The first earthquake site assessments in alberta canada

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The First Earthquake Site Assessments in Alberta, Canada
The First Earthquake Site Assessments in Alberta, Canada
Joseph J. Farrugia
The University of Western Ontario
Supervisor
Dr. Gail M. Atkinson
The University of Western Ontario Joint Supervisor
Dr. Sheri Molnar
The University of Western Ontario
Graduate Program in Geophysics
A thesis submitted in partial fulfillment of the requirements for the degree in Master of Science
© Joseph J. Farrugia 2017
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ii
Abstract
A thorough characterization of the site conditions at Alberta seismic stations is a vital
component in assessing seismic hazard in the province. This thesis provides the first
earthquake site characterizations in Alberta, including shear-wave velocity (VS) depth
profiles, estimates of the average shear-wave velocity in the upper 30 m (VS30) and peak
frequency (fpeak), and their validation for prediction of earthquake site amplification.
National Building Code of Canada site classes are limited to C and D based on VS30
estimates, with D being the predominant site class. Three empirical site amplification
functions are derived from microtremor and earthquake horizontal-to-vertical spectral
ratios (!"#$s) from 52 seismic stations in Alberta that can be correlated with surficial
geology. Softer ground conditions are characteristic of the largest observed amplification
ratios. I show that !"#$s derived from the microtremor survey method provide a valid
measure of earthquake site amplification in Alberta's geologic setting.

iii
Co-Authorship
This thesis is prepared in integrated-article format and includes the following manuscripts
written by Joseph Farrugia and the co-authors. Joseph is the first author on studies
investigating site conditions and earthquake site amplification at Alberta seismic stations.
Joseph performed the analyses described in this thesis and authored these reports with
assistance from the co-authors.
1) Farrugia, J. J., S. Molnar, and G. M. Atkinson (2017). Non-Invasive Techniques for
Site Characterization of Alberta Seismic Stations Based on Shear-Wave Velocity,
manuscript submitted to Bulletin of the Seismological Society of America.
2) Farrugia, J. J., G. M. Atkinson, and S. Molnar (2017). Validation of 1D Earthquake
Site Characterization Methods with Observed Earthquake Site Amplification in
Alberta, Canada, manuscript submitted to Bulletin of the Seismological Society of
America.
The thesis and composed articles were completed under the supervision of Dr. Gail M.
Atkinson and Dr. Sheri Molnar.

iv
Acknowledgements
I would first like to thank my supervisor and co-supervisor, Dr. Gail Atkinson and Dr.
Sheri Molnar, for providing me with the unique opportunity to work with two exceptional
research groups. Their encouragement, candidness, and guidance were essential to the
completion of this thesis, and I am especially grateful for the personal and professional
skills they have helped me to develop through their mentorship.
I have been privileged to travel to various parts of western North America over the years
for fieldwork as well as conferences to present this research. Thank you to the National
Sciences and Engineering Research Council of Canada, TransAlta and Nanometrics for
financially supporting this research.
Thank you to everyone in the Engineering Seismology and Good Vibrations and
Excitations research groups, as well as all my friends in the Earth Sciences, for your
friendships and assistance with various tasks over the years. Shout-out to the “fun-fund”,
games nights, the axis, and our near-hourly trips to Tim Horton’s.
To my parents, thank you for your unconditional love and support, as well as providing the
occasional needed reprieve from thesis related work (usually involving late night bingo).
To my sister Kathleen, my brother Paul, the rest of my family and my closest friends, thank
you for your constant encouragement. Finally, to my girlfriend Samantha, you have been
my rock (pun intended) from the beginning. Your love and support made all of this
possible.

v
Table of Contents
Abstract .............................................................................................................................. ii
Co-Authorship ................................................................................................................... iii
Acknowledgements ........................................................................................................... iv
Table of Contents ............................................................................................................... v
List of Tables .................................................................................................................... viii
List of Figures .................................................................................................................... ix
List of Abbreviations, Symbols, Nomenclature .............................................................. xxvi
Chapter 1 ............................................................................................................................ 1
1. Introduction and Literature Review ............................................................................. 1
1.1 References ................................................................................................................. 8
Chapter 2 .......................................................................................................................... 14
2. Non-invasive Techniques for Site Characterization of Alberta Seismic Stations Based on
Shear-Wave Velocity ..........................................................................................................
14
2.1 Introduction ............................................................................................................. 14
2.2 Non-Invasive Methodologies ................................................................................... 17
2.3 Field Survey and Acquired Data ............................................................................... 21
2.4 Data Preconditioning ............................................................................................... 28
2.5 Dispersion Curves .................................................................................................... 30
2.6 Inversion Method and A Priori Information ............................................................ 33

vi
2.7 Inversion Results ...................................................................................................... 43
2.8 Discussion and Conclusions ..................................................................................... 58
2.9 Data and Resources ................................................................................................. 61
2.10 Acknowledgements ................................................................................................. 62
2.11 References ............................................................................................................... 63
Chapter 3 .......................................................................................................................... 72
3. Characterization of Earthquake Site Amplification in Alberta, Canada ........................
72
3.1 Introduction ............................................................................................................. 72
3.2 Geologic Overview ................................................................................................... 74
3.3 Potential Effects on Local Soil Response ................................................................. 75
3.4 Database Overview .................................................................................................. 76
3.5 Comparison of Earthquake and Microtremor HVSRs .............................................. 79
3.6 Procedure for Determining Peak Frequency (fpeak) .................................................. 84
3.7 Deamplification at High-Frequencies (f > 10 Hz) ..................................................... 89
3.8 Characterizing Site Amplification Based on Surficial Geology ................................. 92
3.9 Correlating fpeak with Depth-to-bedrock .................................................................. 97
3.10 Generalized Amplification Functions ....................................................................... 98
3.11 Uncertainty in fpeak ................................................................................................. 100
3.12 Correlating HVSR Characteristics (fpeak, Apeak) with VS30
......................................... 104
3.13 An Alternative Site Classification Based on Peak Frequency ................................. 105
3.14 Comparing Observed to Theoretical Site Amplification ........................................ 109
3.15 Discussion and Conclusions ................................................................................... 116
3.16 Data and Resources ............................................................................................... 118

vii
3.17 Acknowledgements ............................................................................................... 118
3.18 References ............................................................................................................. 119
Chapter 4 ........................................................................................................................ 128
4. Conclusion ............................................................................................................... 128
4.1 Future Work
........................................................................................................... 129
4.2 References ............................................................................................................. 129
Appendices ..................................................................................................................... 130
Appendix A: Supplementary Figures to Chapter 2 ............................................................. 130
Appendix B: Supplementary Figures to Chapter 3 ............................................................. 176
Appendix C: Constructing Composite Shear-Wave Velocity Profiles .................................. 186
Curriculum Vitae ............................................................................................................ 188

viii
List of Tables
Table 1.1: NBCC VS30 based site classification scheme (Table 6.1.8.A; NRC, 2015). ...... 5
Table 2.1: Geographic coordinates of seismic station sites visited in this study.............. 24
Table 2.2: Investigated seismic station sites in Alberta, Canada...................................... 26
Table 2.3: A Priori inversion information for Alberta seismic station sites..................... 41
Table 2.4: Comparison between estimated depth-to-bedrock values and resonator
thicknesses inferred from inverted VS profiles.......................................................... 55
Table 2.5: Final report of minimum and maximum VSavg estimates with corresponding
VS30-based NBCC site classes................................................................................... 57
Table 3.1: Site condition information and HVSR characeteristics for Alberta seismic
stations. ..................................................................................................................... 80

ix
List of Figures
Figure 2.1: Seismograph stations visited during the July 2016 fieldwork campaign
(circles), at which geophysical data were collected. Black inverted triangles show
the locations of Alberta seismic stations in operation but not visited in this study.. 23
Figure 2.2: Geophysical survey array geometries for (a) Multi-channel analysis of
surface-waves (MASW) and (b) Ambient vibration array (AVA) acquisition; (a)
inverted triangles are shot locations and triangles are geophones; (b) black rings
show sequential array deployment for ‘X’ geometry, red circles for ‘T’ geometry,
and blue circles for ‘L’ geometry.............................................................................. 25
Figure 2.3: Individual (grey) and station average (bold black line) Fourier amplitude
mHVSRs with ±1 standard deviation (grey shaded region). * indicates sites at which
sensors experienced coupling issues with the ground surface.................................. 29
Figure 2.4: Fundamental mode dispersion curve procedure for ATHA (top row) and BR2
(bottom row). MSPAC-based phase velocity-frequency histograms (a, f) with
symbols corresponding to the ring size, r; (b-d, g-i) HRFK dispersion histograms of
utilized array apertures and corresponding dispersion picks (black rings); (e, j)
Interpreted fundamental mode dispersion estimates for ATHA and BR2................ 32
Figure 2.5: Beampower processing of MASW data for stations EDM (top row) and RW3
(bottom row). (a-b) and (d-e) dispersion picks (black rings) based on dispersion
histograms; (c) final interpreted fundamental mode dispersion estimates for EDM;

x
(f) Interpreted fundamental (grey circles) and higher mode (grey squares) dispersion
estimates for RW3. Interpreted dispersion data at low frequencies determined from
HRFK and/or MSPAC procedures (Fig. A5 and A10 in Appendix)........................ 32
Figure 2.6: Seismic station fundamental mode dispersion curves corresponding to the
interpreted NBCC Site Class. The thick black line (VR40 line) is calculated using the
equation VS30 = 1.045(VR40) after Martin and Diehl (2004). Sites without
dispersion data at the VR40 line are not assigned a site class (grey)........................ 34
Figure 2.7: Locations of wells with reported DSI wireline log information (circles) in the
top 100 m and within 50 km of a seismic station (inverted triangles). Quaternary and
Neogene sediment thickness map (Atkinson and Lyster, 2010), is largely unmapped
and highly discontinuous in the Deformation Front. ................................................ 39
Figure 2.8: Workflow for generating a simplified VS-depth profile from dipole shear-
sonic imager (DSI) log information for well: 100/12-04-064-17W5/00. Original DSI
log measurements (light grey line), calculated 100-point moving average (dark grey
line), and interpreted layer boundaries separating distinct geophysical layers (grey
circles). Black line is the resulting simplified VS-depth profile................................ 42
Figure 2.9: ATHA dispersion curve inversion results. (a) Empirical dispersion estimates
(black rings) and the corresponding minimum misfit dispersion curve models for the
1 and 2 layer parameterizations; (b) Corresponding VS-depth profiles and potential
resolution limit (dashed black line) of ~20.9 m........................................................ 45

