Seismicity and Tectonic Interpretation of the Southern Rocky Mountain Trench Near Valemount, British Columbia, Canada

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2020-05-15 Seismicity and tectonic interpretation of the Southern Rocky Mountain Trench near Valemount, British Columbia, Canada

Purba, Joshua Chris Shadday

Purba, J. C. S. (2020). Seismicity and tectonic interpretation of the Southern Rocky Mountain Trench near Valemount, British Columbia, Canada (Unpublished master's thesis). University of Calgary, Calgary, AB. http://hdl.handle.net/1880/112078 master thesis

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Seismicity and tectonic interpretation of the Southern Rocky Mountain Trench near

Valemount, British Columbia, Canada

Joshua Chris Shadday Purba

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

GRADUATE PROGRAM IN GEOLOGY AND GEOPHYSICS

CALGARY, ALBERTA

MAY, 2020

Thesis abstract

The Rocky Mountain Trench is a large geological feature in the Canadian Cordillera with complex structures. Although efforts to understand the structure of the trench have been conducted through refraction-seismic, reflection-seismic, and geological studies, detailed knowledge of the trench is still sparse but crucial to understanding its evolution. Here, I conduct a local seismic study that involves earthquake detection, arrival-time picking, earthquake location, and a tectonic interpretation of the Rocky Mountain Trench in the area of Valemount, British Columbia. I developed and employed a nonlinear, probabilistic multiple-earthquake location for earthquakes detected here. The location provides both earthquake locations and rigorous estimates of their uncertainties. Based on analysing one year of data, my catalogue includes 47 local earthquakes that I identified and located. The results of the multiple-earthquake location presented here illustrates uncertainty reduction in depth from 18 to 5 km compared to the depths of earthquakes calculated based on single-earthquake locations. This lower depth uncertainty permits better inferences of the tectonic development of the Rocky Mountain Trench. The earthquake locations determined here displays a change in the distribution of seismicity around Valemount. Seismicity extends to the west of the RMT and the south of Valemount. While to the north, the seismicity is primarily confined to the trench and areas to the east. The distribution ofseismicity also supports the dome-shaped Malton Gneiss in the subsurface. Seismic velocities are consistent with metamorphic rocks and the presence of significant amount of quartz in crustal rocks.

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Preface

Chapter 1 of the thesis is original, independent work by J. C. S. Purba.

Chapter 2 of the thesis has been submitted to the Bulletin of the Seismological Society of America

as Nonlinear Multiple Earthquake Location and Velocity Estimation in the Canadian Rocky

Mountain Trench by Purba, J. C. S., Dettmer, J., Gilbert, H. (2020). The manuscript is currently

under review for publication in the Bulletin of the Seismological Society of America.

Chapter 3 of the thesis will be submitted to the Geophysical Journal International as Evolution of

the Southern Rocky Mountain Trench using local seismicity by Purba, J. C.S., Gilbert, H., Dettmer,

J. (2020). The manuscript is going to be submitted in May 2020.

Chapter 4 of the thesis is original, independent work by J. C. S. Purba.

Acknowledgments

I would like to thank Borealis Geopower Inc., Nanometrics Inc., and the University of Calgary for their wonderful collaboration that made data acquisition and collection possible. Without these data, my research would not have been possible.

I am very grateful to have my supervisors, Jan Dettmer and Hersh Gilbert, who provide extensive guidance during all stages of the project. They provided encouragement during stressful times, which I genuinely appreciate and never forget. I would also want to acknowledge David Eaton and Daniel Trad, who have been willing to be on the defence committee for my thesis, and Eva

Enkelmann as the neutral chair for my defense.

Thanks to the office mates in the seismology group, especially Juliann Coffey, Katherine Biegel,

Jacquelyn Smale, they were there with me through ups and downs during the master’s program.

And other mates, Pejman Shahsavari and Laleh Khadangi, who has just recently become part of

the office.

I want to mention Genevieve Savard who helped me to create maps for this study. Eva

Enkelmann’s geochronology group helped with meaningful discussions about the geologic

interpretations of this study.

Finally, I would like to appreciate my parents in Indonesia, my two brothers: Victor in the U.S. and

Jeremy in Canada, and a very special person, Victoria Warsito, who has helped me by giving

emotional support and comfort toward the program completion.

Table of Contents

Thesis Abstract ...... ii

Preface ...... iii

Acknowledgement ...... iv

Table of Contents ...... v

List of tables ...... vii

List of figures ...... viii

Chapter 1. Thesis Introduction ...... 1

Statement of contribution ...... 10

Chapter 2. Nonlinear Multiple Earthquake Location and Velocity Estimation in the Canadian

Rocky Mountain Trench ...... 11

Key Points ...... 11

Abstract ...... 11

Introduction ...... 12

Method ...... 15

Simulation Results ...... 22

Simulation 1 ...... 22

Simulation 2 ...... 23

Field Data and Results ...... 25

Discussion and Conclusion ...... 34

Chapter 3. Evolution of the Southern Rocky Mountain Trench using local seismicity ...... 36

Summary ...... 36

Key words ...... 36

1. Introduction ...... 37

1.a Previous Geophysical Studies ...... 43

2. Canoe Reach Earthquake Catalogue ...... 43

2.a The Deployment, Instruments, and Network ...... 43

2. b Earthquake Detection...... 44

3. Description of Earthquake Locations...... 48

3.a Transect A ...... 49

3.b Transect B ...... 49

3.c Transect C ...... 49

3.d Transect D ...... 50

3.e Earthquake Location Uncertainties...... 50

4. Discussion and Conclusion ...... 52

Chapter 4. Conclusions and recommendations ...... 57

Data and Resources ...... 61

References ...... 62

Appendix A copyright permissions ...... 72

Appendix B supplemental information for Nonlinear Multiple Earthquake Location and Velocity

Estimation in the Canadian Rocky Mountain Trench ...... 74

Appendix C supplemental information for Evolution of the Southern Rocky Mountain Trench

using local seismicity...... 84

Appendix D review for MCMC method ...... 88

Appendix E Canoe Reach Earthquake Catalogue ...... 96

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List of tables

Table 2-1 Prior bounds for inversion parameters...... 20

Table 3-1 Detection parameters for the kurtosis and STA/LTA methods in this study...... 45

Table E-1 Canoe Reach earthquake catalogue from September 2017 – August 2018. The catalogue consisted of 47 earthquakes that have been manually inspected. For every inversion parameter, the mode, lower and upper bound of 95%CI are written as mo, x1, and x2. Local magnitude (Ml) is included from Nanometrics ...... 97

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List of figures

Figure 1-1 Map of the Canoe Reach stations. Seismic stations are symbolized as black triangles.

The SRMT, Southern Rocky Mountain Trench; PT, Purcell Thrust; NTA, Kinbasket Lake;

Shuswap MCC, Shuswap Metamorphic Core Complex; MG, Malton Gneiss (modified after

McDonough & Parrish, 1991), V, Valemount. Fault lines are modified after Cui et al. (2018). .. 2

Figure 1-2 Station CRG10 overlooking the active logging zone nearby. Photo taken in September

2017, credit to J. Purba...... 5

Figure 1-3 Image shows a seismic station near Valemount that I serviced in March 2018; credit to J. Coffey...... 5

Figure 2-1 Map of the study area along the RMT. The locations of 10 seismic network stations are shown by triangles. Known fault locations are indicated for normal faults (solid) and thrust faults (dashed). Probabilistic epicentre locations for the 47 earthquakes located in this study are shown by the gray scale (white - low probability, black - high probability). Note that some probability density functions for location overlap each other. The northwestern and southern earthquake clusters are outlined by solid circumferences. The star marks the mode of the epicentre marginal distribution for earthquake 37 ...... 17

Figure 2-2 Results of two simulation studies in terms of absolute error marginal distributions, where true parameter values correspond to values of 0. Earthquakes are sorted according to increasing distance from the network centroid from top to bottom. The 10 nearest events of a total of 47 events are shown. The remaining events are shown in the supplement. Black lines represent simulation 1 and gray lines simulation 2...... 24

