Hz discrete-frequency map at the top of the
glauconitic channel for CLSSA of P-P data. The black polygons indicate the glauconitic
channel. The red polygons indicate crevasse splays. The color bar indicates spectral
amplitude........................................................................................................................... 47
Figure 3.4.3: (a) 90 Hz discrete-frequency map at the top of the glauconitic channel for
the STFT of P-P data; (b) 90 Hz discrete-frequency map at the top of the glauconitic
channel for the CWT of P-P data; (c) 90 Hz discrete-frequency map at the top of the
glauconitic channel for the CLSSA of P-P data. The color bar indicates spectral amplitude.
........................................................................................................................................... 48
Figure 3.4.4: Geometry of the arbitrary line used for the extraction of vertical sections.49
Figure 3.4.5: 30 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spctral amplitude. ....................................................................... 50
Figure 3.4.6: 30 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 50
Figure 3.4.7: 30 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 51
Figure 3.4.8: 60 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 52
Figure 3.4.9: 60 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 52
Figure 3.4.10: 60 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 53
Figure 3.4.11: 90 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
x
curves are the P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation
tops. The color bar indicates spectral amplitude.............................................................. 54
Figure 3.4.12: 90 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 54
Figure 3.4.13: 90 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude. ..................................................................... 55
Figure 3.4.14: (a) 10 Hz discrete-frequency map at the top of glauconitic channel for the
STFT of P-S data; (b) 10 Hz discrete-frequency map at the top of glauconitic channel for
the CWT of P-S data; (c) 10 Hz discrete-frequency map at the top of glauconitic channel
for the CLSSA of P-S data. Red polygons indicate the glauconitic channel. The color bar
indicates spectral amplitude. ............................................................................................ 56
Figure 3.4.15: (a) 20 Hz discrete-frequency map at the top of glauconitic channel for the
STFT of P-S data; (b) 20 Hz discrete-frequency map at the top of glauconitic channel for
the CWT of P-S data; (c) 20 Hz discrete-frequency map at the top of glauconitic channel
for the CLSSA of P-S data. Red polygons indicate the glauconitic channel. The color bar
indicates spectral amplitude. ............................................................................................ 57
Figure 3.4.16: 10 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The color bar indicates spectral amplitude. ............................. 58
Figure 3.4.17: 10 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The color bar indicates spectral amplitude. ............................. 59
Figure 3.4.18: 10 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The color bar indicates spectral amplitude. ............................. 59
Figure 3.4.19: 20 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The black arrows indicate the location of the glauconitic channel
interval. The color bar indicates spectral amplitude. ....................................................... 60
Figure 3.4.20: 20 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The black arrows indicate the location of the glauconitic channel
interval. The color bar indicates the spectral amplitude. ................................................. 61
Figure 3.4.21: 20 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE, and
OST are formation tops. The black arrows indicate the location of the glauconitic channel
interval. The color bar indicates spectral amplitude. ....................................................... 61
xi
Figure 3.5.1:(a) Blocked P-wave velocity, S-wave velocity, and density as well as gamma
ray, medium-depth induction, deep induction logs from well 8-8; (b) P-P AVO response of
the top and base of the upper unit of the Glauconitic Member; (c) P-S AVO response of the
top and base of the upper unit of the Glauconitic Member. The highlighted zone in (a) is
the upper unit of the Glauconitic Member. ....................................................................... 63
Figure 3.5.2: (a) P-P peak-frequency map at the top of the glauconitic channel; (b) P-S
peak-frequency map at the top of the glauconitic channel. The color bar indicates peak
frequency. The red polygon reveals the interpreted glauconitic channel. ........................ 65
Figure 3.5.3: Frequency-derived Vp/Vs ratio at the top of the glauconitic channel. The color
bar indicates values of the frequency-derived Vp/Vs ratio. ............................................... 66
Figure 3.5.4: Vertical display of the frequency-derived Vp/Vs ratio at crossline 129 parallel
to the trending of the channel. The inserted curves are P-wave velocities. COAL1,
GLCTOP, GLCBASE and OST are formation tops. The color bar indicates values of the
frequency-derived Vp/Vs ratio. .......................................................................................... 66
Figure 3.5.5 Schematic illustration of the P-S to P-P domain conversion. Δt is the sampling
rate (Todorov et al., 1999). ............................................................................................... 68
Figure 4.3.1: (a) Vertical display of crossline 129 of the preconditioned P-P data; (b)
Vertical display of crossline 129 of the preconditioned P-S data after bandpass filtering;
(c) Amplitude spectrum of the preconditioned data from inline 47-165, crossline 88-168,
and time 0-3000 ms; (d) Amplitude spectrum of the preconditioned data after bandpass
filtering from inline 47-165, crossline 88-168, and time 0-3000 ms. The color bar indicates
amplitude........................................................................................................................... 75
Figure 4.3.2: (a) Vertical display of crossline 129 of the preconditioned P-S data; (b)
Vertical display of crossline 129 of the preconditioned P-S data after bandpass filtering;
(c) Amplitude spectrum of the preconditioned P-S data from inline 47-165, crossline 88-
168, and time 0-3000 ms; (d) Amplitude spectrum of the preconditioned P-S data after
bandpass filtering from inline 47-165, crossline 88-168 , and time 0-3000 ms. The color
bar indicates amplitude..................................................................................................... 76
Figure 4.3.3: (a) Vertical display of crossline 129 of the preconditioned P-P data after
bandpass filtering; (b) Vertical display of crossline 129 of the bandwidth extrapolated P-
P data; (c) Amplitude spectrum of the preconditioned P-P data after bandpass filtering
from inline 47-165, crossline 88-168, and time 0-3000 ms; (d) Amplitude spectrum of the
bandwidth-extrapolated data from inline 47-165, crossline 88-168, and time 0-3000 ms.
The color bar indicates amplitude. ................................................................................... 78
Figure 4.3.4: (a) Vertical display of crossline 131 of the preconditioned P-S data after
bandpass filtering; (b) Vertical display of crossline 131 of the bandwidth extrapolated P-
S data; (c) Amplitude spectrum of the preconditioned P-S data after bandpass filtering
from inline 47-165, crossline 88-168, and time 0-3000 ms; (d) Amplitude spectrum of the
bandwidth-extrapolated data from inline 47-165, crossline 88-168, and time 0-3000 ms.
The black squares show artifacts. The color bar indicates amplitude. ............................ 79
xii
Figure 4.3.5: (a) Vertical display of crossline 131 of the original bandwidth-extrapolated
P-S data; (b) Vertical display of crossline 131 of the bandwidth extrapolated P-S data with
the specified parameters; (c) Amplitude spectrum of the original bandwidth-extrapolated
P-S data calculated from 47-165, crossline 88-168, and time 1200-1800 ms; (d) Amplitude
spectrum of the bandwidth-extrapolated P-S data with specified parameters calculated
from 47-165, crossline 88-168, and time 1200-1800 ms. The color bar indicates amplitude.
........................................................................................................................................... 81
Figure: 4.3.6: (a) Seismic-well tie between synthetic trace from well 8-8 and bandwidth-
extrapolated P-P seismic data. From left to right the curves are P-wave velocity, S-wave
velocity, density, synthetic trace (blue), extracted composite trace at the well location (red),
and traces along the well path (black). The correlation coefficient is 0.832 over a window
from 1200 ms to 1705 ms.; (b) Time response of the wavelet extracted at the well location;
(c) Amplitude spectrum and phase spectrum of the wavelet. ............................................ 83
Figure 4.3.7: (a) Seismic-well tie between synthetic trace from well 4-16 and bandwidth-
extrapolated P-S seismic data. From left to right the curves are P-wave velocity, S-wave
velocity, density, synthetic trace (blue), extracted composite trace at the well location (red),
and traces along the well path (black). The correlation coefficient is 0.832 over a window
from 1200 ms to 1705 ms; (b) Time response of the.wavelet extracted at the well location;
(c) Amplitude spectrum and phase spectrum of the wavelet. ............................................ 84
Figure 4.3.8: (a) The correlation profile between synthetic traces from nine wells and the
bandwidth-extrapolated P-P data. The total correlation coefficient is 0.670314 over a
window from 800 ms to 1200 ms; (b) The correlation profile between synthetic traces from
nine wells and the bandwidth extrapolated P-S data. The total correlation coefficient is
0.705148 over a window from 1200 ms to 1800 ms. Red numbers are correation
coefficients for each well. ................................................................................................. 85
Figure 4.3.9: Synthetic P-P wedge model using the wavelet extracted from the P-P
bandwidth-extrapolated data. ........................................................................................... 86
Figure 4.3.10: Synthetic P-S wedge model using the wavelet extracted from the P-S
bandwidth-extrapolated data. ........................................................................................... 86
Figure 4.3.11.P-P and P-S tuning curve from the synthetic wedge models ..................... 86
Figure 4.3.12 Vertical display of the bandwidth-extrapolated P-S data at crossline 129
parallel to the trending of the channel. The inserted curves are S-wave velocities.
GLCTOP, GLCBASE, and DET are formation tops. ........................................................ 87
Figure 4.3.13: Vertical display of the bandwidth-extrapolated P-P data at crossline 129
parallel to the trending of the glauconitic channel. The inserted curves are the synthetic P-
P traces. GLCTOP, GLCBASE, and DET are formation tops. GLCBASE/DET represents
the base of the glauconitic channel. .................................................................................. 89
Figure 4.3.14: Vertical display of the bandwidth-extrapolated P-P data at inline 85
perpendicular to the trending of the glauconitic channel. The inserted curves are the
synthetic P-P traces. GLCTOP, GLCBASE, and DET are formation tops. GLCBASE/DET
represents the base of the glauconitic channel. ................................................................ 89
xiii
Figure 4.3.15: Time structure of the base of the glauconitic channel. The color bar
indicates two-way time. ..................................................................................................... 90
Figure 4.3.16: P-P isochron from the top of the glauconitic channel to the base of the
glauconitic channel. The color bar indicates two-way time thickness. ............................ 90
xiv
LIST OF TABLES
Table 1.3.2: Acquisition parameters of the Glauconitic patch of the Blackfoot field (Simin
et al., 1996). ........................................................................................................................ 5
Table 1.3.3: Vertical-component processing workflow (Lu and Margrave, 1998). ........... 6
Table 1.3.4: Radial-component processing workflow (Lu and Margrave, 1998). ............. 7
Table 1.3.6: Classification of the nine wells and available logs for each well. The DT, DTS,
and DEN are P-wave velocity log, S-wave velocity log, and density log respectively. GR
and SP stand for the gamma ray log and spontaneous potential log. ILM and ILD represent
the medium-depth induction and deep induction logs. ....................................................... 9
Table 2.2.1: Formation naming conventions (Potter et al., 1996). Seismic horizons with
these names correspond to the tops of the intervals. ........................................................ 12
Table 2.2.2: Rock properties in oil production well 8-8 (modified from Potter et al., 1996).
........................................................................................................................................... 13
Table 2.2.3: Rock properties in shale-filled dry hole 12-16 (modified from Potter et al.,
1996). ................................................................................................................................ 13
Table 2.2.4: Rock properties in the shale-plugged well 4-16 (modified from Potter et al.,
1996). ................................................................................................................................ 14
Table 2.2.5: Rock properties in the regional well 9-17 (modified from Potter et al., 1996).
........................................................................................................................................... 14
Table 2.4.1: Rock physics parameters for P-P and P-S wedge model construction. ....... 25
Table 2.4.5 Thickness of the glauconitic channel within each well. ................................. 26
1
CHAPTER ONE
Introduction
1.1 Motivation
The objective of this thesis is to map the occurrence of, and distinguish the sand-filled
segment from the shale-plugged section of the glauconitic channel on the Blackfoot 3C-
3D multi-component seismic dataset. The converted-wave data can assist the conventional
vertical-component data interpretation by providing an alternative set of independent
seismic attributes. The Vp/Vs ratio or Poisson's ratio can be conveniently and reliably
extracted from the two or three independent volumes for lithology identification (Margrave
et al., 1998).