xi
Figure 2.10: VSavg profiles calculated using equation (2. 10) from profiles in Figure 2.9b.
Depth lines 5, 10, 15, and 30 m are annotated as well as VS30-based NBCC Site Class
divisions (B, C, D, and E)......................................................................................... 47
Figure 2.11: mHVSR-inversion results for ATHA. (a) Empirical mHVSR curve (black
rings) and the corresponding optimal model solutions for 1 and 2 layer
parameterizations. The grey shaded region is ±1 standard deviation; (b)
Corresponding VS-depth profiles............................................................................... 48
Figure 2.12: VSavg profiles calculated with equation (2. 10) from profiles in Figure 2.11b.
................................................................................................................................... 49
Figure 2.13: Joint-inversion results for ATHA. (a, b) Empirical dispersion estimates and
mHVSR curve (black rings) and corresponding minimum misfit models for 1 and 2
layer parameterizations, respectively. The grey shaded region in is ±1 standard
deviation; (c) Corresponding VS-depth profiles........................................................ 51
Figure 2.14: Joint-inversion VSavg profiles calculated using equation (2. 10) from selected
profiles in Figure 2.13c............................................................................................. 52
Figure 2.15: BR2 dispersion curve inversion results. (a) Empirical dispersion estimates
(black rings) and the corresponding minimum misfit dispersion curve models for the
1 and 2 layer parameterizations; (b) Corresponding VS-depth profiles and potential
resolution limit (dashed black line) of ~73 m........................................................... 53

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Figure 2.16: VSavg profiles calculated with equation (2.10) from profiles in Figure 2.15b.
................................................................................................................................... 54
Figure 2.17: Graphical representation of VS30 ranges (a) calculated for visited seismic
station sites; (b) Associated histogram of NBCC site classes................................... 59
Figure 2.18: Comparison of proxy and in-situ based VS30 estimates. ............................... 60
Figure 3.1: Locations of 518 earthquakes (circles) recorded by seismic stations analyzed
in this study (black inverted triangles)...................................................................... 78
Figure 3.2: Magnitude-hypocentral distance distribution of earthquake records. ............ 78
Figure 3.3: Earthquake and microtremor station-average horizontal-to-vertical spectral
ratios (eHVSRs and mHVSRs, respectively) for four sample seismic stations. ........ 85
Figure 3.4: Relationship between fpeak for eHVSRs and mHVSRs with ±1 standard
deviations.................................................................................................................. 89
Figure 3.5: Horizontal (thick and thin black lines) and vertical (grey line) component
PSA spectra for stations SWHSA (top row), TD011 (middle row), and TD08A
(bottom row). The event moment magnitude (M) and hypocentral distance are given.
................................................................................................................................... 91
Figure 3.6: Comparison of empirical (grey circles) and predicted (CB14/BC16 and
BSSA14/SBSA16; dashed and solid lines, respectively) HVSR distance trends at 20
Hz for stations SWHSA, TD011 and TD08A........................................................... 93

xiii
Figure 3.7: Thickness of Quaternary and Neogene sediments in Alberta (Atkinson and
Lyster, 2010) representing depth-to-bedrock (DTB) with seismic station locations
shown as black triangles. The deformation front is a region in the eastern flanks of
the Rocky Mountains that is characterized as having thin and discontinuous
sediment thickness. ................................................................................................... 94
Figure 3.8: (a-d) eHVSRs and mHVSRs (thin grey and black lines, respectively) grouped
based on their assigned surficial geology and plotted versus the normalized
dimensionless parameter f/fpeak. Weighted average HVSRs (thick solid line) for
sand-silt-clay (C1) and till (C2) categories are also shown with their ±1 standard
deviations (SD); (e) C1 and C2 HVSRs combined and the weighted average (dotted
line) with ±1 SD....................................................................................................... 96
Figure 3.9: Relationship between depth-to-bedrock and fpeak. Dashed line is the optimal fit
through depth-to-bedrock and resonator thickness data points (grey and white
circles, respectively) with the equation fpeak = Vslayer/4d, where the optimal value for
Vslayer is 141.5 m/s..................................................................................................... 98
Figure 3.10: Generalized amplification models for (a) sand-silt-clay and till (ASoil), (b)
muskeg (AMuskeg) and (c) rock (ARock). The empirical HVSR (dotted line) is fitted
with either a Gaussian (a, b) or power function (c) shown as a solid line with ±1
standard deviations (dashed lines). Coefficients for each function are in the legend.
................................................................................................................................. 100

xiv
Figure 3.11: Suggested generic amplification functions for soil (left) and muskeg (right)
sites when the site resonance frequency is poorly known. ..................................... 103
Figure 3.12: Validation test of the generic amplification for soil sites (GSoil) by applying
equation (11) to six seismic stations without an fpeak estimate using depth-to-bedrock
values inferred from AGS Map 551 (Atkinson and Lyster, 2010). ........................ 103
Figure 3.13: Correlations between VS30 values and HVSR characteristics: (a) Apeak and (b)
fpeak. ......................................................................................................................... 105
Figure 3.14: Implementing the site classification based on the frequency of maximum
amplification (fpeak) proposed by Di Alessandro et al. (2012) for Alberta seismic
station HVSRs. Individual eHVSRs and mHVSRs are grouped based on fpeak. The
weighted average (WA) and ±1 standard deviation for each site class is also shown.
................................................................................................................................. 108
Figure 3.15: Correlations between mean maximum (squares) and mean minimum
(circles) VS30 values and site class (Di Alessandro et al., 2012)............................. 109
Figure 3.16: (a) Calculated SRI ratio amplifications of four individual model
parameterizations (see legend; LOH = layers over half-space) for station ATHA; (b)
VS profile of the top 50 m; (c) VS profile of the top 2 km. ...................................... 113
parameterizations (see legend; LOH = layers over half-space) for station TD06A; (b)

xv
parameterizations (see legend; LOH = layers over half-space) for station EDM; (b)
Figure A1: Ambient vibration array setup with five Tromino®
ultra-portable
seismographs at station RDEA. .............................................................................. 130
Figure A2: Active source surface-wave testing setup with Geode system..................... 131
Figure A3: An example of a single-station measurement being performed with a three-
component Tromino sensor at station ATHA for MHVSR analysis...................... 132
Figure A4: Processing results of ambient vibration array recordings at station TD026.
MSPAC-based phase velocity-frequency histograms (a); (b-d) HRFK dispersion
histograms of utilized array apertures..................................................................... 132
Figure A5: Fundamental mode dispersion curve procedure for station EDM. (a-b) HRFK
dispersion histograms of utilized array apertures and corresponding dispersion picks
(black rings); (c) Interpreted fundamental mode dispersion estimates (grey circles).
................................................................................................................................. 133
Figure A6: Fundamental mode dispersion curve procedure for station HON. MSPAC-
based phase velocity-frequency histograms (a) with symbols corresponding to the
ring size, r; (b-d) HRFK dispersion histograms of utilized array apertures and
corresponding dispersion picks (black rings); (e) Interpreted fundamental mode
dispersion estimates (grey circles).......................................................................... 133

xvi
Figure A7: Fundamental mode dispersion curve procedure for station PER. (a-c) HRFK
dispersion histograms of utilized array apertures and corresponding dispersion picks
(black rings); (d) Interpreted fundamental mode dispersion estimates (grey circles).
................................................................................................................................. 134
Figure A8: Fundamental mode dispersion curve procedure for station RDEA. MSPAC-
Figure A9: Fundamental mode dispersion curve procedure for station RW2. (a) HRFK
dispersion histogram of utilized array aperture and corresponding dispersion picks
(black rings); (b) Interpreted fundamental mode dispersion estimates (grey circles).
................................................................................................................................. 135
Figure A10: Fundamental mode dispersion curve procedure for station RW3. MSPAC-
corresponding dispersion picks (black rings); (e) Interpreted fundamental (grey
circles) and higher mode (grey squares) dispersion estimates................................ 135
Figure A11: Fundamental mode dispersion curve procedure for station SNUFA. (a-c)
HRFK dispersion histograms of utilized array apertures and corresponding

xvii
dispersion picks (black rings); (d) Interpreted fundamental mode dispersion
estimates (grey circles). .......................................................................................... 136
Figure A12: Fundamental mode dispersion curve procedure for station STPRA. MSPAC-
ring size, r; (b-c) HRFK dispersion histograms of utilized array apertures and
corresponding dispersion picks (black rings); (d) Interpreted fundamental mode
Figure A13: Fundamental mode dispersion curve procedure for station SWHSA.
MSPAC-based phase velocity-frequency histograms (a) with symbols corresponding
to the ring size, r; (b-c) HRFK dispersion histograms of utilized array apertures and
Figure A14: Fundamental mode dispersion curve procedure for station TD06A. MSPAC-
ring size, r; (b) HRFK dispersion histogram of utilized array aperture and
corresponding dispersion picks (black rings); (c) Interpreted fundamental mode
Figure A15: Fundamental mode dispersion curve procedure for station TD007. (a-c)
dispersion picks (black rings); (d) Interpreted fundamental mode dispersion

xviii
Figure A16: Fundamental mode dispersion curve procedure for station TD008. MSPAC-
ring size, r; (b) Interpreted fundamental mode dispersion estimates (grey circles).138
Figure A17: Fundamental mode dispersion curve procedure for station TD13A. (a-b)
dispersion picks (black rings); (c) Interpreted fundamental mode dispersion
Figure A18: Fundamental mode dispersion curve procedure for station TD028. (a-b)
dispersion picks (black rings); (c) Interpreted fundamental mode dispersion
Figure A19: Fundamental mode dispersion curve procedure for station TD029. MSPAC-
ring size, r; (b-c) HRFK dispersion histograms of utilized array apertures and
Figure A20: Fundamental mode dispersion curve procedure for station TONYA.
MSPAC-based phase velocity-frequency histograms (a) with symbols corresponding
to the ring size, r; (b-d) HRFK dispersion histograms of utilized array apertures and