Figure 2-3 Simulation results: Histograms of hypocentre-parameter mode biases for all earthquakes. Simulation 1 results in gray and simulation 2 results in black...... 25

Figure 2-4 Inversion results for earthquake 37 in terms of 1D marginals of longitude, latitude,

depth, and origin time (top), and Vp, Vp/Vs, p, and s (bottom). Dashed lines represent 95% credibility intervals. The plot boundaries represent𝜎𝜎 the𝜎𝜎 width of the uniform prior distributions, except for latitude and longitude, where bounds were significantly wider than shown to span the full study area. Solid lines show Gaussian distributions with means and standard deviations taken from the marginals for comparison...... 27

Figure 2-5 (Top) Comparison of inversion results in terms of 1D marginals of shared parameters for the location of 47 single earthquakes (gray lines) and multiple-earthquake locations for the same 47 earthquakes (black lines). Dashed lines represent 95% credibility intervals for the multiple-earthquake locations. (Middle) The same information for the northwestern cluster of 18 earthquakes. (Bottom) The same information for the southern cluster of 10 earthquakes...... 28

Figure 2-6 Modes and 95% CIs from the multiple-earthquake inversion for hypocentre parameters

for 47 events (black). For comparison, results from single-earthquake inversions are presented

(gray). In all cases, dots mark marginal distribution modes and error bars indicate the lower and

upper limits of 95% CIs for each parameter. The gray and black symbols are slightly offset in the

horizontal direction for better visualization. The vertical dashed line highlights earthquake 37.

...... 30

Figure 2-7 Same as Fig. 2-6 but for shared parameters. Horizontal black lines are for the joint

inversion results and represent the extent of the 95% Cis. The vertical dashed line highlights

earthquake 37...... 32

Figure 2-8 (Left) P-wave arrival-time residuals for multiple-earthquake inversions (dashed black line) compared to the corresponding single-earthquake results, where residuals for all single- earthquake inversions are shown as a single histogram (solid gray grey). (Right) The same information but for S-wave arrival-time residuals ...... 33

Figure 3-1 Regional map of the RMT (Rocky Mountain Trench) within the Canadian Cordillera

and bordering southeastern Alaska and northwestern Montana (modified after Wheeler et al.,

1991). Five morphogeographic belts: Foreland Fold and Thrust belt, Omineca belt, Intermontane

belt, Coastal belt, and Insular Belt. Red line is showing the central RMT, that extends from latitude

~52o to 54o and marks the transition between the southern and northern RMT. The black box

shows the location of our study area. NRMT, Northern Rocky Mountain Trench; SRMT, Southern

Rocky Mountain Trench; MG, Malton Gneiss; Shuswap MCC, Shuswap Metamorphic Core

Complex; PA, Purcell Anticlinorium; V, Valemount; WG, Wells Gray volcanic field; R, Radium Hot

Spring; C, Crambrook; PT, Purcell Thrust; R, Radium; NTA, North-Thompson Albreda; CF, Canal

Flats; FL, Flathead Lake; MT, Montana...... 40

Figure 3-2 Map of the Canoe Reach network and the seismicity (modified after Cui et al., 2018).

Stations are indicated by black triangles. The RMT, Rocky Mountain Trench; PT, Purcell Thrust;

NTA, North Thompson Albreda; CM, Cariboo Mountains; RM, Rocky Mountains; Kinbasket Lake;

Shuswap MCC, Shuswap Metamorphic Core Complex; MG, Malton Gneiss (modified after

McDonough & Parrish, 1991). Four transect lines are drawn according to seismicity; red shaded zone indicates the earthquake included in corresponding transect line. Colour bar indicates earthquake locations at depth. The northwestern and southern earthquake clusters are outlined inside black ellipses. Three repeating events are located inside black dashed line...... 42

Figure 3-3 Three-component seismograms presenting earthquake number 21 in our catalogue.

This earthquake occurred on 2018-01-21 at 04:26:12 UTC. Waveforms are filtered between 10 -

20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals.

Both STA/LTA and kurtosis detections declared this as a potential earthquake because of

detections in all channels. Traces of plotted for all 10 Canoe Reach stations arranged in numeric

order CRG01-CRG14 from top to bottom. Left column – east-west channel; centre – north-south channel; and right – vertical channel...... 47

Figure 3-4 Depth profile of the earthquake catalogue with error bars included. The error bars indicate the lower and upper 95% CIs, and dotted circles for the modes of earthquake depth distributions from the catalogue (Table 2). (a) Transect A consists of 22 earthquakes. Each earthquake is presented as a circle with a colour according to its depth. The elevation profile is provided above the depth profile. The inverted triangles denote the location of the seismic stations projected to the transect line; red dot for PT, Purcell Thrust; black dot for SRMT, Southern Rocky

Mountain Trench. (b) Transect B includes eight earthquakes. Blue dot marks NTA, North-

Thompson Albreda, projected to the transect line. (c) Six earthquakes are included under transect

C, west of the NTA. Blue dot on the elevation profile marks the projected NTA to the transect line.

(d) Transect D is comprised of 22 earthquakes under transect D, along the SRMT. A cluster of 17 earthquakes in the north located under station CRG10 and other five earthquakes to the south of the depth profile ...... 51

Figure 3-5 Vertical waveforms from three earthquakes that occurred on June 26th, 2018 recorded by station CRG04 (earthquake numbers 41 - bottom, 42 - middle, and 43 - top). These signals

have been filtered from 5 to 15 Hz. In addition to similar P- and S-waves recorded near relative

times of 1 and 2.5 s respectively, the waveforms also exhibit similar signals in their coda out to

times of 8 s and later. Refer to Figure 3-2 for epicentre location of these three earthquakes.... 55

Figure B-1 Results of two simulation studies in terms of absolute error marginal distributions,

where true parameter values correspond to values of 0. Earthquakes sorted according to

increasing distance from the network centroid from top to bottom. Black lines represent simulation

1 (data simulated with uniform half space and inverted with uniform half space) and gray lines

simulations 2 (data simulated with layered half space and inverted with uniform half space) ... 77

Figure B-2 Results of two simulation studies in terms of marginal distributions for shared parameters. Black lines represent simulation 1 (data simulated with uniform half space and

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inverted with uniform half space) and gray lines simulation 2 (data simulated with layered half space and inverted with uniform half space). Dashed lines represent true parameter values for simulation 1...... 78

Figure B-3 Epicentre map for 2D marginal distributions of catalogue earthquake 37. Red is a higher probability, whereas blue is lower probability. The earthquake is a part of the northwestern earthquake cluster...... 78

Figure B-4 Histogram PPDs of parameter latitude, longitude, origin time, and depth between multiple-earthquake (blue) and single-earthquake inversions (black) for 47 earthquakes. Dashed lines are the lower and upper 95% CIs for each parameter. Earthquakes are sorted according to increasing depth from the network centroid. The extent of the depth axis is limited to 20-km depth for better display of results. However, the prior extends to 35-km depth...... 79-81

Figure B-5 (a) Posterior model correlation matrix for multiple-earthquake location with 47 earthquakes. Since the matrix is symmetric, only the upper triangular matrix needs to be considered. The first 188 rows and columns correspond to hypocentre parameters for 47 earthquakes. The last 4 rows and columns correspond to the shared parameters. The colour scale is from red for perfect positive correlation, to white for neutral correlation, to blue for perfect negative correlation. (b) Magnified portion of the correlation matrix for earthquake 37. (c)

Magnified portion of the correlation matrix for the 4 shared parameters and the last 11 earthquakes in the catalogue. The black box highlights the portion for earthquake 37...... 82

Figure B-6 Convergence parameter γ as a function of MCMC step during the inversion. The dashed line marks the converge value of 0.05. Convergence times in the main text refer to achieving a value of γ = 0:05...... 83

Figure B-7 Multiple-earthquake inversion uncertainty scaling with number of earthquakes studies.