Spectral decomposition (Partyka et al., 1999) is a technique that decomposes seismic
data into multiple discrete-frequency volumes. Geologic features of interest can be
delineated through analysis on those discrete-frequency volumes. Several authors have
been investigating the application of spectral decomposition on P-P seismic interpretation.
For example, Partyka et al., 1999 showed that amplitude spectra could be used to delineate
a channel and phase spectra can reveal lateral geologic discontinuities. Marfurt and Kirlin,
2001 introduced a set of new seismic attributes derived from spectral decomposition and
related the peak frequency to the temporal thickness of a thin bed. Castagna et al., 2003
introduced the application of spectral decomposition for hydrocarbon detection by
revealing the low-frequency shadow beneath the gas-charged reservoir. However, few
2
investigations have been done on the application of spectral decomposition of the
converted-wave data.
Harmonic-bandwidth extrapolation (Liang and Castagna, in press) is a bandwidth
extension method based on the physics of wave propagation, which can extend the
frequency components outside of the original bandwidth with high fidelity. This advanced
technique can improve seismic resolution and thus illuminate the thin beds that cannot be
resolved on original seismic data.
In this thesis, conventional P-P and P-S seismic attributes analysis, spectral
decomposition using the Short-Time Fourier Transform (STFT; Cohen and Posch, 1985),
the Continuous Wavelet Transform (CWT; Chakraborty and Okaya, 1995), and
Constrained Least-Squares Spectral Analysis (CLSSA; Puryear et al., 2012), and
harmonic-bandwidth extrapolation are performed on P-P and P-S data to investigate the
resolving ability of each method for the delineation of the glauconitic channel.
The rest of this chapter describes the geologic setting and the multicomponent seismic
dataset acquired by the CREWES project at the University of Calgary. Chapter two
describes conventional P-P and P-S interpretation of these data. Spectral decomposition of
these data is presented in Chapter three. An attempt to improve resolution using harmonic-
bandwidth extrapolation is covered in Chapter four. Discussion and conclusions are
discussed in Chapter five.
3
1.2 Geology Background
Figure 1.2.1 shows the simplified stratigraphic column of the Blackfoot field. The zone
of interest is the channel incision of the Glauconitic Formation of the Upper Mannville
Group of Early Cretaceous age. The glauconitic channel incision is subdivided into three
units corresponding to three phases of the valley incision. All three units may not present
everywhere (Miller et al., 1995) The upper and lower members are made up of fine quartz
sandstones with an average porosity of 18%, while the middle member is the tight lithic
sandstone (Larsen, 1999).The Ostracod Member contains brackish water shale,
Figure 1.2.1: The stratigraphic column of the Blackfoot field (Miller et al., 1995).
4
argillaceous, fossiliferous limestones, and thin quartz sandstones and siltstones (Layer,
1949). The laterally inconsistent low-velocity Bantry Shale at the bottom of the Ostracod
Member is the stratigraphic marker between the Ostracod and Sunburst Member (Coveney,
1960). The Sunburst Member consists of ribbon and sheet sandstones made up of sub-
litharenites. The Detrital Member, at the base of the Mannville Group, has a highly
heterogeneous lithology consisting of chert pebbles, lithic sandstones, siltstones, and shale
(Badgley, 1952).
The primary hydrocarbon in the Blackfoot field is oil, although gas may also be present
in the upper Glauconitic Member (Miller et al., 1995). Based on petrophysical analysis, the
gas mainly comes from the shallow Viking Unit instead of the upper Glauconitic Member
in the study area (Margrave et al., 1998).
1.3 Blackfoot 3C-3D Dataset Review
A 3C-3D survey was conducted over the Blackfoot field in November 1995 as shown
in the black square in Figure 1.3.1. The survey was designed to evaluate the effectiveness
of the integrated P-P and P-S surveys for hydrocarbon exploration and demonstrate that
joint P-P and P-S interpretation provides an alternative perspective for stratigraphic and
structural interpretation, lithology discrimination, and anisotropy analysis (Lawton et al.,
1996). The 3C-3D survey contains two overlapping patches: the Glauconitic patch
targeting the glauconitic channel and the Beaverhill Lake patch focusing on the deep
carbonates. The acquisition parameters of the Glauconitic patch are shown in Table 1.3.2.
Dynamite was buried 18 meters below the surface and used as a source for acquisition.
5
Figure1.3.1: The base map of the Blackfoot field and glauconitic channel incision isopach
(Larsen, 1999).
Table 1.3.2: Acquisition parameters of the Glauconitic patch of the Blackfoot field (Simin
et al., 1996).
Source Parameters
Line orientation:
Source interval:
Source line interval:
Number of source lines:
Total number of source points:
North-south
60 m
210 m
24
720
Receiver parameters
Line orientation:
Receiver interval:
Receiver line interval:
Number of receiver lines:
Total number of receivers:
East-west
60 m
255 m
18
690
6
The seismic processing was performed by Pulsonic Geophysical and Sensor
Geophysical in 1996 (Simin et al., 1996). Lu and Margrave, 1998 reprocessed the
Glauconitic patch by adding the post-stack time migration, the processing workflows of
which are shown in Table 1.3.3 and Table 1.3.4. After component separation and rotation,
the radial component was found to contain energy at all azimuths, whereas the transverse
component showed little to no energy at all azimuths. The Consortium for Research in
Elastic Wave Exploration Seismology (CREWES) believed that there was no significant
shear wave splitting existing in the study area and thus the horizontal component was fully
processed to the radial stacked section only (Simin et al., 1996).
Table 1.3.3: Vertical-component processing workflow (Lu and Margrave, 1998).
VERTICAL COMPONENT PROCESSING WORKFLOW
SEG-D FORMATTED DE-MULTIPLEX INPUT
3D GEOMETRY ASSIGNMENT
TRACE EDIT
TRUE AMPLITUDE RECOVERY
SURFACE CONSISTENT DECONVOLUTION
TIME VARIANT SPECTRAL WHITENING
EVALUATION AND REFRACTION STATIC CORRECTION
VELOCITY ANALYSIS
RESIDUAL SURFACE CONSISTENT STATICS
NORMAL MOVEOUT
TRIM STATICS
FRONT AND MUTING
CDP STACKING
TIME VARIANT SPECTRAL WHITENING
TRACE EQUALIZATION
F-XY DECONVOLUTION
3D PHASE-SHIFT MIGRATION
TRACE EQUALIZATION
BANDPASS FILTERING
TIME VARIANT SCALING
7
Table 1.3.4: Radial-component processing workflow (Lu and Margrave, 1998).
The migrated vertical component and radial component of the Glauconitic patch both
range from inline 47 to 165 and crossline 88 to 168 (Figure 1.3.5). For simplification, the
migrated vertical component of the Glauconitic patch is referred to as P-P data while the
migrated radial component is referred to as P-S data in this study.
There are 12 wells in the Blackfoot dataset package. Two wells (9-5 and 13-16) are
located outside of the seismic survey as shown in Figure 1.3.5 and were not used in this
thesis. Four of the remaining ten wells contain dipole-sonic logs (09-17, 12-16, 04-16, 08-
08), where the well 09-17 is a regional well, wells 12-16 and 4-16 are dry holes in the
channel, and well 08-08 is an oil production well in the channel. Logs from well 1-17 are
RADIAL COMPONENT PROCESSING WORKFLOW
SEG-D FORMATTED DE-MULTIPLEX INPUT
3D GEOMETRY ASSIGNMENT
TRACE EDIT
ASYMPTOTIC BINNING
SURFACE CONSISTENT DECONVOLUTION
TIME VARIANT SPECTRAL WHITENING
EVALUATION AND REFRACTION STATIC CORRECTION
INITIAL P-SV VELOCITY CONSTRUCTION FROM P-P
VELOCITY ANALYSIS
RESIDUAL SURFACE CONSISTENT STATICS
NORMAL MOVEOUT
ACP TRIM STATICS
FRONT AND MUTING
ACP STACKING
TIME VARIANT SPECTRAL WHITENING
TRACE EQUALIZATION
F-XY DECONVOLUTION
3D PHASE-SHIFT MIGRATION
TRACE EQUALIZATION
BANDPASS FILTERING
TIME VARIANT SCALING
8
considered unreliable and were not further analyzed. Thus only nine wells are utilized in
this study. Table 1.3.6 shows the classification of the nine wells and the available logs for
each well.
Figure 1.3.5: Base map of the migrated vertical component and radial component. The blue
line indicates the orientation of inlines, while the red line indicates the orientation of
crosslines.
9
Table 1.3.6: Classification of the nine wells and available logs for each well. The DT, DTS,
and DEN are P-wave velocity log, S-wave velocity log, and density log respectively. GR
and SP stand for the gamma ray log and spontaneous potential log. ILM and ILD represent
the medium-depth induction and deep induction logs.
Well DT DTS DEN GR SP ILD ILM Classification
11-8 Yes / Yes Yes Yes Yes Yes Gas Regional well
12-16 Yes Yes Yes Yes / / / Dry hole in the channel
14-9 Yes / Yes Yes Yes Yes Yes Gas Regional well
1-8 Yes / Yes Yes Yes Yes Yes Oil well in the channel
4-16 Yes Yes Yes Yes / / / Dry hole in the channel
5-16 Yes / Yes Yes Yes Yes Yes Oil well in the channel
8-8 Yes Yes Yes Yes Yes Yes Yes Oil well in the channel
9-17 Yes Yes Yes Yes Yes Yes Yes Gas Regional well
16-08 Yes / Yes Yes Yes / Yes Oil well in the channel
10
CHAPTER TWO
Conventional Joint P-P and P-S Interpretation
2.1 Introduction
Converted-wave seismic exploration records the upward traveling S-wave converted
from the downward propagating P-wave at a reflector. The converted S-wave benefits
geophysicists by providing alternative perspectives to assist in better understanding
ambiguities in interpretation, as opposed to utilizing P-waves alone (Stewart et al., 2003).
Many studies have demonstrated the applications of P-S data including Stewart et al., 2003
and Kristiansen, 2000. Some of the primary findings of these studies are:
Providing an alternative set of independent attributes (velocity and P-S reflectivity).
Low P-wave impedance contrast verification.
Enhanced shallow event and fault imaging.
Enhanced imaging results below strong reflectors and attenuating zones (e. g., gas
chimneys, shale diapirs, mud volcanos, zones beneath salt and basalt).
Efficient Vp/Vs ratio extraction for lithology identification.
P-wave bright spot calibration.
Additional AVO analysis and inversion for velocity and density.
Anisotropy analysis.
4D or time-lapse reservoir monitoring.
11
Mapping the occurrence of the glauconitic channel and distinguishing the shale-plugged
portion from the sand-filled segment are two primary objectives of the Blackfoot 3C-3D
seismic survey. However, the conventional P-P seismic data has been less successful in
fulfilling those objectives. In the upcoming chapter, I followed the interpretation
workflows of CREWES (Yang et al., 1996; Margrave et al., 1997), including extracting
isochron, amplitude, and interval Vp/Vs ratio to map the occurrence and identify the
lithology of the glauconitic channel from P-P and P-S data as well as investigating the
resolving ability of multi-component data on seismic interpretation.
2.2 Sensitivity Analysis
A seismic attribute is defined as a measurement derived from the seismic time,
amplitude, frequency or attenuation that can be used for geologic or geophysical
interpretation (Sheriff, 2002). A sensitivity analysis is usually defined as the procedure of
determining how sensitive is the selected attribute to the desired petrophysical property
such as lithology (Hilterman, 2001), which is usually performed using well-log cross plots.
According to the CREWES reports, the Vp/Vs ratio is a good lithology indicator within the
Blackfoot field. The well logs from four wells (8-8, 4-16, 12-16, and 9-17) having dipole-
sonic S-wave logs are analyzed and cross plotted to verify this conclusion.