xix
Figure A21: Interpreted simplified VS profiles for 23 wells with DSI logs.................... 141
Figure A22: EDM dispersion curve inversion results. (a) Empirical dispersion estimates
(black circles) and the corresponding minimum misfit dispersion curve models for
the 1 and 2 layer parameterizations; (b) Corresponding VS-depth profiles and
potential resolution limit (dashed black line).......................................................... 142
Figure A23: Calculated VSavg profiles with VS30-based NBCC Site Class divisions (B, C,
D, and E) for station EDM...................................................................................... 143
Figure A24: HON dispersion curve inversion results. (a) Empirical dispersion estimates
D, and E) for station HON...................................................................................... 145
Figure A26: RDEA dispersion curve inversion results. (a) Empirical dispersion estimates
D, and E) for station RDEA.................................................................................... 147

xx
Figure A28: RW3 dispersion curve inversion results. (a) Empirical dispersion estimates
for the fundamental (black circles) and second higher mode (black squares), and the
corresponding minimum misfit dispersion curve models for the 1 and 2 layer
parameterizations; (b) Corresponding VS-depth profiles and potential resolution limit
(dashed black line).................................................................................................. 148
D, and E) for station RW3. ..................................................................................... 149
Figure A30: SNUFA dispersion curve inversion results. (a) Empirical dispersion
estimates (black circles) and the corresponding minimum misfit dispersion curve
models for the 1 and 2 layer parameterizations; (b) Corresponding VS-depth profiles
and potential resolution limit (dashed black line)................................................... 150
D, and E) for station SNUFA.................................................................................. 151
Figure A32: STPRA dispersion curve inversion results. (a) Empirical dispersion
D, and E) for station STPRA. ................................................................................. 153

xxi
Figure A34: SWHSA dispersion curve inversion results. (a) Empirical dispersion
D, and E) for station SWHSA................................................................................. 155
Figure A36: TD028 dispersion curve inversion results. (a) Empirical dispersion estimates
D, and E) for station TD028. .................................................................................. 157
Figure A38: PER joint-inversion results. (a) Empirical dispersion estimates (black
circles) and the corresponding minimum misfit dispersion curve models for the 1
and 2 layer parameterizations; (b) Measured mHVSR curve (black circles) and the
corresponding optimal model solutions for 1 and 2 layer parameterizations. The grey
shaded region is ±1 standard deviation; (c) Corresponding VS-depth profiles. ...... 158
D, and E) for station PER. ...................................................................................... 159

xxii
Figure A40: RW2 Rayleigh-wave ellipticity-inversion results. (a) Measured mHVSR
curve (black circles) and the corresponding optimal model solutions for 1 and 2
layer parameterizations. The grey shaded region is ±1 standard deviation; (b)
Corresponding VS-depth.......................................................................................... 160
Figure A41: Calculated VSavg profiles from Rayleigh-wave ellipticity-inversion results in
Figure A40b with VS30-based NBCC Site Class divisions (B, C, D, and E) for station
RW2. The 1 power law over half-space and 2 uniform layers over half-space models
displayed in this figure are not consistent with VS profiles determined through
dispersion-inversion, thus were omitted when calculating VSavg for RW2. ............ 161
Figure A42: RW2 dispersion curve inversion results. (a) Empirical dispersion estimates
Figure A43: Calculated VSavg profiles from dispersion curve inversion results in Figure
A42b with VS30-based NBCC Site Class divisions (B, C, D, and E) for station RW2.
................................................................................................................................. 163
Figure A44: TD007 joint-inversion results. (a) Empirical dispersion estimates (black

xxiii
Figure A50: TD06A joint-inversion results. (a) Empirical dispersion estimates (black

xxiv
D, and E) for station TD06A................................................................................... 171
Figure A52: TD13A joint-inversion results. (a) Empirical dispersion estimates (black
D, and E) for station TD13A................................................................................... 173
Figure A54: TONYA joint-inversion results. (a) Empirical dispersion estimates (black
D, and E) for station TONYA................................................................................. 175
Figure A56: Workflow for generating a composite VS profile to 50 km depth using five
inverted VS profiles with different model parameterizations with 1 and 2 layers over
half-space (LOH). (a) Inverted VS profile assignments from surface to the potential
resolution limit (first dashed line); (b) DSI log VS profile assignments (between
second and third dashed lines); (c) CRANE station 1D velocity models inverted

xxv
from receiver functions assigned from the bottom-depth of the DSI log (third dashed
line) to a depth of 50 km. The grey area is the depth interval for which ten equally
spaced uniform velocity layers were interpreted between the potential resolution
limit (top black dashed line) and the top-depth of the DSI log (bottom dashed black
line) using a linear gradient..................................................................................... 187

xxvi
List of Abbreviations, Symbols, Nomenclature
Apeak Peak amplitude from empirical !"#$
AVA Ambient vibration array
CHBDC Canadian Highway Bridge Design Code
DSI Dipole shear-sonic imager
;!"#$ Earthquake horizontal-to-vertical spectral ratio
;!"#$ Station average earthquake horizontal-to-vertical spectral ratio
f0 Site fundamental resonance frequency
f-k Frequency wavenumber
fpeak Frequency of maximum amplification from !"#$
HRFK High-resolution frequency wavenumber
!"#$ Horizontal-to-vertical spectral ratio
M Moment magnitude
<!"#$ Microtremor horizontal-to-vertical spectral ratio
<!"#$ Station average microtremor horizontal-to-vertical spectral ratio
!"#$ Station average horizontal-to-vertical spectral ratio

xxvii
MASW Multi-channel analysis of surface waves
MSPAC Modified spatial auto-correlation
NBCC National Building Code of Canada
NEHRP National Earthquake Hazard Reduction Program
RL Resolution Limit
VR40 Phase velocity of a Rayleigh-wave with a wavelength of 40 meters
VS Shear-wave velocity
VSavg Average shear-wave velocity
VS30 Time-weighted average shear-wave velocity in the upper 30 meters
1D One-dimensional

1
Chapter 1
1. Introduction and Literature Review
The province of Alberta has historically been seismically quiescent with the majority of
earthquakes occurring in foreland belt of the Rocky Mountains (Schultz et al., 2014). The
marked increase in seismic activity in Alberta over the past decade (Eaton, 2014) and its
connection with oil and gas operations, including hydraulic fracturing, fluid injection and
extraction (e.g., Baranova et al., 1999; Schultz et al., 2016; Atkinson et al., 2016) has
motivated and increase in the number of seismic monitoring stations and networks in the
province (e.g., Schultz and Stern, 2015), in addition to investigations into induced seismic
hazard (e.g., Atkinson et al., 2015). An important consideration for assessing seismic
hazard is the impact that local site conditions of the near-surface have on modifying the
amplitude and frequency content of seismic waves as they travel from the earthquake
source to the surface, which vary significantly from one location to another. These are
known as site effects. This thesis is a compilation of two studies that were performed to
understand the effects local site conditions have on amplifying earthquake ground motions.
To our knowledge, this work comprises the first public-domain earthquake site assessments
in Alberta, Canada.
When slippage occurs along a fault interface (earthquake rupture) seismic waves are
generated and propagate away from the source in all directions. In the context of earthquake
site amplification, attention is often given to vertical propagating shear-waves, which tend

2
to be most affected by changes in material properties in the near-surface (Lermo and
Chávez-García, 1993; Tinsley et al., 2004). Shear-waves are of principal concern to
engineers because this type of wave imparts a lateral load to structures threatening their
structural integrity (Crow and Hunter, 2012). Moreover, these tend to be the components
with the largest amplitudes. As vertically-incident shear-waves propagate through near-
surface soil layers of decreasing impedance, the amplitudes of horizontal-component
ground motions may be amplified according to conservation of energy theory (i.e.
broadband amplification), and/or by resonance in near-surface layers. Broadband
amplification, based on energy-conservation is often referred to as the square-root-
impedance (SRI) amplification. Simplified expressions for resonance (Haskell, 1960;
Kramer, 1996) and SRI (Joyner et al., 1981) amplification are given respectively as:
Resonance Amplification =
=>?>
=@?@
(1.1)
and,
SRI Amplification =
=>?>
=@?@
, (1.2)
where AB and AC are the densities and V1 and V2 are the shear-wave velocities of the first
and second layers, respectively, and the product of A and V is impedance. In general, a
lower velocity soil layer overlying an elastic half-space results in amplification
proportional to the seismic impedance contrast between the two layers.

3
The preferred measure of site response is a standard spectral ratio (SSR). The SSR method
provides the ratio between the spectrum of a particular soil site to the spectrum of a
reference rock site (e.g., Borcherdt, 1970; Borcherdt and Gibbs, 1976). A reference rock
site is representative of the incident free-field motions (Lermo and Chávez-García, 1993),
but for a number of reasons, it may be difficult to find an adequate reference rock site. A
more convenient proxy measure for earthquake site amplification was introduced by
Nogoshi and Igarashi (1971) and popularized by Nakamura (1989), which used three-
component microtremor recordings from a single seismic station to compute the ratio of
horizontal to vertical component ground motions. Microtremors are ambient vibrations (i.e.
background seismic noise) that originate from daily human activities and natural
phenomena and encompass a wide range of frequencies, approximately 0.02 to 50 Hz
(Horike, 1985). The low frequency portion of the ambient noise spectrum (<~1 Hz) is
governed by natural phenomena, whereas high frequencies (>~1 Hz) are caused from
human activities (Okada, 2003). The principal assumption of the single station method is
that amplification of vertical-component motions is relatively small compared to that of
the horizontal components, and thus the horizontal-to-vertical spectral ratio (!"#$) is
considered a first-order proxy-measure of amplification at a site. Lermo and Chávez-García
(1993) showed that the single station method could also be applied to earthquake data
recorded at a site. Both earthquake and microtremor !"#$s have been shown to agree with
earthquake SSRs in terms of peak frequency but typically underestimate SSR amplification
(e.g., Field and Jacob 1995; Bonilla et al., 1997; Bard et al., 1999; Molnar et al., 2016).
Other seismic parameters may contribute to the local amplification of an area including