Uncertainties for earthquake 37 are considered in multiple-earthquake inversion while increasing

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the number of earthquakes in the inversion: single earthquake (green), 2 earthquakes (gray), 4

earthquakes (blue), 8 earthquakes (red), and18 earthquakes (black) ...... 83

Figure C-1 (Figure 1 in Purba et al., 2020) Map of the study area along the RMT. The locations

of 10 seismic stations are shown by triangles. Known fault locations are indicated for normal faults

(solid) and thrust faults (dashed). Probabilistic epicentre locations for the 47 events located in this

study are shown by the gray scale (white - low probability, black - high probability). Note that some probability density functions for location overlap each other. Ellipses outline the northwestern and southern event clusters ...... 85

Figure C-2 Three-component seismograms presenting earthquake number 15 in our catalogue.

This earthquake occurred on 2017-12-02 at 15:12:47 UTC. Waveforms are filtered between 10 -

20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals.

Only kurtosis detection declared this as a potential earthquake because of sufficient number of detections in 11 channels (4 vertical and 7 horizontal channels). Traces of plotted for all 10 Canoe

Reach stations arranged in numeric order CRG01-CRG14 from top to bottom. Left column – east- west channel; centre – north-south channel; and right – vertical channel. Black indicates both kurtosis and STA/LTA have triggered a detection; red for the kurtosis; and green for neither of them...... 86

Figure C-3 Three-component seismograms presenting earthquake number 3 in our catalogue.

This earthquake occurred on 2017-09-23 at 18:27:05 UTC. Waveforms are filtered between 10 -

20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals.

Only STA/LTA detection declared this as a potential earthquake because of sufficient number of detections in 12 channels (6 vertical and 6 horizontal channels). Traces of plotted for all 10 Canoe

Reach stations arranged in numeric order CRG01-CRG14 from top to bottom. Left column – east- west channel; centre – north-south channel; and right – vertical channel. Black indicates both

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kurtosis and STA/LTA have triggered a detection; blue for the STA/LTA; and green for neither of them ...... 87

Figure D-1 (a) random walk without rotation, and (b) with rotation. More efficient step direction and size are achieved through applying rotation. Red dashed line on the right represents the marginal distribution in the rotated axes, which also shows high probability distribution given only few samples ...... 93

Figure D-2 Cauchy (dashed) versus Gaussian (solid) distribution. Note the higher central peak

and heavier tails of the Cauchy distribution ...... 93

Figure D-3 (Same as Figure 2-4). Inversion results for earthquake 37 in terms of 1D marginals of longitude, latitude, depth, and origin time (top), and Vp, Vp /Vs, p,and s, (bottom). Dashed lines

represent 95% credibility intervals. The plot boundaries represent𝜎𝜎 the𝜎𝜎 width of the uniform prior

distributions, except for latitude and longitude, where bounds were significantly wider than shown

to span the full study area. Solid lines show Gaussian distributions with means and standard

deviations taken from the marginals for comparison...... 94

Figure D-4 (Same with Figure B-3). Epicentre map for 2D marginal distributions of catalogue

earthquake 37. Red is a higher probability, whereas blue is lower probability. The earthquake is

a part of the northwestern earthquake cluster ...... 95

Chapter 1. Thesis introduction

The Rocky Mountain Trench (RMT) is a remarkable physiographic linear feature that extends from the border of British Columbia and the Yukon Territory to Flathead Lake in Montana and is an extensive fault system whose underlying structure remains mostly unexamined. The RMT lies in the eastern portion of the Canadian Cordillera. By studying the structure of the Earth beneath the RMT, we can gain knowledge about its formation. One way to investigate the structure and formation of the RMT is by examining geologic maps of the Canadian Cordillera (e.g., Brookfield et al., 1991). However, the underlying structure cannot be interpreted accurately by only considering the exposed surface geology. Seismic studies are crucial for attaining reliable information about the subsurface. An example of seismic studies is the Lithoprobe project that examined Earth's structure across Canada along several seismic reflection and refraction profiles

(Cook et al., 1988; Clowes et al., 1995; Clowes, 2010). An important discovery from this earlier work was that the Moho beneath the cordillera is generally flat and shallow beneath the cordillera, at a depth of ~35 km with only slight variations (Hammer and Clowes, 2004). While results from the Lithoprobe survey provide excellent images along detailed transects, seismic observations outside of these areas are limited. To better understand the structure near the southern RMT, this study considers one year of broadband seismic data collected in southeastern British Columbia in the area surrounding Valemount, which lies nearly 500 km north of the southern Lithoprobe profile. The data were recorded by 10 three-components seismometers, configured in a network spanning the RMT and elongated in the northwest to southeast direction (Figure 1-1).

Figure 1-1. Map of the Canoe Reach stations. Seismic stations are symbolized as black triangles. The SRMT, Southern Rocky Mountain Trench; PT, Purcell Thrust; NTA, North- Thompson Albreda; Kinbasket Lake; Shuswap MCC, Shuswap Metamorphic Core Complex;

MG, Malton Gneiss (modified after McDonough & Parrish, 1991), V, Valemount. Fault lines are modified after Cui et al. (2018).

Extending for about 1600 km, this remarkable linear feature of the RMT has brought interests towards studying its structure. Earlier investigations of the RMT have noted that it is comprised of distinct sections, the northern, central and southern segments (van der Velden & Cook, 1996).

The northern RMT has experienced significant strike-slip faulting with minor extension during the post-mid-Cretaceous, the central segment is characterized by thrusting with minor normal faulting in the Jurassic to Early Cretaceous, and the southern segment is predominantly characterized by extension since the Eocene (summarized in McMechan, 2000). Some strike-slip motion may

continue southward from the northern RMT (e.g., Lambert & Chamberlain, 1988; Murphy 1990;

Pope & Sears, 1997), but little or no strike-slip displacement has not been identified in the southern RMT between 49°N and 50.25°N (e.g., van der Velden & Cook, 1996). This transition between southern and northern portions of the trench is characterized by thrust faults that formed during the Jurassic to Early Cretaceous, but later transitioned to minor normal faults in the

Cenozoic (McMechan, 2000).

One motivation in this study is to investigate whether the Southern RMT (at latitude near 52.5°) around Valemount is still active today. Indications for an active extensional environment in this

section of the trench were dated back in the Eocene (55-45 Ma) when the boundary on the

western margin of the cordillera transitioned to a transform margin (Monger & Price, 2002; Monger

& Gibson, 2019). If the fault is still active today, then examining the pattern of seismicity in the

region can provide insight into the tectonic evolution of the Rocky Mountain Trench and

surrounding faults. My approach to answer this overarching question is to record and interpret

seismic data of the area. Further, the interest of Borealis Geopower in the project is to monitor

local earthquakes in the area of Valemount to consider the area for potential future geothermal

development. Injecting large volumes of fluids into the subsurface of the area can affect the

regional stress field. Improving knowledge in active tectonic of the region will help mitigate the

risk of activating pre-existing faults during future geothermal development, which has become a problem in the case of hydraulic fracturing (Atkitson et al., 2016).

This research included fieldwork in which I was part of a collaborative field team comprised of others from the University of Calgary, Nanometrics Incorporated, and Borealis Geopower.

Fieldwork started in August 2017 and I participated in the deployment of the seismic stations. I contributed to site selection based on road accessibility and optimizing station coverage around

Valemount, and public outreach to the local community about seismic monitoring.

Most locations were near previous logging activity in clear cuts, where forestry roads provided access (Figure 1-2). Some challenges arose when digging 1-m holes to bury the seismometers.

Locations with very little soil overlying shallow bedrock and the dense root systems near the surface required multiple attempts to find suitable sites. For a team of three, installations typically took between two and three hours. In this fieldwork, we spent five days identifying sites and installing the Canoe Reach network.