Table 2.2.1 shows the naming conventions for the formations within the Blackfoot field
and seismic horizons with these names correspond to the tops of the intervals. Table 2.2.2
through Table 2.2.5 are the mean values of P-wave velocity, S-wave velocity, density, and
12
Vp/Vs ratio of each unit in wells 8-8, 12-16, 4-16, and 9-17 in true vertical depth (TVD)
respectively. The sand-filled glauconitic channel in well 8-8 shows the lowest
Abbreviation Unit Name
VIKING Viking
MANN Blairmore-Upper Mannville
COAL1 1st Coal bed
COAL2 2nd Coal bed
COAL3 3rd Coal bed
GLCTOP The Top of The Glauconitic Channel
LITHIC Lithic Channel Unit
GLCSS Glauconitic Channel Porous Sandstone Unit
GLCBASE The Base of The Glauconitic Channel
OST Ostracod
SUN Sunburst
DET Detrital
MISS Shunda-Mississippian
Table 2.2.1: Formation naming conventions (Potter et al., 1996). Seismic horizons with
these names correspond to the tops of the intervals.
13
Name Depth (m) Vp (m/s) Vs (m/s) Den (kg/m3) Vp/Vs (unitless)
VIKING 1348 3904 2067 2511 1.88
MANN 1455 3969 2093 2509 1.89
COAL1 1540 3274 1946 2036 1.68
COAL2 1548 3198 1979 2172 1.75
COAL3 1562 3317 1959 2205 1.69
GLCTOP 1595 3862 2323 2410 1.66
LITHIC 1623 4142 2440 2491 1.69
GLCSS 1628 3793 2300 2381 1.65
DET 1642 4130 2380 2521 1.73
MISS 1662 6008 3143 2675 1.92
Table 2.2.2: Rock properties in oil production well 8-8 (modified from Potter et al., 1996).
Name Depth (m) Vp (m/s) Vs (m/s) Den (kg/m3) Vp/Vs (unitless)
VIKING 1358 3864 2033 2516 1.90
MANN 1458 3983 2097 2527 1.89
COAL1 1539 3036 1826 1995 1.66
COAL2 1547 3198 1822 2124 1.75
COAL3 1560 3181 1937 2057 1.64
GLCTOP 1591 3996 2191 2531 1.82
LITHIC 1617 4134 2279 2571 1.81
DET 1624 4462 2509 2570 1.77
MISS 1641 6054 3207 2683 1.88
Table 2.2.3: Rock properties in shale-filled dry hole 12-16 (modified from Potter et al.,
1996).
14
Name Depth (m) Vp (m/s) Vs (m/s) Den (kg/m3) Vp/Vs (unitless)
VIKING 1347 3852 2069 2515 1.86
MANN 1450 4002 2149 2521 1.86
COAL1 1533 3170 1827 2210 1.73
COAL2 1539 3410 1885 2320 1.80
COAL3 1552 3340 1906 2254 1.75
GLCTOP 1587 4045 2169 2587 1.86
SUN 1607 4275 2416 2569 1.76
DET 1617 4386 2472 2518 1.77
MISS 1653 6020 3242 2711 1.85
Table 2.2.4: Rock properties in the shale-plugged well 4-16 (modified from Potter et al.,
1996).
Name Depth (m) Vp (m/s) Vs (m/s) Den (kg/m3) Vp/Vs (unitless)
VIKING 1355 3613 2034 2549 1.77
MANN 1457 3714 2005 2521 1.85
COAL1 1542 3111 1489 2110 2.08
COAL2 1549 3039 1603 2197 1.89
COAL3 1563 3074 1579 2157 1.94
OST 1604 3533 2009 2446 1.75
SUN 1611 3954 2112 2538 1.87
DET 1626 4120 2183 2540 1.88
MISS 1659 5136 2360 2612 2.09
Table 2.2.5: Rock properties in the regional well 9-17 (modified from Potter et al., 1996).
15
Vp/Vs ratio of 1.591 and 1.658 in the upper and lower units, while the shale-plugged
glauconitic channel in well 4-16 and 12-16 shows Vp/Vs ratios similar to that in the
Ostracod Formation in regional well 9-17. The P-wave velocity, S-wave velocity, Vp/Vs
ratio, and gamma ray values from wells 8-8, 4-16 and 12-16 are cross plotted to investigate
the relationship between lithology and rock properties within the glauconitic channel.
Figure 2.2.6 shows the cross plot of gamma-ray values versus P-wave velocity within the
glauconitic channel. The clean sand-filled glauconitic channel generally exhibits gamma
ray values lower than 40 API units (Wood and Hopkins, 1992). Three meters of clean sand
found at the bottom of the glauconitic channel in 12-16 (green squares) conforms to this
observation, while shales from 12-16 falls in the region of gamma-ray values between 90
Figure 2.2.6: Gamma-ray values versus sonic-log P-wave velocity in the glauconitic
channel for well 8-8, 4-16 and 12-16.
16
to 140 API along with shales from 4-16. The clean sand and shale of three wells have
similar P-wave velocity ranging from 3500 m/s to 4500 m/s and demonstrate that the P-
wave velocity is not sensitive to the increase of the shale content within the glauconitic
channel. However, the cross plot of gamma ray values versus S-wave velocity (Figure
2.2.7) indicates that the S-wave velocity alone can successfully distinguish the sand within
wells 8-8 and 12-16 from the shale within wells 4-16 and 12-16. The shale from the well
4-16 and well 12-16 fall in the cluster of points of S-wave velocity values less than 2200
m/s, while the sand from wells 8-8 and 12-16 have values greater than 2200 m/s. Figure
2.2.8 shows the cross plot of gamma ray values versus Vp/Vs ratio in the glauconitic
channel. The clean sand from well 8-8 and 12-16 have gamma-ray values lower than 40
Figure 2.2.7: Gamma-ray values versus sonic-log S-wave velocity in the glauconitic
channel for well 8-8, 4-16 and 12-16.
17
API and Vp/Vs ratio ranging from 1.55 to 1.75. To the contrary, shales from the 4-16 and
12-16 show Vp/Vs ratio greater than 1.8 and go all the way to 2.1. The well-log cross plots
indicate that the Vp/Vs ratio, as well as S-wave velocity, can be a good lithology indicator
in the glauconitic channel. However, in practice, extracting the S-wave velocity from post-
stack seismic data is not as convenient and robust as extracting the Vp/Vs ratio is. Therefore,
only the Vp/Vs ratio is used in this study for lithology identification within the glauconitic
channel.
Figure 2.2.8: Gamma-ray values versus Vp/Vs ratio in the glauconitic channel in well 8-8,
4-16 and 12-16 (Potter et al., 1996).
18
2.3 Phase Confirmation
In order to assure the accuracy of the interpretation, the phase of the data was checked
by using the workflow below (Hampson-Russell suite, 2013):
Extracting a zero-phase statistical wavelet from inline 70 to 120, crossline 110 to
140, and time 800 ms to 1200 ms for P-P data and 1200 ms to 1800 ms for P-S data
which correspond to the high fold area of the seismic survey and the level of the
zone of interest.
Log editing to remove spurious spikes in well logs.
For P-P data, sonic and density logs are directly used to calculate normal-incident
reflectivity series. A central angle of 20◦ was assigned to calculate P-S reflectivity
series.
Convolving the P-P and P-S wavelet with corresponding reflectivity series to derive
synthetic traces in well 8-8 and correlating with the P-P and P-S seismic data.
Constantly shifting the phase of P-P and P-S wavelets until the maximum cross-
correlation coefficients are reached.
Calculating synthetic traces from the remaining wells using the phase-shifted P-P
and P-S wavelets, correlating these synthetic traces with the P-P and P-S data,
applying stretch and squeeze, and saving the time-depth curves.
Extracting full wavelets from the P-P and P-S data at nine well locations.
This procedure suffers from instabilities which result from the stretching of the synthetic
traces that can cause degradation, loss of high frequency, distortion of the phase spectrum,
and unrealistic side lobes. Therefore, no more than 4 ms stretch was applied on the time-
19
depth curves, and the length of the wavelet was set to 40 ms for P-P data and 80 ms for P-
S data.
Figure 2.3.1 and Figure 2.3.2 show time responses and the amplitude and phase spectra
of the extracted P-P and P-S full wavelets. The average phase of P-P data is 118◦ while the
average phase of P-S data is 39◦. In addition to complex phase information, severe post-
stack migration artifacts have been observed on P-P and P-S data. Therefore, the P-P data
and P-S data were conditioned to remove the post-stack migration artifacts and shifted back
to zero phase. Figure 2.3.3 and Figure 2.3.4 are the comparison of the P-P and P-S data
before and after conditioning. Due to the absence of check shots, synthetic traces were
matched to P-P and P-S data at nine well locations through the stretch, and no more than
4ms stretch was applied to the time-depth curves. The correlation coefficient between the
synthetic trace from well 8-8 and P-P data is 0.731 over a window from 800 ms to 1065
ms (Figure 2.3.5), while the seismic-well tie between synthetic trace from 4-16 and the P-
S data shows a better correlation coefficient of 0.832 over a window from 1200 ms to 1705
ms (Figure 2.3.6).
Figure 2.3.7 shows the correlation coefficients between the synthetic traces from nine
wells and P-P and P-S data respectively. The Greenberg and Castagna, 1992 equation for
the 100% water-saturated case is applied to derive S-wave velocities for the wells that do
not have dipole-sonic shear-wave logs. In general, the P-S correlation is much better than
the P-P correlation in all wells (Potter et al., 1996).
20
(a) (b)
Figure 2.3.1: (a) Time response of the P-P full wavelet extracted at nine well locations; (b)
Amplitude and phase spectra of the P-P full wavelet extracted at nine well locations. The
black dashed line indicates the phase response at each frequency component. The red line
shows that the average phase is 118◦.
(a) (b)
Figure 2.3.2: (a) Time response of the P-S full wavelet extracted at nine well locations; (b)
Amplitude and phase spectra of the P-P full wavelet extracted at nine well locations. The
black dashed line indicates the phase response at each frequency component. The red line
shows that the average phase is 39◦.
.
21
(a)
(b)
Figure 2.3.3: (a) Vertical display of inline 88 of P-P data before conditioning. The red
arrow indicates the post-stack migration artifacts; (b) Vertical display of inline 88 of P-P
data after conditioning.
22
(a)
(b)
Figure 2.3.4: (a) Vertical display of inline 88 of P-S data before conditioning; (b) Vertical
display of inline 88 of P-S data after conditioning.
23
Figure 2.3.5: Seismic-well tie between synthetic trace from well 8-8 and P-P data. From
left to right the curves are P-wave velocity, S-wave velocity, and density, synthetic trace
(blue), extracted composite trace at the well location (red), and traces along the well path
(black). The correlation coefficient is 0.731 over a window from 800 ms to 1065 ms.
Figure 2.3.6: Seismic-well tie between synthetic trace from well 4-16 and P-S data. From
left to right the curves are P-wave velocity, S-wave velocity, density, synthetic trace (blue),
extracted composite trace at the well location (red), and traces along the well path (black).
The correlation coefficient is 0.832 over a window from 1200 ms to 1705 ms.
24
(a)
(b)
Figure 2.3.7: (a) The correlation profile between synthetic traces from nine wells and P-P
data. The total correlation coefficient is 0.642591 over a window from 800 ms to 1200 ms;
(b) The correlation profile between synthetic traces from nine wells and the P-S data. The
total correlation coefficient is 0.760342.over a window from 1200 ms to 1800 ms. Red
numbers are correation coefficients for each well.
2.4 P-P and P-S Horizon Attributes.
Wedge models were constructed to investigate the seismic resolution of the 3D multi-
component data. The mean values of the P-wave velocity, S-wave velocity, and density
between corresponding formation tops (Table 2.4.1) as well as the P-P and P-S full
wavelets extracted at nine well locations were used to construct the synthetic P-P and P-S
wedge models as shown in Figure 2.4.2 and 2.4.3. Figure 2.4.4 shows the tuning curves
25
Table 2.4.1: Rock physics parameters for P-P and P-S wedge model construction.
derived from the synthetic P-P and P-S wedge models. Roughly 36 meters of the
glauconitic channel is below seismic resolution on P-P data, while 27 meters of the
glauconitic channel is below seismic resolution on P-S data. The superior P-S seismic
resolution is due to the change of interval velocity which has a larger effect on seismic
resolution than the change of bandwidth from P-P to P-S domain. Table 2.4.5 shows the
thickness of the glauconitic channel within each well. In the P-S domain, only the channel
interval in shale-plugged well 4-16 is below seismic resolution, while the channel intervals
in wells 16-08, 4-16 and 12-16 are all below seismic resolution in the P-P domain.