4
topographic effects (e.g., Geli et al., 1988; Chàvez-García et al., 1996; Paolucci, 2002;
Hough et al., 2010), “buried valley focusing” amplification effects (e.g., Bard and
Bouchon, 1985) and “basin edge” amplification effects (e.g., Lomnitz, 1999; Narayan,
2005).
For the simple case of a soft soil layer over an elastic half-space, the !"#$ will typically
display a single high amplitude peak at the fundamental site resonance frequency (f0).
Haskell (1960) showed that f0 is related to the thickness (ℎ) and average shear-wave
velocity (VSavg) of the soil layer through the simple expression: f0 = VSavg/4h. Consequently,
thicker soil deposits are expected to have lower peak resonance frequencies compared to
sites characterized by thin soil profiles. Provided that there is a significant impedance
contrast at depth, the !"#$ method is expected to yield an adequate estimate of FG (e.g.,
Lermo and Chávez-García, 1993; Bonilla et al., 1997).
Shear-wave velocity is a main determinant in the resulting peak resonance frequency and
amount of amplification for a site. The time-averaged shear-wave velocity in the upper 30
meters, denoted VS30, is a simplified parameter to account for site response and prevalently
used worldwide. Canadian guidelines for earthquake site classification, such as in the
National Building Code of Canada (NBCC; NRC, 2015), use VS30 as an indicator variable
for site amplification in a six-tiered site classification (Classes A-F; shown in Table 1.1).
This scheme follows the NEHRP classification scheme used in the U.S. (Borcherdt, 1970)
and is also similar to that used in Europe (Eurocode 8, 2004). VS30 is a simplified metric
that correlates well with observed earthquake ground motions and is hence widely used as

5
an explanatory variable to describe site effects in ground motion prediction equations (e.g.,
Abrahamson et al., 2014; Boore et al., 2014; Campbell and Bozorgnia, 2014). There is
currently research focused on incorporating explicit site descriptor variables, such as f0, in
the equations that calculate site amplification (e.g., Braganza and Atkinson, 2016; Hassani
and Atkinson, 2016), as well as site classification systems that exclusively use the
predominant period estimated from spectral ratios (e.g., Zhao et al., 2006; Fukushima et
al., 2007; Di Alessandro et al., 2012).
Table 1.1: NBCC VS30 based site classification scheme (Table 6.1.8.A; NRC, 2015).
NBCC
Site Class
VS30
[m/s]
Description
A > 1500 Hard rock
B 760 < VS30 ≤ 1500 Rock
C 360 < VS30 ≤ 760 Soft rock or firm soil
D 180 < VS30 ≤ 360 Soft soil
E VS30 < 180 Very soft soil
F N/A
Special study soils (e.g.,
liquefiable, peat, organic
soils, etc.)
In the first study (Chapter 2), three-component ambient vibration recordings were collected
during site visits of 28 seismographic stations. Microtremor !"#$s (<!"#$s) are
calculated from these recordings at all stations. For 18 sites, we were able to estimate the
shear-wave velocity structure and subsequently VS30 estimates from the application of non-
invasive velocity profiling methods (both active and passive source) during each site visit.
Active and passive source surface wave array methods differ such that the former utilizes

6
a mechanical or impulsive source (e.g., sledge hammers, drop weights, bulldozers, etc.) to
generate surface waves, whereas the latter measures the ambient field. In general, these
seismic array methods exploit the fact that surface waves are dispersive in media with a
horizontally stratified velocity structure, meaning that different frequencies (wavelengths)
travel with different velocities; shorter wavelength surface waves are confined to the upper
(slower) layers, whereas longer wavelengths travel in faster velocity layers at greater
depths. Hence, a surface wave dispersion curve is a measure of the varying subsurface
velocities with depth for a site, which can be inverted for VS depth profiles.
There is much debate over what types of waves comprise microtremors (e.g., body, surface
and/or diffracted waves) (e.g., Capon, 1969; Lacoss et al., 1969), but considering most
sources of microtremors are located on the bottom of the sea or at the earth’s surface
(Claprod, 2012) it is generally assumed that the microtremor signal is dominated by
Rayleigh waves (Horike, 1985). In simple terms, the Rayleigh-wave velocity (VR) is related
to the wavelength (H) and frequency (f) of the travelling wave by:
"I = HF (1.3)
Generally, the longer the wavelength, the deeper the depth of investigation (i.e. wavelength
is proportional to depth). Convention is that the depth of investigation is roughly half the
maximum wavelength that is recorded in the field (Okada, 2003), and thus, is typically not
known a priori. By estimating the Rayleigh-wave phase velocity for different frequencies
in the observable bandwidth, dispersion curves can be constructed and subsequently
inverted for the shear-wave velocity structure of the site. Non-invasive active and passive

7
source surface wave array methods have been successfully implemented for the purposes
of site characterization (e.g., Hollender et al., 2016). A description of the theories of
analysis for the utilized non-invasive seismic profiling methods implemented in the first
study is given in Chapter 2.2.
In the second study (Chapter 3), we used HVSRs calculated from earthquake recordings
(eHVSRs) and mHVSRs from the first study with other freely available regional datasets,
such as surficial geology and depth-to-bedrock, to characterize earthquake site
amplification at 52 seismic stations in Alberta, Canada. We established three models of
empirical amplification functions at 52 seismic stations for predicting site amplification
based on site surficial geology using a similar methodology as Braganza et al. (2017). Site
amplification functions that are calibrated to empirical data are important for accurately
depicting the expected level of amplification at a site in future local or regional
applications. Generalized amplification functions are generated here for future use in
Alberta. For example, ShakeMaps display the spatial distribution of shaking intensity for a
region in terms of estimated peak ground motions (e.g., peak ground acceleration [PGA]).
ShakeMaps can be generated in near-real time following an earthquake event or as forecasts
of future scenario events.
This thesis provides a comprehensive characterization of site conditions at seismic stations
in Alberta, Canada and an understanding of their role in amplifying ground motions during
earthquake ground shaking. This research has important implications for the analysis of
seismic hazard to vulnerable infrastructure, such as buried and above ground oil and gas

8
pipelines, buried water distribution systems, solid and liquid waste disposal facilities, and
telecommunication systems that are susceptible to critical damage during earthquake
shaking.
1.1 References
Abrahamson, N. A., W. J. Silva, and R. Kamai (2014). Summary of the ASK14 Ground
Motion Relation for Active Crustal Regions, Earthq. Spectra 30 1025-1055.
Atkinson, G. M., H. Ghofrani, and K. Assatourians (2015). Impact of Induced Seismicity
on the Evaluation of Seismic Hazard: Some Preliminary Considerations, Seismol.
Res. Lett. 86, 1009-1021, doi: 10.1785/0220140204.
Atkinson, G. M., D. W. Eaton, H. Ghofrani, D. Walker, B. Cheadle, R. Schultz, R.
Shcherbakov, K. Tiampo, J. Gu, R. M Harrington, Y. Liu, M. van der Baan, and
H. Kao (2016). Hydraulic Fracturing and Seismicity in the Western Canada
Sedimentary Basin, Seismol. Res. Lett. 87, 631-647, doi: 10.1785/0220150263.
Baranova, V., A. Mustaqeem, and S. Bell (1999). A model for induced seismicity caused
by hydrocarbon production in the Western Canada Sedimentary Basin, Canadian
Journal of Earth Sciences, 36, 47-64.
Bard, P. Y. and M. Bouchon (1985). The two-dimensional resonance of sediment-filled
valleys, Bull. Seismol. Soc. Am., 75, 519-541.
Bonilla, L. F., J. H. Steidl, G. T. Lindley, A. G. Tumarkin, and R. J. Archuleta (1997).
Site Amplification in the San Fernando Valley, California: Variability of Site-
Effect Estimation Using the S-Wave, Coda, and H/V Methods, Bull. Seis. Soc.
Am. 87, 710-730.

9
Borcherdt, R. D. (1970). Effects of local geology on ground motion near San Francisco
Bay, Bull Seism. Soc. Am. 60, 29-61.
Borcherdt, R. D. and J. F. Gibbs (1976). Effects of local geological conditions in the
region on ground motions and intensities of the 1906 earthquakes, Bull Seism.
Soc. Am. 66, 467-500.
Boore, D. M., J. P. Stewart, E. Seyhan, and G. M. Atkinson (2014). NGA-West2
equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal
earthquakes, Earthq. Spectra 30 1057-1085.
Braganza, S., G. M. Atkinson, H. Ghofrani, B. Hassani, L. Chouinard, P. Rosset, D.
Motazedian, and J. Hunter (2016). Modeling Site Amplification in Eastern
Canada on a Regional Scale, Seis. Res. Lett. 87, 1008-1021.
Braganza, S., G. M. Atkinson (2017). A Model for Estimating Amplification Effects on
Seismic Hazards and Scenario Ground Motions in Southern Ontario, Canadian
Journal of Civil Engineering, manuscript under review.
Campbell, K. W., and Y. Bozorgnia (2014). NGA-West2 ground motion model for the
average horizontal components of PGA, PGV, and 5%-damped linear acceleration
response spectra Earthq. Spectra 30 1087-1115.
Capon, J., 1969. High-resolution frequency-wavenumber spectral analysis, Proc. IEEE.,
57, p. 1408-1419.
Chàvez-García, F. J., L. R. Sánchez and D. Hatzfeld (1996). Topographic site effects and
HVSR. A comparison between observations and theory. Bull. Seismol. Soc. Am.,
86, 1559-1573.