In September 2017, I went with a group of four to carry out maintenance for the stations and retrieve one month of data. I inspected waveform quality, solar panel and battery performance, and replaced memory cards with new cards. A second maintenance visit took place in March

2018 via snowmobile, with a team of two to retrieve data (Figure 1-3). The third and final visit I

participated in was in early September 2018. During this trip, we replaced memory cards for five

stations and removed the remaining five stations from the field.

After reviewing the data collected during the initial phase of the deployment, I observed that the

data quality was often poor with lots of noise and spurious signals. I therefore omitted these initial

data and only included data recorded since September 1st, 2017 in my analysis. The data

presented in this study spans from September 1, 2017 to August 31, 2018.

Figure 1-2. Station CRG10 overlooking the active logging zone nearby. Photo taken in September 2017, credit to J. Purba.

Figure 1-3. Image shows a seismic station near Valemount that I serviced in March 2018; credit to J. Coffey.

My research included analysing the Canoe Reach dataset. Through my analysis I detected and located 47 local earthquakes in the area between 119.7o to 118.8o W, and 52.3o to 53.1o N. While

many regional and teleseismic earthquakes were also detected, these are not considered in my

study. Significant care was taken in the earthquake detection process. I applied two independent

detection methods, short-time average to long-time average (STA/LTA) ratio and kurtosis-based

detection, which both produced a similar catalogue of earthquakes. Using multiple detection

methods increased confidence that the significant earthquakes in this dataset have been. In the future, applying template matching methods utilizing these 47 earthquakes or an exhaustive autocorrelation could lead to identifying more earthquakes in the area. For the 47 detected earthquakes, a probabilistic earthquake catalogue of hypocentre locations was generated with a nonlinear, probabilistic algorithm (Chapter 2). This approach provides rigorous uncertainty estimation that is important for making tectonic interpretations based on the distribution of earthquakes. Chapter 3 utilizes the probabilistic catalogue to interpret the tectonic evolution of the Southern Rocky Mountain Trench (SRMT).

Studying the one-year data set included pre-processing of raw data (creating a repository of recordings, removing instrument response, filtering, and decimation) and combining data into a continuous stream in miniseed format. Further, I applied the kurtosis and STA/LTA methods for detecting earthquakes. Detection included an association procedure that had to be satisfied for a a declaration for potential earthquakes. All potential earthquake signals were visually inspected before being accepted into a catalogue. I picked P- and S- arrivals for the catalogue to be used for location utilizing a manual procedure. Nonlinear location was applied in a Bayesian framework to produce the probabilistic earthquake catalogue. Finally, chapter 3 presents a tectonic interpretation of the earthquake locations.

Chapter 2 of the thesis, authored by me and Drs. Dettmer and Gilbert, was submitted to the

Bulletin of the Seismological Society of America and is currently under review. This work focuses

on producing a probabilistic earthquake catalogue for the study area with Bayesian methods.

Since little prior knowledge about elastic properties in the study area exists, we use a simple velocity model of a homogeneous half-space and treat the compressional-wave velocity (Vp) and

the compressional-wave to shear-wave velocity ratio (Vp/Vs) as unknowns. Similarly, noise

parameters for P-wave arrival-time picks ( p) and S-wave arrival-time picks ( s) are treated as

unknowns in the inversion. Considering two𝜎𝜎 noise parameters assumes that the𝜎𝜎 noise processes

for P- and S-arrival picks are independent. This assumption is justified, since S-arrival picks are

generally more challenging to make than those for P-waves. A model where the parameter space

includes both physical parameters and noise parameters, is referred to as a hierarchical Bayesian

model (Gelman et al., 2013). This hierarchical model requires nonlinear treatment by the inversion

algorithm, which causes increased computational costs. The nonlinear algorithm I employ is

Metropolis-Hastings sampling of a Markov-chain Monte Carlo probability distribution (Brooks et

al., 2011). While computationally expensive, the hierarchical model results in more general

solutions to the inverse problem and provides more objective uncertainty estimates than methods

that rely on linearization and subjective assumptions for noise and elastic parameters.

In summary, our model includes the hypocentre parameters (latitude, longitude, depth, origin

time) for each earthquake and shared parameters (Vp, Vp/Vs, p, s) that are assumed to be representative of all earthquakes. Prior information is assumed 𝜎𝜎to be𝜎𝜎 uniform for all parameters with bounds chosen wide so that data information, not prior information, predominantly constrains the solution (Dosso, 2002).

Described by the posterior probability density (PPD), the location results do not resemble a

Gaussian shape, which means that significant nonlinearity exists, justifying the computational cost of a numerical sampling approach. I quantify uncertainty by calculating the 95% Credibility Interval for all parameters from the PPD. Significant uncertainty reduction is found in the case of multiple- earthquake location, where the average depth uncertainty is reduced from 18 to 5 km, when

compared to single-earthquake location. The earthquake location information is utilized for tectonic interpretations of the area, which are presented in Chapter 3.

Chapter 3 presents my tectonic interpretation of the distribution of seismicity in the earthquake catalogue. This chapter is a manuscript that will be submitted to Geophysical Journal International in May 2020. The map of seismicity helps us identify faults in the region that appear to be active.

In this region, the Southern Rocky Mountain Trench fault is an important structure that has exhibited multiple styles of deformation.

This study interprets seismicity that occurs near three notable faults in the area. These three faults

are the Southern RMT, the North-Thompson Albreda Fault and the Purcell Thrust. Not only do I

focus on the three major faults in the area, but I also identify other unknown faults based on

interpreting local seismicity. Another notable geological feature in the region is Shuswap

Metamorphic Core Complex (MCC). The Shuswap MCC is a large metamorphic body located in

the hinterland of the Canadian Cordillera (Platt et al., 2015). The Shuswap MCC comprises of

north-south striking domelike structures comprised of high-grade metamorphic and plutonic rocks

in southeastern British Columbia and northeastern Washington (Parrish et al., 1988;

Vanderhaeghe et al., 1999).

The Malton Gneiss (MG) is the northern limit of this extending Shuswap Metamorphic Core

Complex that exhumes to the centre of the southern half of the Canoe Reach network. Perhaps, the exhumation of the MG indicates that it may be a source of active extension in the area. Due to its close location, the metamorphic core complex affects the seismic wave velocities across our study area and plays an important role in exposing the zone of deformation. From the southern

Rocky Mountain Trench in the north and the North Thompson-Albreda to the south of my study area, I observe zones of active extension along these faults at depth. Chapter 3 discusses these

zones of deformation and seeks to improve our understanding of the structure of the southern

Rocky Mountain Trench.

Statement of Contribution

Chapter 2 & 3: Both chapters are based on a data set that was recorded in the field from Sep 1st,

2017 to August 31st, 2018. Joshua Chris Shadday Purba (JP) contributed to station deployment,

maintenance and data retrieval during four field trips in this period. JP conducted organization of

data and signal processing through filtering, instrument response removal, and decimation of

data. JP also performed two detection methods, based on kurtosis and STA/LTA, to identify

potential signals. An association method and manually review potential signals were implemented

by JP. The picking algorithm for arrival times is also written by JP. The implementation for the

location algorithm was guided by Jan Dettmer (JD). The interpretation of the seismicity was aided

by Hersh Gilbert (HG).

Chapter 2: This research was initiated by a collaboration between Borealis Geopower Inc.,

Nanometrics Inc., and the University of Calgary, under the supervision of HG and JD. JD provided

the inversion algorithm which was adapted to this specific study by JP. The hypocentre location

and uncertainty estimation of the 47 earthquakes in the region are the work by JP. All the figures

and tables used in this chapter are the work of JP. The manuscript was written by JP with

contributions by the co-authors. Permissions to use the publication as part of the thesis can be

found in Appendix A.

Chapter 3: This manuscript carries out a tectonic interpretation of the Southern Rocky Mountain

Trench using the 47 hypocentre locations and uncertainties from the multiple-earthquake location

method. All figures and tables used in this chapter are the work of JP. The manuscript was written

by JP with contributions from the co-authors. Permissions to use the publication as part of the

thesis can be found in Appendix A.