Figure 2.4.2: P-P wedge model using rock parameters from Table 2.4.1.
P-Wave
velocity
S-Wave
Velocity
Density
Layer Above the glauconitic channel 4015.8 m/s 2197.2 m/s 2.49 g/cm3
The glauconitic channel 4067.6 m/s 2424.0 m/s 2.52g/cm3
Layer below the glauconitic channel 4096.4 m/s 2255.5 m/s 2.55 g/cm3
26
Figure 2.4.3: P-S wedge model using rock parameters from Table 2.4.1.
Figure 2.4.4: Tuning curves extracted from the P-P and P-S wedge models. The blue lines
represent the P-P tuning curve and the corresponding tuning thickness is 36m. The green
lines represent the P-S tuning curve and the corresponding tuning thickness is 27m.
Table 2.4.5 Thickness of the glauconitic channel within each well.
Well name 1-8 8-8 16-08 4-16 5-16 12-16
Top of the channel (m) 1576.9 1599.9 1565.3 1591.8 1576.0 1595.6
Base of the channel (m) 1620.0 1647.7 1596.4 1611.8 1612.6 1627.7
Thickness (m) 43.1 47.8 31.1 20 36.6 32.1
27
Figure 2.4.6 and Figure 2.4.7 show five events correspondingly picked on P-P and P-S
data. Since the channel pinches out against the regional strata, the Glauconitic Member and
the Ostracod Member were picked together to represent the top of the glauconitic channel.
Due to the unequal seismic resolution of P-P and P-S data, the Wabamun event, a strong
laterally-consistent peak at approximately 1150 ms on P-P data and 1850 ms on P-S data
was picked to represent the base of the glauconitic channel on P-P and P-S data for
attributes analysis.
Figure 2.4.6: Vertical display of crossline 129 of P-P data. VIKING, MANN, COAL1,
GLCTOP/OST, and WABAMUN represent the Viking Member, the Blairmore Member,
the first coal bed, the top of the glauconitic channel, and the Wabamun event on the P-P
domain respectively. The inserted curves are P-P synthetic traces.The color bar represents
reflection strength.
28
Figure 2.4.7: Vertical display of crossline 129 of P-S data. VIKING_PS, MANN_PS,
COAL1_PS, GLCTOP/OST_PS, and WABAMUN_PS represent The Viking Member, the
Blairmore Member, the first coal bed, the top of the glauconitic channel, and the Wabamun
event on the P-S domain respectively. The inserted red curves are P-S synthetic traces. The
color bar represents reflection strength.
Figure 2.4.8 shows the P-P and P-S isochron maps from the top of the glauconitic
channel to the Wabamun event. The P-P isochron (Figure 2.4.8a) delineates a north-south
trending channel and a crevasse splay at the location of well 11-8 by the colors red to
yellow, while the P-S isochron (Figure 2.4.8b) reveals a much more distinctive and
definitive channel in red color and two possible crevasse splays denoted by the colors
yellow to green. The channel revealed by the P-S isochron map conforms to existing well
control better than that from the P-P isochron map. The sensitivity of the isochron attribute
to the glauconitic channel directly reinforces the observations in well-log cross plots
(Figure 2.2.6 and Figure 2.2.7) where the sand and shale within the glauconitic channel
manifest themselves in different S-wave velocity while showing nearly no difference in P-
wave velocity.
29
(a) (b)
Figure 2.4.8: (a) P-P isochron from the top of the glauconitic channel to the Wabamun
event; (b) P-S isochron from the top of the glauconitic channel to the Wabamun event. The
black arrows indicate the channel and the red arrows indicate the possible crevasse splays.
The color bars represents two-way time.
Figure 2.4.9 shows the P-P and P-S amplitude maps at the top of the glauconitic channel.
The bright amplitude on the P-P amplitude map (Figure 2.4.9a) depicts a north-south
trending channel conforming to the trend of oil production wells. The ambiguity rests in
the discontinuity between oil production well 5-16 and dry hole 4-16 shown in the black
square in Figure 2.4.9a. Such an anomalous discontinuity could come from thickness
variations within the glauconitic channel where reflections from the top and base of the
channel destructively interfere with each other. To the contrary, the P-S amplitude map
30
(Figure 2.4.9b) suffers from poor signal-to-noise ratio and fails to reveal any obvious
geological information.
(a) (b)
Figure 2.4.9: (a) P-P amplitude map at the top of the glauconitic channel; (b) P-S amplitude
map at the top of the glauconitic channel. The black square shows the discontinuity in the
glauconitic channel. The color key represents amplitude.
The next step of interpretation proceeds by interactively extracting interval Vp/Vs ratio
from P-P and P-S data. The extraction of interval Vp/Vs ratio from post-stack data involves
transferring two-way time into Vp/Vs ratio, which is given by (Garotta, 1984):
Vp/Vs = (2ΔTps - ΔTpp)/ ΔTpp, (2.4.10)
31
where ΔTpp and ΔTps are the P-P and P-S isochron maps for a particular interval. This
equation is subject to mispicking in which the resulting Vp/Vs is often less realistic than
that indicated by the well-log cross plots. However, even with the existence of this
systematic error, the resulting Vp/Vs is still adequate to reveal lithological variation.
Figure 2.4.11: Interval Vp/Vs ratio extracted from the top of the glauconitic channel to the
Wabanum event.
Figure 2.4.11 shows the interval Vp/Vs ratio extracted from the top of the glauconitic
channel to the Wabanum event. The interval Vp/Vs ratio reveals a distinctive channel
depicted by the colors red, yellow, and green. The zone formed by the color green has a
Vp/Vs ratio around 1.5 and conforms to the trend of sand-filled wells. Shale-plugged wells
are uniformly located in the region illuminated by the color yellow with a Vp/Vs ratio
32
somewhat higher than the sand-filled zone. Regional wells fall in the zone with the highest
Vp/Vs ratio. Due to the influence of mispicking, sand bodies show a Vp/Vs ratio somewhere
around 1.4859 to 1.5668 and surrounding shales falls in the zone of Vp/Vs ratio values
ranging from 1.6275 to 1.7084, which are different from the range of Vp/Vs ratio indicated
in Figure 2.2.8.
33
2.5 Chapter Summary
P-S data shows a better well-tie correlation than P-P data in all wells (Potter et al.,
1996). Five events: the Viking Member, the Blairmore Member, the first coal bed, the top
of the glauconitic channel, and the Wabamun event were correspondingly picked on P-P
and P-S volume. The P-P and P-S isochron map from the top of the glauconitic channel to
the Wabamun event, P-P and P-S amplitude maps at the top of the glauconitic channel, and
the interval Vp/Vs ratio were extracted to delineate the glauconitic channel. The P-S
isochron map from the top of the glauconitic channel to the Wabamun event presents a
much more distinctive and definitive channel than does the P-P isochron map from the
same level (Yang et al., 1996). Whereas, the amplitude anomaly on the P-P amplitude map
at the top of the glauconitic channel depicts a channel conforming to the trend of oil
production wells while nothing can be conclusively interpreted from the P-S amplitude
map at the same level . The interval Vp/Vs ratio map from the top of the glauconitic channel
to the Wabamun event not only successfully delineates a definitive and reliable channel
conforming to existing well control but also distinguishes the sand-filled segment from the
shale-plugged section within the glauconitic channel (Margrave et al., 1997; Margrave et
al., 1998).
34
CHAPTER THREE
P-P and P-S Spectral Decomposition
3.1 Introduction
In 1999 Partyka et al., 1999 pioneered a novel means of seismic interpretation called
seismic spectral decomposition. His method transforms a 3D-seismic volume into the time-
frequency domain using the DFT (Discrete Fourier Transform). The amplitude spectrum
and phase spectrum from the DFT can be used to delineate geologic features such as
channels and faults, as well as mapping temporal-bed thickness and geologic discontinuity.
Figure 3.1.1 schematically illustrates the principle behind seismic-spectral decomposition.
Reflections from layers with various temporal thicknesses tune at different frequencies and
can be preferentially illuminated through the examination of amplitude for each discrete-
frequency component.
The effectiveness of seismic-spectral decomposition relies on identifying the location
of layer responses on composite-seismic traces and calculating the amplitude spectrum of
each, which is subject to the time and frequency resolution of a utilized spectral-
decomposition method. The desire for a better time and frequency resolution motivates the
evolution of spectral-decomposition algorithms. A long-temporal-window discrete Fourier
transform encompasses complex geological features whose amplitude spectra are complex
and are modulated by the spectrum of the wavelet (Partyka et al., 1999). The Short-Time
Fourier Transform (STFT) attempts to overcome this problem by continuously sliding a
temporal window along seismic traces and solving the Fourier coefficients of the signal
within the window at each time sample. This yields the spectra of local geologic features
35
when a shorter window is applied (Oyem, 2014). However, the STFT is subject to the
Gabor limit indicating the resolution of the STFT is fixed once the length of the window
Figure 3.1.1: Principal of layer imaging (Partyka et al., 1999).
function is specified. A wider window offers optimal frequency resolution but poor time
resolution, while a narrow window can provide excellent time resolution but violates the
assumption of orthogonality of the Fourier kernel. Therefore, under this circumstance,
STFT will suffer from spectral smearing defined as unrealistic energy beyond the recorded
bandwidth (Burnett et al., 2003). Wavelet-based methods such as the Continuous Wavelet
Transform (CWT) and S-Transform (Stockwell et al., 1996) use multi-resolution analysis
to vary temporal resolution with frequency (while remaining subject to a constant time-
frequency resolution product) but inevitably provide poor time resolution at low-frequency
components. The Constrained Least-Squares Spectral Analysis (CLSSA) method (Puryear
et al., 2012) overcomes these defects associated with the STFT and CWT. Instead of
solving Fourier series coefficients using the Fourier transform, this inversion based method
uses truncated non-orthogonal sinusoidal-basis functions to directly invert for the Fourier
36
series coefficients of the signal within the temporal window from a sparse-weighted model
in the time-frequency domain.
In this chapter, STFT, CWT, and CLSSA are performed on P-P and P-S data to map the
occurrence as well as identify lithology of the glauconitic channel. Results of the different
methods are compared to evaluate the resolving capacity of each method. The peak-
frequency volumes from the CLSSA of P-P and P-S data are used to calculate the
frequency-derived Vp/Vs ratio for identifying lithological variation within the glauconitic
channel.
3.2 Theory
STFT is a Fourier transform based method which calculates the time-frequency spectrum
of a signal using a sliding-temporal window. The mathematical expression of STFT:
𝑆𝑇𝐹𝑇(𝜏, 𝑓) = ∫ 𝐺(𝑡)𝑤(𝑡 − 𝜏)𝑒−𝑖2𝜋𝑓𝑡 𝑑𝑡, (3.2.1)
where 𝑤(𝑡 − 𝜏) is the window function centered at time 𝜏, 𝐺(𝑡) is the seismic trace to be
transformed, and 𝑒−𝑖2𝜋𝑓𝑡 is the Fourier kernel. 𝑆𝑇𝐹𝑇(𝜏, 𝑓) can be viewed as the Fourier
transform of the 𝐺(𝑡) using the sinusoidal-basis functions truncated by the window
function 𝑤(𝑡). The STFT violates the assumption of the Fourier transform that the
sinusoidal-basis functions must be orthogonal for those frequencies where the window
length is not an integer number of the period. The Fourier transform, under this
circumstance, is no longer the least-squares solution for the Fourier-series coefficients at
those frequency components (Puryear et al., 2012).