10
Claprood, M. (2012). Spatially Averaged Coherency Spectrum (SPAC) Ambient Noise
Array Method; in Shear Wave Velocity Measurement Guidelines for Canadian
Seismic Site Characterization in Soil and Rock, (ed.) J.A. Hunter and H.L. Crow;
Geological Survey of Canada, Open File 7078, p. 94–102.
Crow, H. L. and J. A. Hunter (2012). Chapter 5.0: Shear Wave Guidelines for Non-
technical Users; in Shear Wave Velocity Measurement Guidelines for Canadian
Seismic Site Characterization in Soil and Rock, (ed.) J. A. Hunter and H. L.
Crow; Geological Survey of Canada, Open File 7078, 211-223.
Di Alessandro, C., L. F. Bonilla, D. M. Boore, A. Rovelli, and O. Scotti (2012).
Predominant-Period Site Classification for Response Spectra Prediction Equations
in Italy, Bull. Seismol. Soc. Am. 102, 680-695.
Eaton, D. (2014). Alberta Telemetered Seismograph Network (ATSN): Real-time
Monitoring of Seismicity in Northern Alberta, CSEG Recorder, 39, 30-33.
Eurocode 8, (2004). Design of structures for earthquake resistance—Part 1: General
rules, seismic actions and rules for buildings, EN 1998-1, European Committee
for Standardization (CEN), Brussels, p. 229.
Field, E. H., K. H. Jacob (1995). A comparison and test of various site-response
estimation techniques, including three that are not reference site dependent, Bull.
Seismol. Soc. Am. 85, 1127-43.
Fukushima, Y, L. F. Bonilla, O. Scotti, and J. Douglas (2007). Site classification using
horizontal-to-vertical response spectral ratios and its impact when deriving
empirical ground-motion prediction equations, J. Earthquake Eng. 11, 712–724.

11
Geli, L., P. Bard and B. Jullien (1988). The effect of topography on earthquake ground
motion: a preview and new results. Bull. Seismol. Soc. Am. 78, 42-63.
Haskell, N. A., 1960. Crustal Reflections of Plane SH Waves, J. Geophys. Res. 65, 4147-
4150.
Hassani, B. and G. M. Atkinson (2016). Applicability of the Site Fundamental Frequency
as a VS30 Proxy for Central and Eastern North America, Bull. Seismol. Soc. Am.
106, 653-664.
Hollender, F., C. Cornou, A. Dechamp, F. Renalier, S. Thomassin, and P.-Y. Bard
(2016). Characterization of French accelerometric permanent network stations
with surface-wave based methods: importance of joint use of active and passive
methods, Love and Rayleigh waves; in Proceedings, 16th World Conference on
Earthquake Engineering, Santiago, Chile, January 2017.
Horike, M. (1985). Inversion of phase velocity of long-period microtremors to the s-
wave-velocity structure down to the basement in urbanized areas, J. Phys. Earth
33 59-96.
Hough, S. E., J. R. Altidor, D. Anglade, D. Given, M. G. Janvier, J. Z. Maharrey, M.
Meremonte, B. S. Mildor and C. Prepetit (2010). Localized damage caused by
topographic amplification during the 2010 M 7.0 Haiti earthquake, Nature
Geoscience, 3, 778-782.
Joyner, W. B., R. E. Warrick, and T. E. Fumal (1981). The effect of Quaternary alluvium
on strong ground motion in the Coyote Lake, California, earthquake of 1979,
Bull. Seismol. Soc. Am. 71, 1333–1349.

12
Kramer, S. L. (1996). Geotechnical Earthquake Engineering, Prentice Hall, 653 p.
Lacoss, R. T., E. J. Kelly, and M. N. Toksöz (1969). Estimation of seismic noise structure
using arrays, Geophysics 29 21-38.
Lermo, J. and F. J. Chávez-García (1993). Site effect evaluation using spectral ratios with
only one station, Bull. Seismol. Soc. Am. 83, 1574-1594.
Lomnitz, C., (1999). The End of Earthquake Hazard, Seis. Res. Lett. 70, 387-388.
Molnar, E., J. F. Cassidy, S. Castellaro, C. Cornou, H. Crow, J. A. Hunter, S.
Matsushima, F. J. Sànchez-Sesma, A. Yong (2016). Application of MHVSR for
site-characterization: state-of-the-art, Proceedings of the 16th World Conference
on Earthquake Engineering, Santiago, Chile, January 2017.
Nakamura, Y. (1989). A method for dynamic characteristics estimation of subsurface
using microtremor on the ground surface. QR RTRI, 30, 25-33.
Narayan, J.P., (2005). Study of Basin-edge Effects on the Ground Motion Characteristics
Using 2.5-D Modelling, Pure appl. geophys. 162, 273-289.
Nogoshi, M. and T. Igarashi (1971). On the amplitude characteristics of microtremor
(Part 2); Journal of the Seismological Society of Japan, 24, 26-40 (in Japanese,
with English abstract).
National Research Council (NRC; 2015). National Building Code of Canada 2015,
Volume 1, Division B, Part 4.
National Research Council (NRC; 2015). National Building Code of Canada 2015,
Volume 1, Division B, Part 4.

13
Okada, H., 2003. The Microtremor Survey Method. Department of Earth and Planetary
Sciences, Hokkaido University, Sapporo, Hokkaido, Japan. 150 p.
Paolucci, R., 2002. Amplification of earthquake ground motion by steep topographic
irregularities. Earthquake Engng, Struct. Dyn. 32, 1831-1853.
Schultz, R., V. Stern, and Y. J. Gu (2014), An investigation of seismicity clustered near
the Cordel Field, west central Alberta, and its relation to a nearby disposal well, J.
Geophys. Res. Solid Earth, 119, 3410-3423, doi:10.1002/ 2013JB010836.
Schultz, R., and V. Stern (2015). The Regional Alberta Observatory for Earthquake
Studies Network (RAVEN), CSEG Recorder, 40, 34-37.
Schultz, R., H. Corlett, K. Haug, K. Kocon, K. MacCormack, V. Stern, and T. Shipman
(2016). Linking fossil reefs with earthquakes: Geologic insight to where induced
seismicity occurs in Alberta, Geophys. Res. Lett. 43, 2534-2542,
doi:10.1002/2015GL067514.
Tinsley, J., S. E. Hough, A. Yong, H. Kanamori, E. Yu, V. Appel, and C. Wills (2004).
Geotechnical Characterization of TriNet Sites: A Status Report. Seis. Res. Lett.
75, 505-514.
Zhao, J. X., K. Irikura, J. Zhang, Y. Fukushima, P. G. Somerville, A. Asano, Y. Ohno, T.
Oouchi, T. Takahashi, and H. Ogawa (2006). An empirical site-classification
method for strong-motion stations in Japan using H/V response spectral ratio,
Bull. Seismol. Soc. Am. 96, 914–925.

14
Chapter 2
2. Non-invasive Techniques for Site Characterization of Alberta Seismic
Stations Based on Shear-Wave Velocity
2.1 Introduction
Collecting in-situ geophysical measurements at seismographic sites is critical to
interpretation and modeling of recorded earthquake motions and hazards. In most cases,
however, seismic stations are deployed without detailed geotechnical characterization of
subsurface ground conditions, and the shear-wave velocity (VS) depth profile and time-
averaged shear-wave velocity in the upper 30 meters (VS30) are typically unknown.
Canadian guidelines for earthquake site classification, such as in the National Building
Code of Canada (NBCC; NRC, 2015), were adopted from the provisionary standards set
by National Earthquake Hazard Reduction Program (NEHRP; e.g., Building Seismic
Safety Council, 2009) in 2005 (Finn and Wightman, 2003). The adopted NEHRP six-tiered
site classification (Classes A-F) uses VS30 as an indicator variable for site amplification.
These site classes were similarly adopted in the 2015 Canadian Highway Bridge Design
Code (CHBDC). VS30 is a simplified metric that has been shown to correlate well with
observed earthquake ground motions and hence widely used as an explanatory variable to
describe site effects in ground motion prediction equations (e.g., Abrahamson et al., 2014;
Boore et al., 2014; Campbell and Bozorgnia, 2014). In the absence of velocity information,
the soil undrained shear strength, #J, average standard penetration resistance, N60, or

15
measurements from cone penetration tests can be used to estimate VS30 (Finn and
Wightman, 2003; Wair et al., 2012).
It is well known that seismic waves propagating through soft soil profiles are amplified
relative to those observed at hard rock sites (e.g., Shearer and Orcutt, 1987; Borcherdt,
1970) and that the character of ground motions observed at the surface (amplitude,
frequency and duration) are demonstrably linked to the VS structure of the site (Kramer,
1996). Broad-band amplification occurs from a seismic impedance gradient between near-
surface materials and underlying hard bedrock conditions, which shortens wavelengths and
increases their amplitudes over a wide range of frequencies (Shearer and Orcutt, 1987).
Resonance amplification is initiated by a marked subsurface impedance contrast, allowing
shear-waves at specific frequencies to resonate between the free surface and the soft soil-
bedrock interface (Hunter and Atukorala, 2012). The frequency at which shear-waves
resonate at a site is dependent on the average shear-wave velocity (VSavg) and thickness (Z)
of the soil deposit and is expressed through the following equation (Haskell, 1960; Kramer,
1996):
FK = 2L + 1
?NOPQ
RS
, for L = 0, 1, 2, 3 … (2.1)
where fn is the resonance frequency at mode n, and n = 0 for the fundamental mode (FG).
In recognition of the importance of the shear wave velocity structure in controlling site
amplification, a number of remote-sensing-based methods have been proposed to evaluate
site velocity (i.e. VS30) on a regional scale. Proxy-based methods, which do not require site-

16
specific studies, include the utilization of topographic slope (Allen and Wald, 2009),
discretized terrain classes (Yong et al., 2012) and lithologic unit and age (Wills et al., 2000;
Wills and Clahan, 2006) to estimate VS30. Application of proxy-based methods is extremely
efficient and beneficial in areas suffering from a dearth of in-situ site condition
information. However, because these methods are predictions of a predictor (VS30), concern
has been raised regarding the uncertainty that is compounded during the application of each
proxy (Yong et al., 2016). In general, VS30 estimates derived from proxies have large
uncertainties, which map into even greater uncertainty in the estimation of site response.
The high-resolution topographic slope method (Allen and Wald, 2009), for example,
assumes that steep topographic gradients are associated with cohesive rock and very low
gradients with unconsolidated basin infill. This technique is less effective in areas
characterized by low topographic gradients with exposed bedrock at the surface (Allen and
Wald, 2009).
At the local site scale, a number of methods involving the application of invasive and non-
invasive geophysical surveys have been developed to determine in-situ one-dimensional
(1D) shear-wave velocity-depth profiles (e,g., Hunter and Crow, 2012 and references
therein). Invasive P-S logging was accomplished at all KiK-net stations in Japan (Aoi et
al., 2004), whereas surface seismic and standard penetration tests were used to investigate
seismic station site conditions in Turkey (Sandıkkaya et al., 2010). A wide range of in-situ
measurements, combined with information on surficial geology, are used to determine VS30
in the United States (Yong et al., 2013) and Taïwan (Lee et al., 2001). Seismic network
sites have most often been classified using non-invasive seismic surveys: some examples