Chapter 2. Nonlinear Multiple Earthquake Location and Velocity Estimation in the Canadian Rocky Mountain Trench

Key points

● Nonlinear multiple-earthquake location method reduces uncertainty.

● Rigorous location uncertainty quantification in an area with little prior knowledge.

● Probabilistic earthquake catalogue for central Canadian Rocky Mountain Trench with low depth uncertainty.

Abstract

Calculating earthquake hypocenters requires careful treatment, particularly when prior knowledge

of the study area is limited. The prior knowledge, such as wave velocity and data noise, are often

assumed to be known in earthquake location algorithms. Such assumptions can greatly simplify

the inverse problem but are less general than nonlinear approaches. A nonlinear treatment is of

particular importance when uncertainty quantification of locations is of interest. We present a

nonlinear multiple-earthquake location method applicable when little prior knowledge of the area exists. Efficient Markov-chain Monte Carlo sampling is employed in conjunction with a hierarchical

Bayesian model that treats earthquake hypocenter parameters as well as P-wave velocity, ratio

in P-/S-wave velocity, and P- and S-data noise standard deviations as unknown. Hypocenters for

multiple earthquakes are located concurrently to provide sufficient constraints for the parameters

P-wave velocity, ratio in P-/S-wave velocity, and P- and S-data noise standard deviations, which

are shared among events. The algorithm is applied to simulated and field data. With field data, 47

event hypocenters are located in one year of data from 10 sensors in the Canadian Rocky

Mountain Trench. To analyze the probabilistic solutions, we compare single-earthquake and

multiple-earthquake location for the 47 events and find that multiple-earthquake location produces

better-constrained solutions compared to the single-event case. In particular, depth uncertainties

are significantly reduced for multiple-earthquake location. The algorithm is inexpensive

considering it is based on a Markov-chain Monte Carlo approach and highly objective, requiring little practitioner choice for tuning.

Introduction

The estimation of earthquake hypocenter locations is crucial to reveal faults, but significant challenges exist for location studies. The under-determined and nonlinear nature of the location inverse problem is often addressed by several assumptions to form an over-determined and linearized inverse problem. For example, assuming seismic velocity structure as known can result in an over-determined problem (Sambridge, 1986). Nonlinearity is often addressed by linearization for practical reasons (Geiger, 1910; Flinn, 1965; Husen and Hardebeck, 2010), because linearized inversion is computationally less costly and the location problem is weakly nonlinear for some applications (Buland and Gilbert, 1976). Despite the advantage of inexpensive computation, linearization has some limitations. For instance, solutions to linearized inverse problems are commonly obtained iteratively by Gauss-Newton or damped least-squares methods starting from an assumed location (e.g., Sambridge and Kennett, 1986; Aster et al., 2019) which makes solutions dependent on a starting model and can cause subjective results. In addition, model specification is limited to weakly nonlinear parameterizations that permit linearization. For example, the degree of nonlinearity depends on the complexity of the chosen velocity model

(Sambridge and Kennett, 1986). Moreover, solution uncertainty is only valid within the linearization assumptions and may be of limited use (Tarantola, 2005). Nonlinear approaches overcome these limitations at significant computational cost.

Increases in computer performance led to increased consideration of the non-linear problem.

Earlier works focus on nonlinear optimization for parameter estimation (e.g., Kennett and

Sambridge, 1992; Billings and Zhu, 1994) and later works include probabilistic methods for parameter estimation and uncertainty quantification (e.g., Lomax et al., 2000, 2014). Efforts also

include consideration of complex velocity models (e.g., Husen et al., 2003) that are typically assumed to be known. However, unknown or poorly known velocity structure is a significant issue for linearized and nonlinear location methods. A widely applied approach is to base inversions on predicting travel times for a simple velocity model and then inferring station corrections to account for errors in the velocity model (e.g., Pujol, 1988; Shearer, 1997; Pujol, 2000).

The location of multiple earthquakes can also be considered a problem of relocation, where precise, relative earthquake locations are estimated for many earthquakes (Waldhauser and

Ellsworth, 2000). This double-difference approach sacrifices the ability to obtain absolute locations to improve precision: Errors due to path effects are avoided by pairing earthquakes occurring in close proximity in clusters. Relative travel times from cross-correlated waveforms further improve precision (Shearer, 1997). The linearized nature of the double-difference approach makes application to large catalogues possible and permits uncertainty estimation although within the limits of the linearized assumptions or bootstrap methods (Waldhauser and

Ellsworth, 2000).

In cases where earthquakes do not cluster, absolute locations are favoured. For our work, nonlinear Bayesian approaches (e.g., Tarantola, 2005) to absolute location are of particular interest. Hierarchical Bayesian models (e.g., Malinverno and Briggs, 2004; Dettmer et al., 2007,

2012; Bodin et al., 2012; Gelman et al., 2013) have been applied to multiple-earthquake location

where velocity errors are addressed by station corrections (Myers et al., 2007). Such hierarchical

models provide significant generality, including probabilistic phase labels (Myers et al., 2009).

Nonlinear Bayesian treatment also provides a straightforward solution to treat velocity parameters

of the Earth model as unknown. The effects of uncertainties on earthquake locations have been

considered in layered 1-D velocity models (e.g., Gesret et al., 2015) and for application of locating

seismic earthquakes for geometries and data typical in micro-seismic applications (e.g., Eaton,

2018). This estimation of both velocity structure and earthquake locations can be considered a

tomography problem and is typical in local earthquake tomography (Kissling, 1988; Thurber,

1992; Kissling et al., 1994). A Bayesian treatment of local earthquake tomography can be achieved in 3-D, however, this approach requires significant computational cost (Piana Agostinetti et al., 2015; Zhang et al., 2016).

Our work considers a nonlinear Bayesian formulation of the location problem for multiple events with a hierarchical noise model and unknown velocity structure. The motivation for this formulation is rooted in the desire to study seismicity employing modest seismic networks in regions with little or no prior knowledge that are characterized by limited seismicity. We consider data recorded during a 1-year period on 10 temporary broadband seismograph stations deployed near

Valemount, British Columbia, in the Rocky Mountain Trench (RMT). The data are challenging with only few, low-magnitude events and significant cultural noise. The limited previous geophysical studies in the area pose an additional challenge to characterize the distribution of earthquakes.

The RMT is characterized as a transitional structure between the Canadian Cordillera to the west, which is characterized by low seismic wave speeds (lithospheric averages), and the craton of the

North American interior, which possesses higher seismic wave speeds (e.g., Mercier et al., 2009;

Kao et al., 2013; Bao et al., 2014; Chen et al., 2019). The nearest study focusing on seismic velocities considered reflected and refracted waves from explosive sources 450 km to the south

(Zelt and White, 1995). That work found P-wave velocities of 5.7 km/s to 5-km depth, and ~6.1 km/s to 20-km depth in the vicinity of the RMT. More significant velocity structure was observed below 20-km depth. More specific information is not available for the portion of the RMT considered here which precludes using available velocity models to accurately locate local seismicity.

Our hierarchical model is parameterized by hypocentre parameters (latitude, longitude, depth and origin time) for each earthquake and 4 shared parameters that include compressional velocities

(Vp), the ratio of compressional to shear wave velocities (Vp/Vs), and the standard deviations for

the noise on picked P and S arrival times. We employ an adaptive Markov-chain Monte Carlo

(MCMC) sampling (Brooks et al., 2011) that results in only modest computational cost. We demonstrate the algorithm with simulated and field data. For field data, the locations of 47 events are located, recorded by a network of 10 stations using a desktop computer. All event depths are less than 20 km, with the majority at depths between 15 and 20 km. As a result, this catalogue of events is not well suited for estimating velocities as a function of depth. However, inversion results show that absolute location uncertainty is reduced significantly by simultaneously locating multiple events compared to locations obtained for single events.