37
Compared to the STFT, the CWT was designed to avoid this problem, the mathematical
equation of which is written as (Chakraborty and Okaya, 1995):
𝑊(𝑎, 𝑏) = 1
√𝑎∫ 𝜓 (
𝑡−𝑏
𝑎)𝐺(𝑡)𝑑𝑡, (3.2.2)
where 𝜓(𝑡) is the mother wavelet, 𝑎 and 𝑏 are the scale and translation factors, 𝜓(𝑡−𝑏
𝑎)
constructs a wavelet dictionary scaled and translated from the selected mother wavelet
𝜓(𝑡), 𝑊(𝑎, 𝑏) is the time-frequency spectrum represented by the scale 𝑎 and translation
𝑏. With an orthogonal-wavelet dictionary, the equation above indicates that signal 𝐺(𝑡)
can be decomposed into a summation of the mother wavelets with different scale and
translation factors (Oyem, 2014). The CWT provides higher-frequency resolution for low-
frequency components and higher-time resolution for high-frequency components, which
is desirable for hydrocarbon exploration (Sinha et al., 2005).
The most recently developed Constrained Least-Squares Spectral Analysis (CLSSA) is
an inversion-based spectral-decomposition technique that directly solves the normal
equation for the Fourier series coefficients when the sinusoidal-basis functions are not
orthogonal by applying an iteratively reweighted least-squares regularization algorithm to
the complex spectral-decomposition inverse problem using a minimum support function.
Starting from the common definition of the forward problem (Puryear et al., 2012):
Fm = d, (3.2.3)
where F is the forward operator or the sinusoidal basis functions, m is the column vectors
of the model parameters (superposition of unknown Fourier coefficients) and d is the
38
windowed seismic trace. The Hilbert transform is applied to transform real seismic traces
into complex signals,
d = dr + idi, (3.2.4)
where dr is the windowed segment of a real seismic trace, di is the Hilbert transform of the
windowed segment of a seismic trace, and d is the analytical signal. The least-mean-square
solution to equation 3.2.3 is given by:
m = (F*F)-1F*d, (3.2.5)
where F* is the complex conjugate transpose matrix of F. The orthogonality of F is usually
breached when the data are truncated by a window. The weighting functions Wm and Wd
are applied to the model and seismic data to constrain and stabilize the inversion of
equation 3.2.3. The final weighted normal equation becomes:
Fwmw = Wdd, (3.2.6)
where Fw = WdFWd and mw = Wm-1m. The Tikhonov regularization is applied to
reformulate the ill-posed equation 3.2.6 by replacing it with a well-posed minimization
problem. The analytical Lagrange solution to the equation 3.2.6 can be then written as:
mw = F*w (FwF*
w + αI)-1Wdd, (3.2.7)
where α is the regularization parameter used to control the sparsity and stabilize the
inversion. The matrix mw is computed by Gaussian elimination. The model parameters are
thus reconstructed by:
m = Wmmw. (3.2.8)
39
The resultant frequency spectrum of the data m is then updated through an iteratively
reweighted least-squares regularization algorithm until a satisfactory result is achieved.
Marfurt and Kirlin, 2001 extended the Partyka et al., 1999 algorithm to narrow-band
thin-bed tuning analysis and discovered another set of seismic texture attributes. The peak
frequency is defined as the frequency at which the amplitude is maximum and can be
directly related to the two-way time thickness of a thin bed. The analytical expression
between the peak frequency and temporal thickness starts from the impulse response of a
thin-bed model shown in Figure 3.2.1:
g(t) = r1δ(t-t1) + r2δ(t-t1-T), (3.2.9)
where r1 is the reflection coefficient of the top of the thin bed, r2 is the reflection coefficient
of the base of the thin bed, and T is the two-way time thickness of the thin bed. If r1/r2 < 0,
the seismic response of the thin bed was defined as an odd-pair dominated response which
is commonly seen in a thin sand bed embedded in a hard shale matrix. If r1/r2 >0, the
corresponding seismic response is defined as an even-pair dominated response.
The Fourier transform of equation 3.2.9 can be written as:
g(f) = r1exp(-i2πft1) + r2exp(-i2πf(t1+T)), (3.2.10)
where f is the frequency and g(f) is the complex Fourier spectrum. Simplifying the
amplitude spectrum of g(f) with trigonometric identities gives:
G(f) = [r12 + r2
2 + 2r1r2cos(2πfT)]1/2. (3.2.11)
For an even-pair dominated response, equation 3.2.11 reaches its maximum at the
frequency equal to the reciprocal of the two-way time thickness, T. For an odd-pair
40
dominated response, the peak frequency is reached at the frequency equal to half of the
reciprocal of the two-way time thickness.
Figure 3.2.1: Thin bed model (Marfurt and Kirlin, 2001).
With the correct registration of P-P and P-S data, following Vetrici and Stewart 1996,
the peak-frequency attribute can be directly used for lithology identification by expanding
equation 2.4.10:
Vp/Vs = (2ΔTps - ΔTpp)/ΔTpp. (2.4.10)
Three assumptions must be made to relate the Vp/Vs ratio to the P-P and P-S peak
frequency:
1. The sparse layer model is valid for both P-P and P-S wave mode.
2. A single layer has identical P-P and P-S reflection pattern.
41
3. The window function is sufficiently short to isolate the Fourier spectrum of a single
layer.
The second assumption, to be more specific, indicates that whenever a single layer
manifests itself as an odd- or even-pair dominated response in the P-P domain, it will
manifest itself as an odd- or even-pair in the P-S domain as well. It is intuitive that such an
assumption may not be universally met and thus requires calibration before applying to the
entire volume.
With the three assumptions met, substituting two-way time thickness with peak
frequency gives the analytical expression of the frequency-derived Vp/Vs ratio:
Vp/Vs = 2Fpeakpp/Fpeakps -1. (3.2.11)
Fpeakpp and Fpeakps are the peak frequencies of a thin bed response within each analyzing
window in the P-P and P-S domain despite the evenness and oddness. Compared to
conventional post-stack multi-component interpretation, instead of analyzing the Vp/Vs
ratio on horizon maps, equation 3.2.11 can directly provide a Vp/Vs ratio volume different
than that calculated from AVO inversion.
3.3 Quality Control
Unlike the CLSSA and CWT, the STFT is subject to spectral smearing dependent on
window length and thus requires quality control or parameter testing before applying to the
entire survey. Based on the correlation profile of well 8-8, approximately 48 m of the
glauconitic channel corresponds to 25 ms on P-P data and 32 ms on P-S data. Therefore,
42
as a shorter window is applied, fewer low-frequency components will be harvested in the
resultant time-frequency spectrum. In order to maintain as much low-frequency signal as
possible, while acquiring a satisfactory time resolution for the subsequent frequency-
derived Vp/Vs ratio analysis, the 40 ms STFT and CLSSA, as well as the CWT with the
Morlet wavelet, were applied to the trace at inline 72 and crossline 129 of P-P and P-S data
to test for spectral smearing.
As expected, the time-frequency spectra of the 40 ms STFT of P-P and P-S data shows
severe spectral smearing that makes it impossible to interpret any geologic features
conclusively. After substituting the 40 ms window with a 100 ms window for STFT, no
unrealistic energy was found at each frequency component for the STFT of P-P data.
However, anomalous energy was found at low-frequency components (< 10 Hz) for the
STFT of P-S data which is not indicated by the amplitude spectrum of the trace at inline
72 and crossline 129 of P-S data (Figure 3.3.1d). Instead of testing a larger window to avoid
spectral smearing, the decision was made to analyze discrete-frequency components at
every 10 Hz for the STFT, CWT, and CLSSA of P-P and P-S data. Figure 3.3.2 and Figure
3.3.3 are the time-frequency spectra of the trace at inline 72 and crossline 129 for the STFT,
CWT, and CLSSA of P-P and P-S data respectively. The time-frequency spectra showed
no indication of spectral smearing at the analyzed bandwidth for the CWT and CLSSA of
P-P and P-S data with the pre-determined parameters.
43
(a) (b)
(b) (d)
Figure 3.3.1: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
100 ms STFT of P-P data; (b) Time-frequency panel of the trace at inline 72 and crossline
129 for the 100 ms STFT of P-S data; (c) Amplitude spectrum of the trace at inline 72 and
crossline 129 of P-P data; (d) Amplitude spectrum of the trace at inline 72 and crossline
129 of P-S data. The color bar indicates the spectral amplitude.
44
(a) (b) (c)
Figure 3.3.2: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
STFT of P-P data; (b) Time-frequency panel of the trace at inline 72 and crossline 129 of
The CWT of P-P data; (c) Time-frequency panel of the trace at inline 72 and crossline 129
for the CLSSA of P-P data. The color bar indicates spectral amplitude.
(a) (b) (c)
Figure 3.3.3: (a) Time-frequency panel of the trace at inline 72 and crossline 129 for the
STFT of P-S data; (b) Time-frequency panel of the trace at inline 72 and crossline 129 of
The CWT of P-S data; (c) Time-frequency panel of the trace at inline 72 and crossline 129
for the CLSSA of P-S data. The color bar indicates spectral amplitude.
45
3.4 Multi-Component Frequency Attributes Analysis.
The inversion-based CLSSA will automatically abandon frequency components of a
decomposed trace when live samples are below the pre-set threshold. This setting will bring
blank spaces to the edge of a horizon map where the fold of seismic survey is low and thus
become a problem for further interpretation analysis. Therefore, the range of P-P and P-S
seismic surveys are constrained to inline 50 to 150 and crossline 100 to 160 to avoid the
artifact.
Figure 3.4.1 through Figure 3.4.3 are the 30 Hz, 60 Hz, and 90 Hz discrete-frequency
maps at the top of the glauconitic channel for the STFT, CWT, and CLSSA of P-P data.
The glauconitic channel appears at the 30 Hz discrete-frequency maps for the three
methods. A distinctive channel and two crevasse splays can be observed at the 60 Hz
discrete-frequency maps at the analyzed horizon for the three methods as indicated by the
black and red polygons in Figure 3.4.2. The amplitude related to the glauconitic channel is
below one-third of the maximum amplitude of the 90 Hz discrete-frequency map indicating
the disappearance of the glauconitic channel (Figure 3.4.3). Anomalous bright amplitudes
displayed as a red color on the 30 Hz and 60 Hz STFT discrete-frequency maps result from
utilizing a 100 ms window which fails to isolate the seismic response of the glauconitic
channel from the interference of the strong coal-bed reflection.
46
(a) (b) (c)
Figure 3.4.1: (a) 30 Hz discrete-frequency map at the top of the glauconitic channel for the
STFT of P-P data; (b) 30 Hz discrete-frequency map at the top of the glauconitic channel
for the CWT of P-P data; (c) 30 Hz discrete-frequency map at the top of the glauconitic
channel for the CLSSA of P-P data. The color bar indicates spectral amplitude.
47
(a) (b) (c)
Figure 3.4.2: (a) 60 Hz discrete-frequency map at the top of the glauconitic channel for the
STFT of P-P data; (b) 60 Hz discrete-frequency map at the top of the glauconitic channel
for the CWT of P-P data; (c) 60 Hz discrete-frequency map at the top of the glauconitic
channel for CLSSA of P-P data. The black polygons indicate the glauconitic channel. The
red polygons indicate crevasse splays. The color bar indicates spectral amplitude.
48
(a) (b) (c)
Figure 3.4.3: (a) 90 Hz discrete-frequency map at the top of the glauconitic channel for the
STFT of P-P data; (b) 90 Hz discrete-frequency map at the top of the glauconitic channel
for the CWT of P-P data; (c) 90 Hz discrete-frequency map at the top of the glauconitic
channel for the CLSSA of P-P data. The color bar indicates spectral amplitude.
49
The investigation of the vertical extension of the glauconitic channel proceeds by
analyzing vertical sections of an arbitrary line that crosses the majority of wells (Figure
3.4.4). Figure 3.4.5 through Figure 3.4.7 are the 30 Hz discrete-frequency vertical sections
of the arbitrary line for the STFT, CWT, and CLSSA of P-P data respectively. The black
arrows indicate the location of the glauconitic channel. The STFT cannot separate the
glauconitic channel interval from the coal bed due to the effect of the 100 ms window.
Additionally, the CWT also fails to isolate the glauconitic channel from the coal bed at the
analyzed frequency, which reflects the genetic defect of the CWT that it offers poor time
resolution at low-frequency components. To the contrary, the CLSSA clearly images the
glauconitic channel interval without interference from the coal beds.
Figure 3.4.4: Geometry of the arbitrary line used for the extraction of vertical sections.