17
are sites in Iran (Zaré, 1999; Zare and Sinaiean, 2014), France (Hollender et al., 2016) and
Puerto Rico (Odum et al., 2007).
Two well-established non-invasive surface-wave dispersion techniques were implemented
in this study to garner site condition information for seismic station sites in Alberta,
Canada. Both active-source multichannel analysis of surface waves (MASW) and passive-
source ambient vibration array (AVA) seismic methods were applied. We also computed
microtremor horizontal-to-vertical Fourier amplitude spectral ratios (mHVSRs) using
single-station three-component ambient noise recordings. For each site, dispersion and
mHVSR data sets were independently and jointly inverted to produce site-specific VS depth
profiles assuming 1D theory.
The motivation for conducting this study was two-fold: (1) test the applicability of non-
invasive geophysical techniques for obtaining VS profiles and NBCC site classifications for
seismic stations in Alberta; and (2) enable validation of earthquake site amplification
models for sites in Alberta (Farrugia et al., under review). The former is the focus of this
paper, including description of the methodologies we used to calculate VS depth profiles.
The study is important because there are currently more than 100 seismographic stations
deployed on various soils across Alberta, but very little information on their site conditions.
2.2 Non-Invasive Methodologies
At large distances from the sources, it is generally assumed that the microtremor signal is
dominated by surface waves, especially at source-to-site distances greater than one
wavelength (Arai and Tokimatsu, 2004); surface waves have a lower geometric attenuation

18
rate compared to that of body waves (Socco and Strobbia, 2004). By only processing
vertical component recordings in this study, we assume that the dominant wave type is the
Rayleigh surface-wave (Horike, 1985), such that principal particle motion is in the vertical
direction, however, consideration of horizontal polarities (Love waves; involve transverse
motion) may help to reduce the risk of the misattribution of modes and improve the
resulting velocity model set (Hollender et al., 2016). Rayleigh waves are generated by the
interaction of longitudinal and transverse body waves in the presence of a free boundary,
such as soil-air surface, and are the most commonly exploited surface-waves.
In vertically heterogeneous layered media Rayleigh wave propagation is governed by
dispersion, meaning different frequencies (wavelengths) travel with different velocities
within different depth ranges. Shorter wavelength Rayleigh waves travel slower than those
with longer wavelengths because they are confined to the lower velocity layers nearest the
surface compared to higher velocity layers at depth; the distribution of phase velocity as a
function of frequency is the dispersion curve. Because the velocity of Rayleigh waves
depends on the elastic properties of the subsurface (mainly VS), it is possible to invert for
the layered earth structure of a site based on surface-wave dispersion curves calculated
from field measurements. In the case of vertically heterogeneous layered media where
velocity increases with depth, the propagation velocity of surface-waves decreases with
increasing frequency and is referred to as normally dispersive.
MASW and AVA are efficient and convenient non-invasive VS depth profiling techniques
that seek to obtain surface-wave dispersion curve data from recordings collected by an

19
array of sensors on the ground surface. They differ in that MASW is an active-source (e.g.,
hammer impact) method and AVA makes use of the recorded ambient noise (i.e.,
microtremor) field. Non-invasive techniques and processing procedures utilized in this
study are explained thoroughly in Hunter and Crow (2012) and references therein, and are
only briefly discussed here.
One processing technique we applied to obtain surface-wave dispersion data sets from
AVA recordings is the modified spatial auto-correlation (MSPAC; Bettig et al., 2001). Aki
(1957) developed the spatial auto-correlation (SPAC) method and demonstrated that for
symmetrical circular arrays, background seismic noise could be related to the nature and
characteristics of the propagation medium through the evaluation of spatial auto-
correlation functions, assuming that ambient noise is a spatiotemporal stochastic process
that is stationary in both domains. Bettig et al. (2001) developed the MSPAC method to
include the use of irregularly shaped arrays, making acquisition in urban settings more
tenable. In contrast to SPAC, MSPAC does not require azimuthally averaged auto-
correlation ratios (AV@,V>
) to be computed at a constant radius, instead they are computed
between rings with radius values WB and WC in the plane (W, X),
AV@,V>
Y =
C
Z V>
>[V@
> cos
_V
` _
cos a − X
V>
V@
Z
G
. (2.2)
The spatial auto-correlation ratio is computed as the ratio of the auto-correlation function
of the signal recorded at one station to the auto-correlation function of the signal recorded
at a station nearby separated by a measured distance. Here, X is the azimuthal direction
between stations, a is the azimuth of wave propagation, Y is the angular frequency and is

20
equal to 2cF, and dI Y is the frequency dependent Rayleigh wave velocity. From
properties of the definition of the Bessel functions of zeroth and first order, eB, equation
(2.2) can be simplified to:
AV@,V>
Y =
C`f _
_ V>
>[V@
> W eB
_V
`f _ V@
V>
. (2.3)
For a given array, sub-arrays (g) are defined by station pairs (h, i) that satisfy WjB < Wlm <
WjC and spatially averaged auto-correlation ratios are computed as,
Aj Y =
B
Z
A Wlm, Xlm, Y
Wg1< Whi< Wg2
ΔXlm, (2.4)
where A Wlm, Xlm, Y are auto-correlation ratios calculated between station pairs, ΔXlm =
0.5 XlmoB − Xlm[B , and values for WjB and WjC are obtained by minimizing the ratio
∆Wj/Wj. The surface-wave dispersion curve is computed through nonlinear inversion of
SPAC ratios to determine dI Y for a range of frequencies (Bettig et al., 2001).
Measurements are repeated using concentric arrays of increasing radius to widen the
frequency range for which dispersion curves are valid.
Synchronized recordings collected via AVA acquisition were also analyzed using the high-
resolution frequency wavenumber (HRFK; Capon, 1969) method. Unlike MSPAC, HRFK
works best if the microtremor signal has a limited azimuthal distribution (Molnar, 2012).
In this case, the beampower of signals recorded from an array of sensors is computed for
very short time windows between specified velocity and wavenumber ranges. The
wavenumber coordinates (kx and ky) corresponding to the peak in the wavenumber plane

21
are then iteratively refined to an arbitrarily small precision (Wathelet, 2008) and
subsequently used to estimate phase-velocity (c):
d =
CZq
jr
>
ojs
>
. (2.5)
The peak of the f-k spectrum occurs at a wavenumber corresponding to the vector velocity
of a propagating wave (Capon, 1969). In this way, a histogram for each frequency band is
created at the observed maxima using all the time-windowed phase velocities. HRFK is an
improvement over the earlier f-k method (Asten and Henstridge, 1984; Horike, 1985),
which introduced weighting factors to each receiver contributing to the array output
calculation, such that the energy carried by the least coherent signals is minimized for those
particular wavenumbers (Wathelet, 2008).
MASW was popularized in the late 1990’s by Park et al. (1998, 1999) and is a modified
version of the spectral analysis of surface-waves (SASW; Stokoe and Nazarian, 1985)
technique. The two differ because MASW takes advantage of the advances made in seismic
acquisition technology that now offer multichannel recording functionality, but otherwise
are similar in principle. For this technique, surface-waves are generated by a vertically
oriented impulsive source (e.g., impact, random, steady-state vibration mechanism) at a
measured distance from the first receiver (near-offset distance) of a linear array of receivers
oriented parallel to the source. Dispersion histograms were extracted from MASW signals
by applying the f-k method.
2.3 Field Survey and Acquired Data

22
Over a two-week period in July of 2016, we collected geophysical data at 28 seismic station
sites (Fig. 2.1; see Table 2.1 for the geographic coordinates of seismic stations). These sites
were prioritized with the objective being to visit the maximum number of operational
seismic stations with the greatest variety of distinct site response types (determined from
earthquake horizontal-to-vertical component ratios, H/V; Farrugia and Atkinson, 2015). In
addition, we looked for sites with straightforward grounds access, sufficient space, and flat,
unobstructed ground surface conditions. Our survey area can be roughly demarcated by
four geographic locations: the city of Calgary (south), the town of Ranfurly (east), the town
of Grande Cache (west), and the town of Red Earth Creek (north). We visited seismic
stations in the monitoring networks: Regional Alberta Observatory for Earthquake Studies
(RAVEN), Canadian National Seismograph Network (CNSN), Alberta Telemetered
Seismograph Network (ATSN), Canadian Rockies and Alberta Network (CRANE), and
TransAlta Dam Monitoring Network (TD).
Surface-wave signal collection for MASW processing was completed using a 24-channel
Geode in-field seismograph in continuous recording mode, with twelve 4.5 Hz vertical land
geophones. The seismic source was an 8 lbs. (3.63 kg) sledge hammer vertically struck on
a steel plate. An offset distance of 5 m was primarily used and a minimum of five hammer
impacts were delivered at both ends of the linear array with interstation separations of 1
and 3 m (Fig. 2.2a). Hammer impacts were stacked at both ends of the array during
processing to improve the signal-to-noise ratio.