Method

The location inverse problem uses four hypocentre parameters per earthquake: hypocentre longitude, latitude, depth, and origin time. For the area of interest in this study, limited seismological prior knowledge exists, which hinders estimating hypocentre locations. In addition, the available data are limited to recordings at 10 seismograph stations that are distributed across an aperture of less than 40 km in the north-south direction and 30 km east-west due to limited access in the region (Figure 2-1). The configuration of station and events hampers our ability to carry out tomographic studies. Therefore, we extend the hypocentre parameterization to include four shared parameters for the seismic velocities and data residuals. The seismic velocity model assumes a homogeneous half-space with a constant compressional-wave velocity (Vp) and

compressional-wave to shear-wave velocity ratio (Vp/Vs). We schoose this simple parameterization to limit the number of unknown parameters which is consistent with Ockham’s razor (e.g. MacKay, 2003). Under this simplifying assumption, seismic travel times are computed based on the Euclidean distance between stations and events, and predicted arrival times are

determined following an origin time . To examine the impact of theory errors caused by

𝜏𝜏

employing a uniform half space as a velocity model, we carry out a simulation study in the following section.

The residual-noise model accounts for picking errors and theory errors due to assumptions in our method, such as the velocity model parameterization. The noise model assumes independent, identically distributed (IID) Gaussian noise and that residual noise distributions for P and S arrival times are independent. Hence, the noise model is described by P-wave and S-wave standard deviations. Since the residual noise is a combination of theory errors and measurement errors, no reliable, independent estimates exist for standard-deviation parameters p and s. Therefore,

we assume broad, uniform prior distributions for these parameters. 𝜎𝜎 𝜎𝜎

Due to the limited number of stations used here, the data contain at most 20 arrival times

corresponding to the P- and S-wave arrivals at each of the 10 stations. However, the area exhibits significant cultural noise due to traffic (automobile and train) and other activity (e.g., forestry), and significantly fewer arrival times are typical for most earthquakes. This limitation results in large hypocentre uncertainty stemming, in part, from poor prior constraints on seismic wave speeds.

We overcome the issue by carrying out the concurrent locations of all 47 catalogue earthquakes,

where the shared parameters are estimated jointly by all earthquakes.

Figure 2-1. Map of the study area along the RMT. The locations of 10 seismic network stations are shown by triangles. Known fault locations are indicated for normal faults (solid) and thrust faults (dashed). Probabilistic epicentre locations for the 47 earthquakes located in this study are shown by the gray scale (white - low probability, black - high probability). Note that some probability density functions for location overlap each other. The northwestern and southern earthquake clusters are outlined by solid circumferences. The star marks the mode of the epicentre marginal distribution for earthquake 37.

The location problem is nonlinear and considered here without linearization by applying numerical sampling via Metropolis-Hastings sampling (MHS, Hastings, 1970), a widely applied MCMC method. Specifically, we employ a Bayesian framework and MHS for the estimation of the posterior probability density (PPD) which represents the solution to the inverse problem. For M model parameters m and N observed data dobs, Bayes’ theorem is given by

( ) ( ) = , (1) ( ) 𝐨𝐨𝐨𝐨𝐨𝐨 𝐿𝐿 𝐦𝐦 𝑃𝑃 𝐦𝐦 𝑃𝑃�𝐦𝐦�𝐝𝐝 � 𝐨𝐨𝐨𝐨𝐨𝐨 𝑃𝑃 𝐝𝐝

where ( ) is the likelihood function and = [ , , , , Vp, Vp/Vs, p, s] is the model with =

𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 1,…,Nev𝐿𝐿, 𝐦𝐦and Nev is the number of earthquake𝐦𝐦 s.λ The𝜑𝜑 prior𝑧𝑧 𝜏𝜏 ( ) is assumed𝜎𝜎 𝜎𝜎 to be uniform for 𝑖𝑖all parameters over wide bounds (Table 2-1) since only little 𝑃𝑃prior𝐦𝐦 knowledge exists and to let data information primarily constrain the solution.

Under the assumption of IID Gaussian errors, the data covariance matrix is = I, where 2 𝑗𝑗 𝑗𝑗 indexes the data sets for P- and S-wave arrival times and I is the identity matrix.𝐂𝐂 𝜎𝜎 It follows that

(e.g.,𝑗𝑗 Tarantola, 2005)

1 1 ( ) = ( ) ( ) = 2 exp , (2) 2 ( ) 𝑇𝑇 𝑃𝑃 𝑆𝑆 𝑗𝑗 𝑗𝑗 𝑁𝑁𝑗𝑗⁄2 𝑁𝑁 2 𝑗𝑗 𝐿𝐿 𝐦𝐦 𝐿𝐿 𝐦𝐦 𝐿𝐿 𝐦𝐦 � �− 𝑗𝑗 𝐫𝐫 𝐫𝐫 � 𝑗𝑗=1 2π 𝜎𝜎𝑗𝑗 𝜎𝜎

where the data residuals = ( ) are given by the difference of observed data and 𝐨𝐨𝐨𝐨𝐨𝐨 𝐨𝐨𝐨𝐨𝐨𝐨 𝐫𝐫𝑗𝑗 𝐝𝐝𝑗𝑗 − 𝐝𝐝𝑗𝑗 𝐦𝐦 𝐝𝐝𝑗𝑗 predicted data ( ), and NP and NS are the number of picks for P and S arrivals across the

𝐝𝐝𝑗𝑗 𝐦𝐦 network, respectively. Note that = , for both observed and predicted data, and Cd is a

𝐝𝐝 �𝐝𝐝p 𝐝𝐝s� diagonal matrix including Cp and Cs. The normalizing constants in eq. (2) for both P and S data

are important since these provide appropriate noise scaling. By employing the full likelihood

function, instead of a misfit function limited to only the exponent in eq. (2), this approach permits

the estimation of p and s (e.g., Malinverno and Briggs, 2004). Computational challenges arise

𝜎𝜎 𝜎𝜎

for nonlinear multiple-earthquake location due to the computational cost of the MH algorithm for large numbers of parameters, which requires appropriate tuning of the algorithm (Rosenthal,

2009; Mosegaard, 2012). We apply a specific form of diminishing adaptation (Dosso, 2002; Dosso et al., 2014) that has been shown to be effective in geophysical inference. The approach estimates the posterior model covariance matrix to provide both efficient step directions and step sizes.

𝑚𝑚 The estimation process exploits an 𝐂𝐂initial estimate that is based on a Laplace (linear)

𝑚𝑚 approximation (Laplace, 1986) around an arbitrary𝐂𝐂 starting model as

𝐦𝐦𝑠𝑠

= ( + ) , (3) 𝑇𝑇 −𝟏𝟏 −𝟏𝟏 −𝟏𝟏 𝐂𝐂�𝑚𝑚 𝐉𝐉 𝐂𝐂𝑑𝑑 𝐉𝐉 𝐂𝐂�

where J is the Jacobian evaluated at and is a prior covariance matrix employed to obtain a

𝑠𝑠 useful estimate when data information𝐦𝐦 is poor𝐂𝐂 �(Dosso et al., 2014). The estimate significantly �𝑚𝑚 improves initial sampling performance in many problems, even if is not in proximity𝐂𝐂 with the

𝑠𝑠 mode of the solution. In our work, is chosen by a random draw𝐦𝐦 from the prior distribution.

s Algorithm convergence is generally𝐦𝐦 faster for starting models closer to the mode of the PPD

(Brooks et al., 2011). However, in this application, convergence rates were virtually unaffected by

the choice of starting model.

After ~10,000 MCMC samples intended as burn-in period, empirically a few percent of the total

time required for the inversion, is replaced with a (nonlinear) sampling estimate of that

𝑚𝑚 𝑚𝑚 further improves efficiency by avoiding𝐂𝐂� the linearization of eq. (3). Note that perturbations𝐂𝐂 are

applied in principle-axes (PA) space to individual parameters, not by a multivariate Gaussian

distribution. The rotation to PA space is based on the singular value decomposition of = .