50
Figure 3.4.5: 30 Hz discrete-frequency vertical section of the arbitrary line for the STFT of
P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spctral amplitude.
Figure 3.4.6: 30 Hz discrete-frequency vertical section of the arbitrary line for the CWT of
P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
51
Figure 3.4.7: 30 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
Figure 3.4.8 through Figure 3.4.10 are the 60 Hz discrete-frequency vertical sections of
the arbitrary line for the STFT, CWT, and CLSSA of P-P data respectively. The black
arrows indicate the location of the glauconitic channel. The channel is completely
contaminated by the interference of the strong coal-bed reflection and can not be identified
at the analyzed frequency for the STFT of P-P data. Compared to the 30 Hz CWT vertical
section of the arbitrary line, the 60 Hz CWT vertical section can separate the channel from
the coal-bed reflection but fails to distinctively reveal the tuning pattern within the channel
at the analyzed frequency. However, The 60 Hz CLSSA vertical sections showed the best
time resolution at the analyzed frequency while presenting a distinctive tuning pattern
within the channel system.
52
Figure 3.4.8: 60 Hz discrete-frequency vertical section of the arbitrary line for the STFT of
P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
Figure 3.4.9: 60 Hz discrete-frequency vertical section of the arbitrary line for the CWT of
P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
53
Figure 3.4.10: 60 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The black arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
Figure 3.4.11 through Figure 3.4.13 are the 90 Hz discrete-frequency vertical sections
of the arbitrary line for the STFT, CWT, and CLSSA of P-P data respectively. The red
arrows indicate the locations of the glauconitic channel. The range of amplitude of the
channel interval is from 0.019 to 0.028 at the analyzed frequency for the three methods,
which fall in the bottom one-third of the range of the displayed data. Therefore, the 90 Hz
of P-P data are believed to be the limits of the frequency components which contain the
information of the glauconitic channel.
54
Figure 3.4.11: 90 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
curves are the P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation
tops. The color bar indicates spectral amplitude.
Figure 3.4.12: 90 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
55
Figure 3.4.13: 90 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-P data. The red arrows indicate the location of the glauconitic channel. The inserted
curves are P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation tops.
The color bar indicates spectral amplitude.
The narrow bandwidth of P-S data restricts the possibility of analyzing the glauconitic
channel on multiple discrete-frequency maps and vertical sections. The channel only
appears on the 10 Hz and 20 Hz discrete-frequency maps at the horizon of the top of the
glauconitic channel for the STFT, CWT, and CLSSA of P-S data, as shown in Figure 3.4.14
and Figure 3.4.15. The bright amplitude illuminates a channel (red polygons in Figure
3.4.14 and Figure 3.4.15) westward to the trend of oil production wells that cannot be
identified on the P-S conventional amplitude map at the same level (Figure 2.4.9b), which
is in accordance with the Margrave et al., 1998 observation.
56
(a) (b) (c)
Figure 3.4.14: (a) 10 Hz discrete-frequency map at the top of glauconitic channel for the
STFT of P-S data; (b) 10 Hz discrete-frequency map at the top of glauconitic channel for
the CWT of P-S data; (c) 10 Hz discrete-frequency map at the top of glauconitic channel
for the CLSSA of P-S data. Red polygons indicate the glauconitic channel. The color bar
indicates spectral amplitude.
57
(a) (b) (c)
Figure 3.4.15: (a) 20 Hz discrete-frequency map at the top of glauconitic channel for the
STFT of P-S data; (b) 20 Hz discrete-frequency map at the top of glauconitic channel for
the CWT of P-S data; (c) 20 Hz discrete-frequency map at the top of glauconitic channel
for the CLSSA of P-S data. Red polygons indicate the glauconitic channel. The color bar
indicates spectral amplitude.
58
Figure 3.4.16 through Figure 3.4.18 are the 10 Hz discrete-frequency vertical sections of
the arbitrary line for the STFT, CWT, and CLSSA of P-S data respectively. Vertical
sections at the analyzed frequency for the three methods are filled with vertical strikes
which resemble acquisition footprints. The glauconitic channel cannot be identified on any
of the vertical sections at the analyzed frequency. However, CLSSA can maintain an
acceptable time resolution for the imaging of the coal-bed reflection at the frequency
component as low as 10 Hz, while the STFT and CWT fail to present any reliable geologic
information.
Figure 3.4.16: 10 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The color bar indicates spectral amplitude.
59
Figure 3.4.17: 10 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The color bar indicates spectral amplitude.
Figure 3.4.18: 10 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The color bar indicates spectral amplitude.
60
Figure 3.4.19 to Figure 3.4.21 are the 20 Hz discrete-frequency vertical sections of the
arbitrary line for the STFT, CWT, and CLSSA of P-S data respectively. The black arrows
indicate the glauconitic channel interval. However, the channel is laterally inconsistent and
contaminated by acquisition footprints and the STFT, CWT, and CLSSA fail to image the
glauconitic channel interval independent of the interference from the coal-bed reflection.
Figure 3.4.19: 20 Hz discrete-frequency vertical section of the arbitrary line for the STFT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The black arrows indicate the location of the glauconitic
channel interval. The color bar indicates spectral amplitude.
61
Figure 3.4.20: 20 Hz discrete-frequency vertical section of the arbitrary line for the CWT
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The black arrows indicate the location of the glauconitic
channel interval. The color bar indicates the spectral amplitude.
Figure 3.4.21: 20 Hz discrete-frequency vertical section of the arbitrary line for the CLSSA
of P-S data. The inserted curves are S-wave velocities. COAL1, GLCTOP, GLCBASE,
and OST are formation tops. The black arrows indicate the location of the glauconitic
channel interval. The color bar indicates spectral amplitude.
62
3.5 Frequency-Derived Vp/Vs Ratio Analysis.
In conventional seismic attributes analysis, the interval Vp/Vs ratio gives the most
deterministic interpretation on the glauconitic channel. The desire of deriving the Vp/Vs
ratio from frequency domain originates the algorithm in equation 3.2.11. It is intuitive that
the second assumption of equation 3.2.11 may not be universally valid and thus require
calibration. The blocked P-wave velocity, S-wave velocity, and density as well as the deep
induction, medium-deep induction, and gamma-ray logs are shown in Figure 3.5.1 to verify
the second assumption. The upper unit of the Glauconitic Member (highlighted zone in
Figure 3.5.1a) was regarded as a single layer to test the consistency between P-P and P-S
reflection patterns. Figure 3.5.1b and Figure 3.5.1c are the P-P and P-S AVO curves of the
top and base of the upper unit of the Glauconitic Member. The maximum offset of the
Blackfoot 3C-3D seismic survey is approximately 1550 m, whereas the glauconitic channel
appears at the average depth of 1560 m. Considering the relationship between offset and
depth, it is not probable for this multi-component seismic data to reach an incident angle
of 60◦. Therefore, the P-P and P-S reflectivity series of the upper unit of the Glauconitic
Member can be treated as odd-pair dominated responses. In addition, CLSSA exhibits the
best time and frequency resolution among the three analyzed methods and thus was
selected for the calculation of the frequency-derived Vp/Vs ratio.
63
(a)
(b) (c)
Figure 3.5.1:(a) Blocked P-wave velocity, S-wave velocity, and density as well as gamma
ray, medium-depth induction, deep induction logs from well 8-8; (b) P-P AVO response of
the top and base of the upper unit of the Glauconitic Member; (c) P-S AVO response of
the top and base of the upper unit of the Glauconitic Member. The highlighted zone in (a)
is the upper unit of the Glauconitic Member.
64
Following Partyka et al., 1999, the P-P and P-S time-frequency volumes of CLSSA
were normalized to remove the wavelet overprint for the desired single layer response. For
computational efficiency, only the zone of interest (800 ms to 1200 ms for P-P data and
1200 ms to1800 ms for P-S data) was normalized to extract the P-P and P-S peak-frequency
volumes. Figure 3.5.2 shows the peak-frequency maps at the top of the glauconitic channel
for P-P and P-S data. The values of the P-P peak frequency (Figure 3.5.2a) range from 41
Hz to 72 Hz denoted by the colors green to light red, nevertheless, the P-S peak-frequency
map (Figure 3.5.2b) shows a much narrower range of values from 14 Hz to 20 Hz denoted
by the colors yellow to green. The yellow color on the P-S peak-frequency map delineates
a north-south trending channel (shown in red polygon) conforming to existing well control,
while the same channel can not be identified on the P-P peak-frequency map at the same
level. However, no peak frequency variation within the channel can be observed on the P-
S peak-frequency map, which indicates the failure of the P-S peak-frequency attribute to
reveal the thickness variation within the glauconitic channel.
The correlated P-wave velocity and S-wave velocity logs are interpolated using the
inverse distance to the power of two algorithm to construct a velocity model for the P-S to
P-P domain conversion. The P-P peak-frequency volume and the P-S peak-frequency
volume in the P-P domain are then taken into equation 3.2.11 to calculate the resultant
frequency-derived Vp/Vs ratio volume. Figure 3.5.3 and Figure 3.5.4 show the frequency-
derived Vp/Vs ratio map at of the top of the glauconitic channel and the vertical section of
the frequency-derived Vp/Vs ratio at crossline 129 respectively. Compared to the cross plot
of gamma-ray values versus Vp/Vs ratio in the glauconitic channel (Figure 2.2.8), the range
of values of the frequency-derived Vp/Vs ratio at the analyzed horizon is from 4.23 to 8.76
65
which does not have a physical meaning. In addition to unrealistic values of the frequency-
derived Vp/Vs ratio, the variation of the frequency-derived Vp/Vs ratio fails to reflect the
change of lithology within the glauconitic channel on the horizon map and vertical section.
(a) (b)
Figure 3.5.2: (a) P-P peak-frequency map at the top of the glauconitic channel; (b) P-S
peak-frequency map at the top of the glauconitic channel. The color bar indicates peak
frequency. The red polygon reveals the interpreted glauconitic channel.
66
Figure 3.5.3: Frequency-derived Vp/Vs ratio at the top of the glauconitic channel. The color
bar indicates values of the frequency-derived Vp/Vs ratio.
Figure 3.5.4: Vertical display of the frequency-derived Vp/Vs ratio at crossline 129 parallel
to the trending of the channel. The inserted curves are P-wave velocities. COAL1,
GLCTOP, GLCBASE and OST are formation tops. The color bar indicates values of the
frequency-derived Vp/Vs ratio.
67
The comparison of the P-P peak-frequency map at the top of the glauconitic channel
(Figure 3.5.2a) and the frequency-derived Vp/Vs ratio at the same level (Figure 3.5.3)
suggests a possible explanation for the failure of the frequency-derived Vp/Vs ratio. The
feature illuminated by the green, yellow, and light red colors on the P-P peak-frequency
map looks almost identical to the feature depicted by the green to yellow colors on the
frequency-derived Vp/Vs ratio map, which implies that the P-P peak-frequency volume
dominants the resultant frequency-derived Vp/Vs ratio. This observation reveals that the P-
S peak-frequency fails to represent the two-way time thickness of a single layer.
The application of equation 3.2.11 implies an assumption that P-P and P-S data have
the same bandwidth, which may be unlikely in reality. Unavoidably, the P-S peak-
frequency volume extracted from the P-S time-frequency volume of the CLSSA represents
the peak frequency of the signal within each analyzing window instead of the peak
frequency of a single-layer response within each analyzing window. The bias can also be
introduced from the unsophisticated P-P-to-P-S-domain conversion. The schematic
illustration of the P-S to P-P domain conversion is shown in Figure 3.5.5. The domain
conversion using a 3D-velocity field interpolated from correlated P-wave and S-wave
velocity logs is a resampling process which will smooth the original data by degrading a
regular sampled P-S peak-frequency trace in P-S time into an irregular sampled trace in P-
P time if there are errors in the utilized time-depth curves, which may be responsible for
the failure of the frequency-derived Vp/Vs ratio. Even though the P-P and P-S AVO curves
(Figure 3.5.1b and Figure 3.5.1c) indicate that the second assumption is valid at the location
of well 8-8, there is no warranty that this assumption will be valid throughout the entire
survey. However, it is convenient to bypass the second assumption by using the real
68
component of the CLSSA spectrum which only reveals the Fourier spectrum of the even
component of a single layer.