23
Figure 2.1: Seismograph stations visited during the July 2016 fieldwork campaign
(circles), at which geophysical data were collected. Black inverted triangles show the
locations of Alberta seismic stations in operation but not visited in this study.
Calgary
Ranfurly
Grande Cache
Red Earth Creek
Esri, HERE, DeLorme, MapmyIndia, ©
OpenStreetMap contributors, and the GIS user
community
112°W
112°W
114°W
114°W
116°W
116°W
118°W
120°W
110°W
56°N
56°N
54°N
54°N
52°N
52°N
50°N
Legend
Project Seismic Station
Geophysical Survey Site (Successful)
Geophysical Survey Site (Unsuccessful)

24
Table 2.1: Geographic coordinates of seismic station sites visited in this study.
Station Degrees Latitude Degrees Longitude
ATHA 54.7140 -113.3140
BR2 53.3294 -117.8606
EDM 53.2220 -113.3500
GCA 53.8677 -119.1565
HON 55.0780 -114.0465
LGPLA 53.1170 -115.3550
LYA 51.1552 -113.4730
NOR 52.4900 -116.0500
PER 53.6825 -116.0420
RDEA 56.5510 -115.3180
RW2 53.3494 -111.7469
RW3 54.4415 -113.6513
SNUFF 54.6781 -117.5398
STPRA 55.6610 -115.8320
SWHSA 54.8990 -116.7520
TD005 53.0140 -115.4110
TD006 53.0010 -115.6220
TD007 52.9070 -115.6160
TD008 52.8040 -115.4320
TD009 52.3210 -116.3230
TD012 52.1310 -115.3970
TD022 51.1770 -114.2290
TD026 51.2930 -114.7070
TD028 51.2490 -114.5880
TD029 52.2170 -115.2000
TD06A 52.9500 -115.5210
TD13A 52.0080 -114.7680
TONYA 54.4054 -117.4908
Ambient noise array data for AVA methods were collected using up to 5 Micromed (now
MoHo s.r.l) Trominos®
; these are ultra-portable all-in-one seismographs with three
orthogonal high resolution electrodynamic sensors fitted with an internal GPS receiver
capable of achieving high timing accuracy (~1 µs) and able to register frequencies over a
large bandwidth (0.1 to 256 Hz). One of the three array geometries were used (depending
on the space available at the site): (1) ‘L’ geometry with 3 Trominos, (2) ‘T’ geometry with
4 Trominos and (3) ‘X’ or cross geometry with 5 Trominos (Fig. 2.2b). Each array provides
reliable phase velocities over a particular frequency bandwidth within resolution and

25
aliasing limits. The array aperture (size, radius) was adjusted a minimum of three times per
site to retrieve reliable phase velocities over the full bandwidth of the dispersion curve.
Interstation separations ranged from 5 to 30 m (in the X and Y direction; see Fig. 2.2b).
Microtremor vibrations were recorded for a minimum of 20 minutes per array setup at a
sampling rate of 128 Hz. Table 2.2 summarizes the data that were collected.
From a theoretical standpoint, AVA acquisition is only valid when performed on a level
surface. At some sites, uneven ground topography or site access limited the radius of the
largest array (e.g., RW2, TD06A, TD13A). For those sites for which we successfully
completed AVA processing, all sensors used in the array can be assumed to have been
located in a flat plane.
Figure 2.2: Geophysical survey array geometries for (a) Multi-channel analysis of
surface-waves (MASW) and (b) Ambient vibration array (AVA) acquisition; (a)
inverted triangles are shot locations and triangles are geophones; (b) black rings
show sequential array deployment for ‘X’ geometry, red circles for ‘T’ geometry,
and blue circles for ‘L’ geometry.
-30 -15 -5 0 5 15 30
X [m]
-30
-15
-5
0
5
15
30
Y
[m]
0 10 20 30 40
X [m]
(a) (b)

26
Table 2.2: Investigated seismic station sites in Alberta, Canada.
Station
Array
Setup
XY
Interstation
Separation
[m]
Site Observations Station
Array
Setup
XY
Interstation
Separation
[m]
Site Observations
ATHA
3 arrays
T-geometry
5/15/30
Firm clayey-sandy topsoil
Single station measurements made in gated area: (1)
on concrete foundation, and (2) on gravely topsoil
SWHSA
3 arrays
X-geometry
5/10/15
Heavy rain the night before; poor coupling with
water-saturated ground surface
Soft pebbly topsoil
BR2
3 arrays
X-geometry
5/15/30 Soft to firm topsoil TD006
3 arrays
T-geometry
5/15/30
Rough terrain with tall vegetation
Loose sandy topsoil underlain by firmer clayey soil
EDMa 3 arrays
T-geometry
5/15/30
Gravely to soft sandy topsoil
Single station measurement made on concrete
foundation of station housing
TD06A
1 array
T-geometry
5
Station housing situated in a marsh
Array measurements made on adjacent gravel road
GCA
3 arrays
T-geometry
5/15/30
Array measurements made on wet gravel road
adjacent station housing
TD007
3 arrays
X-geometry
5/15/30
Gravelly topsoil underlain by firmer clayey soil
Poor coupling with water-saturated ground surface
HON
3 arrays
L-geometry
5/15/30 Firm to loose sandy topsoil TD008
3 arrays
L-geometry
5/15/30
Clayey topsoil interspersed with small pebbles
Large facility nearby; potential noise source
LGPLA
3 arrays
T-geometry
5/15/30
Sandy topsoil in upper 5 cm underlain by firmer
clayey soil
TD009
3 arrays
X-geometry
5/15/30 Firm topsoil interspersed with small pebbles
LYA
3 arrays
T-geometry
5/15/30
Heavy rain during measurements
Gravely top soil saturated with water; large puddles
TD012
3 arrays
X-geometry
5/15/30
Station situated on steep hill
Array measurements made on adjacent plateau;
ground surface is soft-weathered bedrock
NOR
3 arrays
L-geometry
5/15/30
Sandy topsoil interspersed with small pebbles
Station situated on the edge of a flat short-grassed
plateau protruding out from a steeply inclined hill
TD13A
3 arrays
L-geometry
5/15/20 Soft topsoil and hilly topography
PER
3 arrays
T-geometry
5/15/30
First few centimeters are soft sandy topsoil underlain
by more compact sandy soil
TD005
3 arrays
L-geometry
10/20/30
Station situated on rough terrain with tall vegetation;
measurements made on gravel road

27
RDEA
3 arrays
X-geometry
5/15/30
Loose topsoil underlain by firmer soil interspersed
with small to large pebbles
TD022
3 arrays
T-geometry
5/15/30
Hilly topography
Soft topsoil underlain by firmer sandy to clayey soil
RW2
1 array
L-geometry
5
Soft sandy topsoil in the first few centimeters
underlain by more compact sandy soil
Station situated in heavy undergrowth
TD026
3 arrays
L-geometry
5/15/30
Soft topsoil underlain by glacial till and gravel
Pipes buried ~6ft below trending N-S
RW3a 3 arrays
T-geometry
5/15/30 Soft topsoil underlain by firmer soil TD028
3 arrays
X-geometry
5/15/30 Sandy soil and flat topography
SNUFA
3 arrays
X-geometry
5/10/30
Ground surface uneven; crests in middle of the array
TD029
3 arrays
T-geometry
5/15/30 Soft to firm topsoil; station located in small valley
STPRA
2 arrays
L-geometry
15/30 Sandy topsoil interspersed with small pebbles TONYA
3 arrays
L-geometry
5/15/30 Clayey topsoil with minor amounts of pebbles
a
Multi-channel analysis of surface waves (MASW) processed for these sites with 1 and 3 m interstation spacing distances.
Bolded station codes are the 18 seismic station sites we were able to retrieve reliable dispersion characteristics

28
2.4 Data Preconditioning
We preprocessed and executed surface-wave dispersion analysis of MASW and AVA data
with the Geopsy freeware (v. 2.9.1; Wathelet, 2008) We used the software kit Grilla (v.
6.1; MoHo s.r.l) for performing mHVSR analysis of Tromino recordings.
The following steps were taken to prepare ambient vibration recordings for extraction of
dispersion characteristics: (1) vertical component Tromino recordings of each array were
precisely synchronized using GPS time markers (frequency band > 0.3 Hz) and (2) if
necessary, signals belonging to impulsive noise sources (i.e. walking near the instruments)
at the beginning and end of each recording were removed.
We applied HVSR analysis to the Fourier amplitude spectra computed from the Trominos
for each sensor trace. The entirety of each trace was partitioned into 60 s time windows.
Contemporaneous partitions of each component were smoothed with a 20% cosine window
and subsequently used to calculate microtremor horizontal-to-vertical spectral ratios
(mHVSRs) between 0.125 and 50 Hz by dividing the geometric mean of the two horizontal
components by the vertical component. The individual 60 s windowed-mHVSRs were then
averaged across all time windows to generate a single mHVSR for each sensor (grey lines
in Figure 3) and for all array apertures (e.g., 5, 15, 30 m). The mHVSRs were then
manipulated in MATLAB to produce the average mHVSR (denoted !"#$%) for each
seismic station site, as shown in Figure 2.3.

29
Figure 2.3: Individual (grey) and station average (bold black line) Fourier
amplitude &'()*s with ±1 standard deviation (grey shaded region). * indicates
sites at which sensors experienced coupling issues with the ground surface.
Preparation of surface wave recordings for MASW analysis was a two-step process. Due
to the continuous recording functionality of the Geode in-field seismograph, each
geophone saved ground motion data in 30 s long SEGY files. Thus we: (1) merge
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
ATHA
0.2 1 10 50
-0.5
0
0.5
1
BR2
0.2 1 10 50
-0.5
0
0.5
1
EDM
0.2 1 10 50
-0.5
0
0.5
1
GCA
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
HON
0.2 1 10 50
-0.5
0
0.5
1
LGPLA
0.2 1 10 50
-0.5
0
0.5
1
LYA
*
0.2 1 10 50
-0.5
0
0.5
1
NOR
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
PER
0.2 1 10 50
-0.5
0
0.5
1
RDEA
0.2 1 10 50
-0.5
0
0.5
1
RW2
0.2 1 10 50
-0.5
0
0.5
1
RW3*
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
SNUFA
0.2 1 10 50
-0.5
0
0.5
1
STPRA
0.2 1 10 50
-0.5
0
0.5
1
SWHSA
0.2 1 10 50
-0.5
0
0.5
1
TD005
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
TD006
0.2 1 10 50
-0.5
0
0.5
1
TD007
0.2 1 10 50
-0.5
0
0.5
1
TD008
0.2 1 10 50
-0.5
0
0.5
1
TD009
*
0.2 1 10 50
-0.5
0
0.5
1
Log
10
(HVSR)
TD012
0.2 1 10 50
-0.5
0
0.5
1
TD022
0.2 1 10 50
-0.5
0
0.5
1
TD026
0.2 1 10 50
-0.5
0
0.5
1
TD028
0.2 1 10 50
Frequency [Hz]
-0.5
0
0.5
1
Log
10
(HVSR)
TD029
0.2 1 10 50
Frequency [Hz]
-0.5
0
0.5
1
TD06A
0.2 1 10 50
Frequency [Hz]
-0.5
0
0.5
1
TD13A
0.2 1 10 50
Frequency [Hz]
-0.5
0
0.5
1
TONYA