𝑚𝑚 Importantly, the MCMC proposal distribution is then constrained in direction by the rotation𝐂𝐂 matrix𝐔𝐔𝐔𝐔𝐔𝐔

and in size by the singular values which represent variances in the direction of principal axes.

To𝐕𝐕 allow occasional large steps, we employ a Cauchy rather than a Gaussian distribution as a

proposal distribution (Dosso, 2002). The application of a principle axes rotation permits

perturbation of individual elements of the rotated parameter vector which is more efficient than

employing a multivariate Gaussian proposal with covariance (Dosso et al., 2014).

𝐂𝐂𝑚𝑚

Table 2-1. Prior bounds for inversion parameters.

Explanation Lower bound Upper bound

𝒎𝒎 longitude -118oW -120oW

𝜑𝜑𝑖𝑖 latitude 52oN 52.5oN

λ𝑖𝑖 depth 0 km 35 km

𝑧𝑧𝑖𝑖 Origin time relative to 0 s 10 s the first P- arrival 𝜏𝜏𝑖𝑖

Vp P-wave velocity 4 km/s 7 km/s

Vp/Vs P- to S- velocity ratio 1.42 2

p Noise in P- arrival 0 2s

𝜎𝜎 s Noise in S- arrival 0 2s

𝜎𝜎

The MCMC sampling produces a solution to the inverse problem in terms of a large ensemble of model parameter sets that are consistent with data and prior information and approximate the

PPD of the problem. Inferences about Earth properties can be extracted from this PPD estimate by various metrics. Many of these are straightforward (e.g., the posterior mean parameter estimates). Some important metrics are obtained by marginalization, which can be applied in

several contexts. Marginal distributions for individual parameters, e.g., for parameter , are

𝑖𝑖 obtained by integration 𝑚𝑚

( | ) = ( ) ( | ) , (4) ′ ′ 𝑃𝑃 𝑚𝑚𝑖𝑖 𝐝𝐝 ∫𝑀𝑀 𝛿𝛿 𝑚𝑚𝑖𝑖 − 𝑚𝑚𝑖𝑖 𝑃𝑃 𝐦𝐦 𝐝𝐝 𝑑𝑑𝐦𝐦 where δ is the Dirac delta function. The concept generalizes to higher-order marginals and is

applied here to epicentre and hypocentre marginals for multiple earthquakes. A second important

inference metric we extract from marginal distributions are credibility intervals (CIs). We choose

95% CIs which represent the highest probability density (i.e., the narrowest) intervals that contain

95% probability.

To judge convergence, the location method employs two independent Markov chains with

independent starting models. Inferences from the two chains in terms of marginal distributions

(eq. 4) normalized to unity are compared periodically during the sampling process. Once these

marginals agree to within a pre-defined tolerance , the inversion is deemed to have converged.

The difference in marginal distributions for judging𝜸𝜸 convergence is always taken to be the

maximum difference for the parameter vector. For the convergence test, all parameters are considered unitless by scaling to [0,1]. Empirically, = 0.1 produces acceptable results. For a better visual presentation, we choose = 0.05. 𝜸𝜸

𝜸𝜸

Simulation Results

This section presents the results from two simulation studies to illustrate the performance of the algorithm for known true models. Simulation 1 considers a case where the true model is consistent with the assumed model in the inversion. Therefore, no theory error exists in this case. Simulation

2 considers data based on a velocity model with a single layer over a half space and then assumes a uniform half space in the inversion. Therefore, this case includes theory error and we study the effect of this error on the results.

Simulation 1

In this simulation, travel-time data are computed using a uniform half space velocity model with

Vp = 6.0 km/s and Vp/Vs = 1.68. The geometry of the seismic network is taken from the field measurements. Similarly, the 47 simulated earthquakes have hypocenters based on the catalogue presented later in this paper. The computed data are contaminated by zero-mean,

Gaussian-distributed noise with standard deviations p = 0.13 s and s = 0.18 s. Multiple-

earthquake location is carried out under the assumption𝜎𝜎 of a uniform elastic𝜎𝜎 half-space. Figure 2-

2 shows the results in terms of total error marginal densities, sorted according to hypocenter

distance from the network centroid. These marginals are obtained by subtracting the true model

parameter values form the posterior marginals of the solution. The results demonstrate that the

true parameter values fall within the estimated uncertainties for all earthquakes. In addition,

uncertainties increase with hypocenter distance from the centroid, and uncertainties are larger for

depth and origin-time offset, compared to latitude and longitude. Figure 2-3 shows biases of marginal distribution modes with respect to true parameter values. The histogram show that modes are not significantly biased.

Simulation 2

The second simulation considers the case where data are computed for a layered velocity model which is not accounted for in the inversion. Therefore, this simulation considers the estimation of hypocenter locations in the presence of theory error due to velocity-model mismatch. The motivation of this section is to provide justification for the assumption of a uniform half space in the location algorithm for our specific case. A previous study (Zelt and White, 1995, Figure 4) estimated Vp structure of a transect crossing the RMT ~450 km south-east of Valemount. That study infers modest velocity-depth dependence near the RMT in the top 20 km. Based on this information, we define a velocity model consisting of a single 5-km thick layer with Vp = 5.7 km/s and Vp/Vs = 1.69 over a half space of Vp = 6.1 km/s and Vp/Vs = 1.69. We compute travel-time

data with this model via ray shooting and add zero-mean, Gaussian-distributed noise with

standard deviations p = 0.13 s and s = 0.18 s. The geometry is identical to that in simulation 1.

The simulated data are inverted with our algorithm assuming a uniform half-space with unknown

Vp, Vp/Vs ratio and noise parameters. Figure 2-2 shows total error marginal densities in

comparison to simulation 1. Simulation 2 does not perform significantly worse than simulation 1, suggesting only modest theory error. Figure 2-3 shows biases of marginal distribution modes in comparison to simulation 1. Both simulations perform similarly. We conclude that the assumption of a uniform half space is a parsimonious model choice that is justified for this specific case with limited information content due to network limitations for areas with limited velocity-depth dependence in the top 20 km of crust.

Figure 2-2. Results of two simulation studies in terms of absolute error marginal distributions, where true parameter values correspond to values of 0. Earthquakes are sorted according to increasing distance from the network centroid from top to bottom. The 10 nearest events of a total of 47 events are shown. The remaining events are shown in the supplement. Black lines represent simulation 1 and gray lines simulation 2.

Figure 2-3. Simulation results: Histograms of hypocentre-parameter mode biases for all earthquakes. Simulation 1 results in gray and simulation 2 results in black.

Field Data and Results

This section describes the results from applying the nonlinear multiple-earthquake location method to the RMT data. This dataset includes one year of continuous sampling by 10 broadband sensors (120 s) surrounding the Rocky Mountain Trench in the area of the Canoe Reach geothermal field in western BC (Figure 2-1) between August 2017 and August 2018. One challenge with this study area is that it has largely gone unexplored by earlier geophysical investigations, leaving its pattern of faulting and level of seismicity poorly constrained. It is this lack of prior information that makes employing a nonlinear earthquake location approach that requires few assumptions attractive. Through continuously sampling this area, our deployment of

10 seismometers detected 47 local earthquakes in the study area during one year of recording.

To assess the effectiveness of our approach, we carry out inversions for locations of single earthquakes as well as multiple earthquakes. We apply the multiple-earthquake inversions to the complete dataset of all 47 earthquakes and two separate earthquake clusters of 18 and 10 earthquakes, which are located in the northwestern and southern portions of our study area, respectively. We first present detailed inversion results for earthquake 37 (see catalogue information in Supplement Table E-1).