Figure 3.5.5 Schematic illustration of the P-S to P-P domain conversion. Δt is the sampling
rate (Todorov et al., 1999).
3.6 Chapter Summary.
In this chapter, the STFT, CWT, and CLSSA were applied to P-P and P-S data to
delineate the glauconitic channel. A north-south trending channel with two crevasse splays
were identified on the 60 Hz discrete-frequency map at the top of the glauconitic channel
for the STFT, CWT, and CLSSA of P-P data, while the STFT, CWT, and CLSSA of P-S
data reveal a less clear channel westward to the trend of oil production wells at 10 Hz and
20 Hz. The STFT is restricted by the Garbor limit (time-frequency tradeoff) and provides
the least-satisfactory interpretation for both P-P and P-S data. The CWT reveals the channel
on the analyzed discrete-frequency maps for P-P and P-S data and offers good time
resolution at frequency components greater than 30 Hz but could not clearly indicate the
tuning pattern within the glauconitic channel for P-P data. The CLSSA offers the best time
69
resolution while maintaining an optimal frequency resolution at every analyzed frequency
component for P-P and P-S data. The analysis on the P-P and P-S peak-frequency volumes,
as well as the frequency-derived Vp/Vs ratio attribute, fails to reveal the variation of the
two-way time thickness and the change of lithology within the glauconitic channel, which
results from the narrow bandwidth of the P-S data.
70
CHAPTER FOUR
P-P and P-S Harmonic-Bandwidth Extrapolation
4.1 Introduction
Limited seismic resolution prevents the base of the glauconitic channel from being
simultaneously revealed on P-P and P-S data and thus restricts the possibility of extracting
the deterministic interval Vp/Vs ratio from the channel interval. The limited bandwidth of
P-S data prohibits the peak frequency from representing two-way time thickness of a single
layer and thus brings the failure of the application of frequency-derived Vp/Vs ratio to
identify lithology within the glauconitic channel. Therefore, a much more definitive
understanding of the lithology variation within the glauconitic channel can be obtained, if
any improvement can be made on either of these two critical parameters. Technically,
seismic resolution is determined by the bandwidth of seismic data (Widess, 1973; Kallweit
and Wood, 1982), so the most straightforward and optimal solution to the limited resolution
of seismic data is to design a much more comprehensive acquisition and utilize
sophisticated seismic processing. For example, increasing the sampling rate from 2 ms to
1 ms will double the Nyquist frequency, which enables seismic data to record more detailed
geologic features. However, this solution is outside the scope of this project.
Some seismic resolution improving methods can be found in geophysical literature (e.g.,
Young et al., 2005). These methods arbitrarily manipulate low-frequency components into
desired high-frequency content without bearing any physical meaning, which will
inevitably mislead the focus of interpretation to artifacts. Liang and Castagna (in press)
proposed a bandwidth extension technique called harmonic-bandwidth extrapolation,
71
which is a method based on the physics of the wave propagation. In the following chapter,
harmonic-bandwidth extrapolation will be applied to P-P and P-S data to investigate an
improvement in seismic resolution. High-resolution Vp/Vs will be extracted with this
method to distinguish the sand-filled segments from the shale-plugged section within the
glauconitic channel.
4.2 Theory
Harmonic-bandwidth extrapolation has evolved from pre-existed algorithms. Partyka et
al., 1999, as well as Marfurt and Kirlin, 2001, showed the amplitude spectrum of a single
layer is sinusoidal. Puryear and Castagna, 2008 showed a thin-bed response could be
decomposed into a summation of odd and even impulse pairs of different scales. Zhang
and Castagna, 2011 introduced an inversion method for reflectivity series using basis
pursuit algorithm (Chen et al., 2001). Liang and Castagna (in press) started with assuming
the blocky earth model is valid, and thus the spectrum of reflectivity series can be viewed
as a superposition of sinusoidal basis functions. This assumption is an extension of the fact
that a single-layer response can be represented as a summation of impulse pairs with
different scales (Puryear and Castagna, 2008) and the Fourier spectrum of an impulse pair
is sinusoidal (Bracewell, 1986; Partyka et al., 1999; Marfurt and Kirlin, 2001). The
algorithm of harmonic-bandwidth extrapolation starts with defining odd and even impluse
pairs as (Liang and Castagna, in press):
(t) = r∙δ(t + Δt/2) + r∙δ(t -Δt/2), (4.2.1)
and
(t) = r∙δ(t + Δt/2) – r∙δ(t – Δt/2) (4.2.2)
72
where, δ(t) is the Dirac delta function, r is the magnitude of an impulse pair, and Δt is the
temporal thickness of a single layer. The corresponding Fourier spectrum of the even and
odd impulse pairs are given by:
(f) = 2r∙cos(π∙Δt∙f) (4.2.3)
and
(f) = i2r∙sin(π∙Δt∙f). (4.2.4)
Since the reflectivity series can be viewed as a summation of even and odd impulse pairs
referenced to an analyzing point (Puryear and Castagna, 2008). The Fourier spectrum of a
reflectivity series can be decomposed into a summation of sinusoidal basis functions. For
a temporal analysis window of 2N+1 discrete points with a sampling rate of dt, any impulse
pair centered at the time zero can be expressed as:
r(t,n) = r1 δ(t + n∙dt) + r2 δ(t + n∙dt) = x∙ (t,n) + y∙ (t,n) (4.2.5)
where, n∙dt is half of the time thickness of the impulse pair with n from 0 to N, and x and
y are the magnitudes of the odd and even pairs. The Fourier spectrum then can be written
as:
R(f,n) = 2x∙ cos(2π∙n∙dt∙f) + i2y∙sin(2π∙n∙dt∙f). (4.2.6)
Taking the Fourier transform of a reflectivity series within the 2N+1 analyzing window
yields:
R(f) = ∑ [𝑥𝑛 cos(2π ∙ n ∙ dt ∙ 𝑓) + i2𝑦𝑛 sin(2π ∙ n ∙ dt ∙ 𝑓)]𝑁𝑛=0 , (4.2.7)
where 𝑥𝑛 and 𝑦𝑛 are column vectors of the magnitude of the odd and even impulse pairs.
73
Seismic traces can be viewed as a wavelet convolved with a reflectivity series in the
time domain, which is equivalent to the spectrum of the wavelet times the spectrum of the
reflectivity series in the frequency domain. Within a usable spectral band with an
acceptable signal-to-noise ratio, dividing out the spectrum of the wavelet will provide the
reflectivity spectrum within the limit of the wavelet. Therefore, the normalized data
spectrum is linked with the sinusoidal-basis functions vectors through (Liang and
Castagna, in press):
d = Gm + n, (4.2.8)
where d is the normalized data spectrum, G is the sinusoidal-kernel matrix, m is the model
parameters specifically the matrix of the magnitude of impulse pairs, and n is the prediction
error. The basis pursuit algorithm solves for coefficients for all frequency-varying
sinusoidal basis in equation 4.2.8 by simultaneously minimizing both the L2 norm of the
error term and the L1 norm of the solution regularized by the regularization factor λ (Zhang
and Castagna, 2011):
min [||d-Gm||2 + λ||m||1]. (4.2.9)
A higher value of regularization factor λ is primarily used in the data with poor signal-to-
noise ratio to obtain optimal results by increasing sparsity, while a lower value of λ will
release constraints on the model parameters to reveal more detail under the circumstance
of high signal-to-noise ratio. The basis pursuit algorithm solves for 𝑥𝑛 and 𝑦𝑛, and thus the
frequency-extrapolated reflectivity series is obtained by directly taking the inverse Fourier
transform of equation 4.2.7:
74
r(t) = 1
2∑ [(𝑥𝑛 + 𝑦𝑛)δ(t + ndt) + (𝑥𝑛 − 𝑦𝑛)δ(t − ndt)𝑁
𝑛=0 ]. (4.2.10)
The success of harmonic-bandwidth extrapolation does not only depend on the accuracy
of the decomposition of the complex spectrum into a summation of the sinusoidal-basis
functions but also the sufficiency of the sampled spectrum. To be more specific, the
normalized data spectrum must obtain sufficient recoverable frequency periodicities. The
frequency components that are completely out of the useable bandwidth shall never be
recovered (Liang and Castagna, in press).
4.3 P-P and P-S Harmonic-Bandwidth Extrapolation
The regularization factor λ in harmonic-bandwidth extrapolation controls the sparsity
of the inversion. A high value of λ is preferable in the data with a poor signal-to-noise ratio
to achieve optimal inverted results by increasing sparsity. However, the sparser the model
is, the less geologic information will be contained in the data. To invert for as much
geologic information as the data can possibly contain, a 10/20-60/90 Hz bandpass filter
and a 5/10-25/40 Hz bandpass filter were applied to the preconditioned P-P data and P-S
data to remove artifacts that might decrease the stability of harmonic-bandwidth
extrapolation, while still maintaining the integrity of the frequency components
encompassing the glauconitic channel. Figure 4.3.1 and Figure 4.3.2 show the vertical
displays of crossline 129 before and after bandpass filtering for P-P and P-S data
respectively. The bandpass filters remove the steps beyond the usable bandwidth of the
preconditioned P-P and P-S data (frequency components from 85 Hz to 100 Hz in Figure
4.3.1c and frequency components from 50 Hz to 100 Hz in Figure 4.3.2c).
75
(a) (b)
(c) (d)
Figure 4.3.1: (a) Vertical display of crossline 129 of the preconditioned P-P data; (b)
Vertical display of crossline 129 of the preconditioned P-S data after bandpass filtering;
(c) Amplitude spectrum of the preconditioned data from inline 47-165, crossline 88-168,
and time 0-3000 ms; (d) Amplitude spectrum of the preconditioned data after bandpass
filtering from inline 47-165, crossline 88-168, and time 0-3000 ms. The color bar indicates
amplitude.
76
(a) (b)
(c) (d)
Figure 4.3.2: (a) Vertical display of crossline 129 of the preconditioned P-S data; (b)
Vertical display of crossline 129 of the preconditioned P-S data after bandpass filtering;
(c) Amplitude spectrum of the preconditioned P-S data from inline 47-165, crossline 88-
168, and time 0-3000 ms; (d) Amplitude spectrum of the preconditioned P-S data after
bandpass filtering from inline 47-165, crossline 88-168 , and time 0-3000 ms. The color
bar indicates amplitude.
77
Harmonic-bandwidth extrapolation extends the bandwidth of the P-P and P-S data by
1.5 from the original conditioned bandwidth. Figure 4.3.3 and Figure 4.3.4 show the
vertical displays of crossline 129 of the bandwidth extrapolated P-P and P-S data
respectively. Unexpected artifacts have been observed on the P-S bandwidth-extrapolated
data. The area shown in the black squares in Figure 4.3.4b reveal several noticeable phase
reversals that do not appear on the original P-S data (Figure 4.3.4a). These spurious events
are consequences of the poor signal-to-noise ratio of P-S data. The inversion window set
for harmonic-bandwidth extrapolation was the entire recording length, and the non-
stationary analytical wavelets internally extracted from seismic data were utilized to
normalize the data spectrum for P-P and P-S data, which is believed to characterize the
actual progress of seismic-wave propagation. The original consideration for using an
analyzing window over the entire recording length was to encompass as many low-
frequency components as possible, through which the regularization factor λ can be
released to a point where the inverted results are not too sparse to reveal subtle geologic
features. However, sparse layer inversion using the basis pursuit, the vital step in the
harmonic-bandwidth extrapolation, is a trace-by-trace inversion method that does not
require any lateral constraints but rather dictionaries comprised of wedge models, and
therefore the linear optimization is only responsible for each trace rather than the entire
volume, which indicates that instead of stabilizing inversion, harmonic-bandwidth
extrapolation over the entire recording length amplified the intrinsic problem of the poor
signal-to-noise ratio of P-S data.