30
individual SEGY files for each geophone into single MSEED files and (2) crop waveforms
for all geophone traces containing hammer impacts using 1 s time windows. MASW data
were collected from continuous surface-wave recordings at two station sites (EDM and
RW3).
2.5 Dispersion Curves
Surface-wave dispersion estimates were made under two assumptions: (1) the subsurface
structure is horizontally stratified and (2) Rayleigh surface-waves dominate the
microtremor wave-field. For 10 soil sites, poor instrument coupling, limited bandwidth
and/or a low signal-to-noise ratio prevented us from resolving dispersion characteristics.
As an example, Figure A4 in Appendix shows the dispersion histograms for station TD026
resulting from MSPAC and HRFK processing using three utilized array apertures. In this
case, the dispersion histograms are ambiguous and lack a clear phase velocity dominance
at any particular frequency. Other stations with similar dispersion characteristics were
omitted from further investigation in this study. We were able to determine dispersion
curves for 18 out of the 28 seismic station sites visited; the fundamental mode surface-
wave dispersion curve, as well as higher modes if present, were subjectively interpreted.
Figure 2.4 presents two examples of dispersion curve picks made based on MSPAC and
HRFK dispersion histograms leading to the interpretation of the fundamental mode
dispersion curve for the seismic station sites ATHA and BR2. The resolving power of an
array depends on the diameter and receiver layout of the deployed array and in general is
represented as the region between the high frequency aliasing limit and low frequency

31
resolution limit. These delimiters are commonly referred to as the minimum (kmin) and
maximum resolved wavenumber (kmax), respectively (kmin and kmax limits are shown in Fig.
2.4). Following the work of Woods and Lintz (1973), Wathelet (2008) demonstrated the
use of the theoretical array response function to evaluate kmin and kmax, whereas Tokimatsu
(1997) derived empirical relationships for kmin and kmax that depend only on the minimum
and maximum interstation separations, Dmin and Dmax respectively, of the deployed array:
+,-. =
01
2345
, (2.6)
+,67 =
01
2389
. (2.7)
Reliable dispersion estimates are selected within these empirical-based thresholds.
Although dispersion picks were generally made within resolution and aliasing limits, in
some cases we interpreted outside these bounds if the histogram clearly displayed high bin
counts and/or were consistent with the dispersion characteristics of multiple array setups
for the same site.
The beampower processing of MASW data for seismic stations EDM and RW3 are shown
in Figure 2.5. For RW3, histograms calculated using MASW analysis revealed a higher
mode dispersion curve in addition to the fundamental mode. The remainder of the
dispersion curve picks from HRFK and MSPAC analyses can be found in the electronic
supplement to this article (Fig. A4-A20 in Appendix). Our interpreted accuracy of the
manually retrieved dispersion data is included here as ±0.001 s/m.

32
Figure 2.4: Fundamental mode dispersion curve procedure for ATHA (top row) and
BR2 (bottom row). MSPAC-based phase velocity-frequency histograms (a, f) with
symbols corresponding to the ring size, r; (b-d, g-i) HRFK dispersion histograms of
utilized array apertures and corresponding dispersion picks (black rings); (e, j)
Interpreted fundamental mode dispersion estimates for ATHA and BR2.
Figure 2.5: Beampower processing of MASW data for stations EDM (top row) and
RW3 (bottom row). (a-b) and (d-e) dispersion picks (black rings) based on

33
dispersion histograms; (c) final interpreted fundamental mode dispersion estimates
for EDM; (f) Interpreted fundamental (grey circles) and higher mode (grey squares)
dispersion estimates for RW3. Interpreted dispersion data at low frequencies
determined from HRFK and/or MSPAC procedures (Fig. A5 and A10 in Appendix).
In Figure 2.6 the fundamental mode dispersion curves are presented for the 18 seismic
station sites as well as their corresponding VS30-based NBCC Site Class, determined using
their intersection with the VR40 line (Brown et al., 2000a, 2000b; Martin and Diehl, 2004),
where VR40 is the phase-velocity of a 40 m wavelength Rayleigh-wave. Using 53 VS profiles
from California, Martin and Diehl (2004) showed that differences between observed and
predicted values of VS30 based on the VR40 method are small (generally below 10%) with
an average error of 5%. The VR40 method thus is able to provide an efficient and reliable
preliminary estimate for VS30 prior to inversion. The VR40 line method indicates a NBCC
Site Class D predominance in Alberta with a lesser number of seismic station sites
classified as having C site class conditions.
2.6 Inversion Method and A Priori Information
!"#$% and dispersion curve data sets were inverted for 1D VS-depth profiles using an
improved neighbourhood algorithm based on the work originally proposed by Sambridge
(1999), using the dinver surface wave inversion tool (Wathelet et al., 2004; Wathelet,
2008), which is part of the Geopsy software package.
The neighborhood algorithm used in this study is a stochastic (Monte Carlo) direct-search
method that looks to optimize the misfit function in a multi-dimensional parameter space.

34
Figure 2.6: Seismic station fundamental mode dispersion curves corresponding to
the interpreted NBCC Site Class. The thick black line (VR40 line) is calculated using
the equation ():; = =. ;?@((*?;) after Martin and Diehl (2004). Sites without
dispersion data at the (*?; line are not assigned a site class (grey).
The misfit function in the case for dispersion curve inversion is defined as:
!CDECFG-HI =
7J8K7L8
M
N8
M.O
.O
-PQ , (2.8)
where RG- is the velocity of the measured dispersion curve at frequency E-, RS- is the
velocity of the calculated dispersion curve at frequency E-, T- is the standard deviation of
the frequency samples considered and UV is the number of frequency samples (data points)
considered. If no certainty is provided, then T- is replaced by RG- in equation (2.7).
Because the absolute amplitude of the empirical !"#$% cannot be directly tied to the
maximum amplitude of the ellipticity, only the frequency of peak amplitude is considered
in the evaluation of the misfit function for !"#$% inversion:
VS30
=360 m/s
VS30
=760 m/s
VS30
=180 m/s
NBCC Site Class B
NBCC Site Class C
NBCC Site Class D
NBCC Site Class E
1 2 3 4 5 10 20 30 40 50 100
Frequency [Hz]
0
100
200
300
400
500
600
700
800
900
1000
Phase
Velocity
or
V
S30
[m/s]
ATHA
BR2
HON
PER
STPRA
SWHSA
TD06A
RW3
TD029
SNUFA
TD007
TD028
TONYA
EDM
RDEA
RW2
TD008
TD13A
V
S30

35
!CDECFWXX =
YZ [5[]83[9^4_K YZ L4_L`_4^[J
GYZ [5[]83[9^4_
, (2.9)
where EQ is the frequency of maximum of amplification, and aEQ W7IWb-,W.c6X is the
standard deviation of the experimental peak frequency, which is based on the empirical
!"#$%. In the case of joint inversion of dispersion curve and !"#$% data sets, the misfit
function is proportional to the sum of the individual misfit functions defined in equations
(2.8) and (2.9). If the soil structure and model are nearly identical, the misfit function will
have at least one minimum that describes a unique set of model parameters. It is more likely
that the misfit function exhibits many local minima for which a multitude of sets of model
parameters equally minimize equations (2.8) and (2.9). Therein lies the non-unicity of the
inversion problem.
Similar to other direct-search methods, the neighbour algorithm generates a pseudo-
random seed number that corresponds to a set of model parameters for which a dispersion
curve and/or Rayleigh-wave ellipticity is calculated (i.e. the forward problem). The misfit
function is evaluated for all the previous forward model computations, which is used to
guide the program as it searches for model parameters to improve the current model. More
specifically, the neighbour algorithm: (1) generates ns models in parameter space and
constructs Voronoi cells around each of them and (2) calculates the misfit function for the
most recently generated ns set of models; (3) nr models are identified as having the lowest
misfit of all the models generated so far and ns new models are generated by performing a
uniform random walk (using a Gibbs sampler) to each of the nr cells previously selected
(i.e. ns/nr in each new cell) to a new location in the parameter space but restricted to the

36
chosen cell; (4) return to step (2). In each iteration efforts are concentrated in areas of the
parameter space that are surrounded by better data-fitting models. The information from
previous samples is used to drive the algorithm forward in an adaptive sampling manner.
!"#$% and dispersion curve data sets were inverted for 1D VS-depth profiles using an
improved neighbourhood algorithm based on the work originally proposed by Sambridge
(1999), using the dinver surface wave inversion tool (Wathelet et al., 2004; Wathelet,
2008), which is part of the Geopsy software package. The dinver program runs as a
graphical user interface allowing the user to enter starting model input parameters
including compression-wave velocity (VP), VS, density, and Poisson’s ratio, which are
either fixed to a value or set to a range. Furthermore, each parameter is independently
assigned a bottom depth (thickness). We retained the default values for Poisson’s ratio (0.2
to 0.5), VP (200 to 5000 m/s) and density, which is fixed at 2000 kg/m3
. Molnar et al. (2010)
demonstrated that the quantitative uncertainty of model parameters is slightly biased when
parameters are fixed in the inversion (e.g., as done for density in this study), however,
obtaining an uncertainty distribution of model parameters is not the aim of this study. Our
rationale for using default values for Poisson’s ratio, VP and density is that Rayleigh-wave
dispersion is less sensitive to these parameters than it is to thickness and VS; for example,
in an earlier study, Xia et al. (1999) conducted a parameter sensitivity test and showed that
changes in VP and density of 25% resulted in small changes to the Rayleigh-wave phase
velocity (less than or equal to about 8%). The least sensitive parameter is VP, which is
computed from VS using Poisson’s ratio. Wathelet and Jongmans (2003) showed that as
Poisson’s ratio tends to 0.5, the effect of VP on the soil layers is reduced. For a single layer

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