spectral decomposition and harmonic bandwidth

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




ALBERTA, CANADA

ii

Yang Mu APPROVED:

Dr. John P. Castagna, Committee Supervisor

Department of Earth and Atmospheric Sciences

Dr. Evgeni Chesnokov, Committee member


Dr. Heather Bedle, Committee member


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.




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


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


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




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




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



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 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 3.4.14: (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





indicates spectral amplitude. ............................................................................................ 57


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









OST are formation tops. The black arrows indicate the location of the glauconitic channel

interval. The color bar indicates spectral amplitude. ....................................................... 60




interval. The color bar indicates the spectral amplitude. ................................................. 61




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)


(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


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



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


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


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


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).


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


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).


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)



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)



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)


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)


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)


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)




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)




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


The color bar indicates spctral amplitude.

Figure 3.4.6: 30 Hz discrete-frequency vertical section of the arbitrary line for the CWT of



The color bar indicates spectral amplitude.

51





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




Figure 3.4.9: 60 Hz discrete-frequency vertical section of the arbitrary line for the CWT of




53





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



curves are the P-wave velocities. COAL1, GLCTOP, GLCBASE, and OST are formation

tops. The color bar indicates spectral amplitude.





55





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)





indicates spectral amplitude.

57

(a) (b) (c)





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.


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







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.



and OST are formation tops. The black arrows indicate the location of the glauconitic

channel interval. The color bar indicates spectral amplitude.

61




channel interval. The color bar indicates the spectral amplitude.




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)


(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)


(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


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


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



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



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.

92

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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spectral decomposition and harmonic bandwidth

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