78
(a) (b)
(b) (c)
Figure 4.3.3: (a) Vertical display of crossline 129 of the preconditioned P-P data after
bandpass filtering; (b) Vertical display of crossline 129 of the bandwidth extrapolated P-P
data; (c) Amplitude spectrum of the preconditioned P-P data after bandpass filtering from
inline 47-165, crossline 88-168, and time 0-3000 ms; (d) Amplitude spectrum of the
bandwidth-extrapolated data from inline 47-165, crossline 88-168, and time 0-3000 ms.
The color bar indicates amplitude.
79
(a) (b)
(c) (d)
Figure 4.3.4: (a) Vertical display of crossline 131 of the preconditioned P-S data after
bandpass filtering; (b) Vertical display of crossline 131 of the bandwidth extrapolated P-S
data; (c) Amplitude spectrum of the preconditioned P-S data after bandpass filtering from
inline 47-165, crossline 88-168, and time 0-3000 ms; (d) Amplitude spectrum of the
bandwidth-extrapolated data from inline 47-165, crossline 88-168, and time 0-3000 ms.
The black squares show artifacts. The color bar indicates amplitude.
80
Another explanation for the disappointing P-S bandwidth extrapolation results may be
related to the wavelet used for normalizing the data spectrum. The non-stationary analytical
wavelets internally extracted from seismic data indeed take the attenuation of wave
propagation into consideration. However, it is intuitive that if a non-stationary analytical
wavelet is extracted from the seismic zones contaminated by random noises and is further
used to normalize the spectrum of the input data, harmonic-bandwidth extrapolation will
inevitably produce unpredictable artifacts. Therefore, the bandwidth-extrapolation window
was narrowed down to the level of the zone of interests which is from 1200 ms to 2000 ms
for P-S data and a 100 ms stationary full wavelet extracted at nine well locations was used
for the P-S bandwidth extrapolation. Figure 4.3.5 shows the comparison between the
original P-S harmonic-bandwidth extrapolation and the P-S harmonic-bandwidth
extrapolation with the specified parameters. The black squares in Figure 4.3.5a and Figure
4.3.5b indicate the differences. Harmonic-bandwidth extrapolation with the specified
parameters can improve the lateral consistency of events and reduce the occurrence of
random artifacts.
81
(a) (b)
(c) (d)
Figure 4.3.5: (a) Vertical display of crossline 131 of the original bandwidth-extrapolated
P-S data; (b) Vertical display of crossline 131 of the bandwidth extrapolated P-S data with
the specified parameters; (c) Amplitude spectrum of the original bandwidth-extrapolated
P-S data calculated from 47-165, crossline 88-168, and time 1200-1800 ms; (d) Amplitude
spectrum of the bandwidth-extrapolated P-S data with specified parameters calculated from
47-165, crossline 88-168, and time 1200-1800 ms. The color bar indicates amplitude.
82
Bandwidth extrapolation extends the frequency components outside of the band of the
original data, and thus synthetic traces calculated from well logs need to be re-correlated
with the bandwidth extrapolated data to update time-depth curves. Figure 4.3.6 and Figure
4.3.7 are the correlation profiles between synthetic traces from well 8-8 and 4-16 and
bandwidth-extrapolated P-P and P-S data. Figure 4.3.8 shows the total correlation profiles
between synthetic traces from nine wells and P-P and P-S bandwidth-extrapolated data.
Only a bulk time shift was applied to tie the synthetic traces with the P-P and P-S
bandwidth-extrapolated data. The correlation profile between the bandwidth-extrapolated
P-S data and synthetic traces from nine wells shows a better tie than that between P-P
bandwidth-extrapolated data and synthetic traces from nine wells. Synthetic wedge models
were constructed to evaluate the improvement in seismic resolution after harmonic-
bandwidth extrapolation for P-P and P-S data. The wavelets used for correlating synthetic
traces with the bandwidth-extrapolated P-P and P-S data and the rock physics parameters
specified in Table 2.4.1 are utilized to construct P-S and P-S wedge models. These results
are shown in Figure 4.3.9 and Figure 4.3.10. The tuning thickness of the glauconitic
channel for the P-P and P-S bandwidth extrapolated data are approximately 21 m and 27
m respectively (Figure 4.3.11). These figures show that the P-P tuning thickness is
improved by approximately 15 m while the P-S tuning thickness remains constant after
harmonic-bandwidth extrapolation, which is further confirmed by the vertical display of
the P-S bandwidth-extrapolated data at crossline 129 (Figure 4.3.12).
83
(a)
(b) (c)
Figure: 4.3.6: (a) Seismic-well tie between synthetic trace from well 8-8 and bandwidth-
extrapolated P-P seismic data. From left to right the curves are P-wave velocity, S-wave
velocity, density, synthetic trace (blue), extracted composite trace at the well location (red),
and traces along the well path (black). The correlation coefficient is 0.832 over a window
from 1200 ms to 1705 ms.; (b) Time response of the wavelet extracted at the well location;
(c) Amplitude spectrum and phase spectrum of the wavelet.
84
(a)
(b) (c)
Figure 4.3.7: (a) Seismic-well tie between synthetic trace from well 4-16 and bandwidth-
extrapolated P-S seismic data. From left to right the curves are P-wave velocity, S-wave
velocity, density, synthetic trace (blue), extracted composite trace at the well location (red),
and traces along the well path (black). The correlation coefficient is 0.832 over a window
from 1200 ms to 1705 ms; (b) Time response of the.wavelet extracted at the well location;
(c) Amplitude spectrum and phase spectrum of the wavelet.
85
(a)
(b)
Figure 4.3.8: (a) The correlation profile between synthetic traces from nine wells and the
bandwidth-extrapolated P-P data. The total correlation coefficient is 0.670314 over a
window from 800 ms to 1200 ms; (b) The correlation profile between synthetic traces from
nine wells and the bandwidth extrapolated P-S data. The total correlation coefficient is
0.705148 over a window from 1200 ms to 1800 ms. Red numbers are correation
coefficients for each well.
86
Figure 4.3.9: Synthetic P-P wedge model using the wavelet extracted from the P-P
bandwidth-extrapolated data.
Figure 4.3.10: Synthetic P-S wedge model using the wavelet extracted from the P-S
bandwidth-extrapolated data.
Figure 4.3.11.P-P and P-S tuning curve from the synthetic wedge models
87
Figure 4.3.12 Vertical display of the bandwidth-extrapolated P-S data at crossline 129
parallel to the trending of the channel. The inserted curves are S-wave velocities. GLCTOP,
GLCBASE, and DET are formation tops.
The disappointing P-S bandwidth-extrapolated data restricts the potential of extracting
high-resolution Vp/Vs for lithology identification since the top and base of the glauconitic
channel can not be separated on the P-S bandwidth-extrapolated data. Therefore, the
interpretation was primarily focused on the P-P bandwidth-extrapolated data. Figure 4.3.13
and Figure 4.3.14 are the vertical displays of the P-P bandwidth-extrapolated data at
crossline 129 and inline 85. The 15 m increase in tuning thickness revealed by the synthetic
P-P wedge model indicates that the glauconitic channel interval at the nine well locations
is all above tuning after the bandwidth extrapolation. However, as the glauconitic channel
gradually thins out from well 1-8 to 9-17, and 8-8 to 11-8, the bandwidth-extrapolated P-P
data fails to reveal this gradationally changing geologic feature as seen in inline 85 (Figure
4.3.14) perpendicular to the trending of the channel. The seismic section from the location
88
of well 8-8 to 11-8 fails to indicate the thickness variations of the channel as a laterally
consistent peak. Instead of picking the peak indicated by synthetic traces from the majority
of wells, the zero-crossing above the indicated peak was chosen to represent the base of
the glauconitic channel. Figure 4.3.15 shows the time structure of the base of the
glauconitic channel and Figure 4.3.16 is the isochron of the glauconitic channel interval.
However, the improvement in P-P time resolution brought by harmonic-bandwidth
extrapolation is still not adequate to present a distinctive and definitive channel system.
Analysis on the bandwidth-extrapolated P-P and P-S data reinforces the importance of
the assumption of harmonic-bandwidth extrapolation that the bandwidth of input data
needs to contain sufficient frequency periodicities of single layers within the usable
bandwidth. To be more specific, for P-S data the harmonic-bandwidth extrapolation can
not recover enough frequency periodicities to improve seismic resolution. However, the
frequency periodicities recovered by harmonic-bandwidth extrapolation for P-P data are
not adequate to bring the entire glauconitic channel above tuning.
89
Figure 4.3.13: Vertical display of the bandwidth-extrapolated P-P data at crossline 129
parallel to the trending of the glauconitic channel. The inserted curves are the synthetic P-
P traces. GLCTOP, GLCBASE, and DET are formation tops. GLCBASE/DET represents
the base of the glauconitic channel.
Figure 4.3.14: Vertical display of the bandwidth-extrapolated P-P data at inline 85
perpendicular to the trending of the glauconitic channel. The inserted curves are the
synthetic P-P traces. GLCTOP, GLCBASE, and DET are formation tops. GLCBASE/DET
represents the base of the glauconitic channel.
90
Figure 4.3.15: Time structure of the base of the glauconitic channel. The color bar indicates
two-way time.
Figure 4.3.16: P-P isochron from the top of the glauconitic channel to the base of the
glauconitic channel. The color bar indicates two-way time thickness.
91
4.4 Chapter Summary
In this chapter, harmonic-bandwidth extrapolation was applied to P-P and P-S data to
investigate the improvement in seismic resolution. Harmonic-bandwidth extrapolation
produces statistically good ties between synthetic traces from existing well control and the
bandwidth-extrapolated P-P and P-S data. P-S data lacking sufficient frequency
periodicities within the usable bandwidth showed no significant improvement in seismic
resolution after harmonic-bandwidth extrapolation, while a synthetic wedge model
indicates a 15 m increase in tuning thickness after harmonic-bandwidth extrapolation for
P-P data. However, the limited improvement in seismic resolution is still not adequate to
delineate a distinctive and definitive channel on the P-P bandwidth-extrapolated data. The
observation not only reinforces the importance of usable bandwidth on harmonic-
bandwidth extrapolation but also emphasizes the essence of the harmonic-bandwidth
extrapolation algorithm in that the method does not invent the frequency components
zeroed out by seismic processing.
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CHAPTER FIVE
Conclusions
Conventional P-P and P-S seismic attribute analysis, spectral decomposition, and
harmonic-bandwidth extrapolation are performed on P-P and P-S data to delineate the
glauconitic channel system. The interval Vp/Vs ratio extracted from the top of the
glauconitic channel to the Wabamun event provides the most deterministic interpretation
of the distribution and lithology variation of the glauconitic channel. The glauconitic
channel appears in the 30 Hz, 60 Hz, and 90 Hz discrete-frequency maps and vertical
sections for the STFT, CWT, and CLSSA of P-P data, while the same channel can only be
observed on 10Hz and 20Hz discrete-frequency maps and vertical sections for the STFT,
CWT, and CLSSA of P-S data. The CLSSA provides superior time-frequency resolution
over the CWT and STFT for P-P and P-S data. The frequency-derived Vp/Vs ratio fails to
delineate the channel as well as the Vp/Vs ratio from conventional seismic attributes
analysis did. The synthetic P-P and P-S wedge models indicate a 15 m improvement in the
P-P seismic resolution while the P-S seismic resolution remains constant after harmonic-
bandwidth extrapolation. However, the improvement in the P-P seismic resolution from
harmonic-bandwidth extrapolation is still not sufficient to delineate a distinctive and
definitive channel conforming to existing well control.
The interpretation of the glauconitic channel system on different types of data
demonstrates the importance of the bandwidth of seismic data on seismic interpretation.
To be more specific, the mispicking resulting in unrealistic values of the Vp/Vs ratio in
conventional seismic-attributes analysis is a consequence of the unequal bandwidth of P-P
93
and P-S data. The narrow bandwidth of P-S data prohibits the P-S peak-frequency from
representing the two-way time thickness of a single layer and leads to the failure of
frequency-derived Vp/Vs ratio. Insufficient recoverable frequency periodicities within the
usable bandwidth of P-S data result in the failure of harmonic-bandwidth extrapolation. In
summary, the dynamite-excited converted-wave data with a narrow bandwidth hindered
resolution of the glauconitic channel.
94
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