Figure B-3 shows the epicentre marginal distribution for earthquake 37, located near the northwestern cluster of earthquakes. The inversion for earthquake 37 is only constrained by 6 P-

and 7 S-wave arrival times. The parameter estimates (taken to be the mode of the marginal

distributions) for the errors on these picks are 0.05 s for P and 0.12 s for S, which is consistent

with P arrivals generally being clearer to pick in these data. The 1D marginal distributions and

95% CIs for the hypocentre (latitude, longitude, depth, origin time) and shared (Vp, Vp/Vs, p, s)

parameters of this earthquake are shown in Figure 2-4. Significant uncertainty exists 𝜎𝜎for 𝜎𝜎all parameters when locating this earthquake individually. For Vp the 95% CI extends 1.4 km/s

(between 5.2 and 6.6 km/s) and for Vp/Vs it extends 0.45 between 1.45 and 1.9. The uncertainty for p is from 0.01 to 0.4 s and for s from 0.04 to 0.8 s. These large uncertainties in shared parameters𝜎𝜎 cause significant uncertainty𝜎𝜎 for the earthquake location. The 95% CI for depth is 16 km wide (between 3 and 19 km), for longitude 10 km wide, and for latitude 7 km wide. Importantly, nonlinear effects are visible in the asymmetric, tailed, and peaked distributions (Figure 2-4) that do not resemble Gaussian shape.

Figure 2-5 summarizes the inversion results for shared parameters of multiple-earthquake and single-earthquake locations. Three sets of results are presented for the full catalogue, for the northwestern cluster, and for the southern cluster. These results show that multiple-earthquake location significantly reduces the uncertainty of shared parameters in all three cases. In particular, as the number of earthquakes increases from 10 to 18, and finally to 47, uncertainty consistently decreases. The most significant decrease in uncertainty is observed when increasing the number of earthquakes from 10 to 18. In addition, we observed that single-earthquake results generally include the multiple-earthquake results within their uncertainties, suggesting that the results for single earthquakes are consistent with those for multiple earthquakes but much more uncertain.

We conclude that the information about these shared parameters is consistent among earthquakes.

Figure 2-4. Inversion results for earthquake 37 in terms of 1D marginals of longitude, latitude, depth, and origin time (top), and Vp, Vp/Vs, p, and s (bottom). Dashed lines represent 95% credibility intervals. The plot boundaries represent the width of the uniform prior distributions, 𝜎𝜎 𝜎𝜎 except for latitude and longitude, where bounds were significantly wider than shown to span the full study area. Solid lines show Gaussian distributions with means and standard deviations taken from the marginals for comparison.

Figure 2-5. (Top) Comparison of inversion results in terms of 1D marginals of shared parameters for the location of 47 single earthquakes (gray lines) and multiple-earthquake locations for the same 47 earthquakes (black lines). Dashed lines represent 95% credibility intervals for the multiple-earthquake locations. (Middle) The same information for the northwestern cluster of 18 earthquakes. (Bottom) The same information for the southern cluster of 10 earthquakes.

For multi-earthquake locations of all 47 events, the inversion includes 188 hypocenter parameters and 4 shared parameters. Compared to individual-earthquake location of earthquake 37, the width of the 95% CI for Vp is reduced from ~1.4 to 0.2 km/s and only extends from 5.9 to 6.1 km/s. The

width of the 95% CI for the Vp/Vs ratio is reduced to 0.1 and is estimated to be between 1.6 and

1.7 compared to 1.45 to 1.9 for the single earthquake inversion of earthquake 37.

To further explore the benefit of locating multiple earthquakes, the effect of ray geometry and number of earthquakes is examined. We carry out multiple-earthquake location of a cluster of 18

earthquakes near the northwestern corner of the study area and for a cluster of 10 earthquakes in the southern part of the study area (locations of both clusters are shown as ellipses in Figure

2-1). The width of the 95% CI for Vp for the northwestern cluster is 0.3 km/s, and for the southern

cluster 0.4 km/s. The results in terms of shared parameters for both clusters are similar to those

of 47 earthquakes and suggest that spatial variability in velocity is unlikely to be severe in the

area. The difference in the results is insignificant despite the different data used in each case of

multiple-earthquake inversions. In addition, the effect of the ray geometry and number of

earthquakes influences the uncertainty of the shared parameters. Since the northwestern cluster

is closer to the network and contains more earthquakes, it produces narrower 95% CIs for velocity

than the southern cluster.

Figure 2-6 and 2-7 summarize the main result of this study in terms of 95% CIs and compares

the results of single-earthquake inversions to those of multiple-earthquake inversions. Given the

limited amount of available data and the significant cultural noise sources in the area, multiple-

earthquake location provides significant advantages over single-earthquake locations.

Uncertainties are significantly reduced for all parameters during the multiple-earthquake

inversion. Single-earthquake inversions produce large depth uncertainties, 15 km on average

(Fig. 2-6). Inverting multiple earthquakes reduces these uncertainties to an average of 5 km,

providing clearer distinction of earthquake depths that can be useful for tectonic interpretation.

Figure 2-6. Modes and 95% CIs from the multiple-earthquake inversion for hypocentre parameters for 47 events (black). For comparison, results from single-earthquake inversions are presented (gray). In all cases, dots mark marginal distribution modes and error bars indicate the lower and upper limits of 95% CIs for each parameter. The gray and black symbols are slightly offset in the horizontal direction for better visualization. The vertical dashed line highlights earthquake 37.

Locating earthquake 37 as part of this multiple-earthquake inversion for the full catalogue, we find that the width of the 95% CI for depth reduces to only 3 km (from 9 to 12 km). This large reduction in depth uncertainty is a result of a reduction in the uncertainties in the shared parameters of seismic wave speeds (Vp and Vp/Vs) and noise parameters (Fig. 2-7).

The reduction in depth uncertainties allow for the catalogue to be better utilized for examining the structure of the region and the tectonic processes responsible for its formation. Although the 95%

CIs in Figure 2-6 and 2-7 provides a compact presentation of the results, 1D marginal distributions

(Figure B-4) and epicentre marginal distributions Figure 2-1 are also provided. In particular, Figure

B-4 provides an uncertainty comparison in terms of marginal distributions for the cases of multiple- earthquake locations for the full catalogue and the corresponding single-earthquake locations.

The earthquake catalogue is also summarized in Table E-1, including uncertainty estimates.

The location errors observed here are significant in comparison to relocation studies (e.g.,

Waldhauser and Ellsworth, 2000). In linearized relocations uncertainties of less than 1 km in depth and less than 100m in the horizontal are common (Waldhauser and Ellsworth, 2000, Figure 6).

However, the data considered here are from a network with limited coverage and only 10 stations.

In addition, we do not consider relative locations, but absolute locations based on hand-picked phase arrival times. In addition, we do not apply correlation techniques to estimate relative travel times.

The epicentre marginals presented in Figure 2-1 show varying degrees of correlation that are consistent with the network shape (elongated in a northwest-southeast direction). Accordingly, epicentre-location uncertainties are elongated perpendicular to the trend of the network in the northeast-southwest direction and uncertainties are generally larger for earthquakes that are farther from the centroid of the network.

Figure 2-7. Same as Fig. 2-6 but for shared parameters. Horizontal black lines are for the joint inversion results and represent the extent of the 95% Cis. The vertical dashed line highlights earthquake 37.

Finally, we consider inversion results in terms of data residuals in Figure 2-8. Because of including a greater number of observations, inversions that simultaneously solve for the locations of multiple earthquakes generally produce larger P- and S-residuals. The spread in the pattern of residuals from the multiple-earthquake inversions confirms this trend, as we observe the residuals to be distributed more widely (with a greater number of larger residuals) than those for the single- earthquake inversions. However, we see from the distribution of residuals (Fig. 2-8) that the differences are minor and suggest that inversions considering single or multiple earthquakes can similarly fit the observations.

Figure 2-8. (Left) P-wave arrival-time residuals for multiple-earthquake inversions (dashed black line) compared to the corresponding single-earthquake results, where residuals for all single- earthquake inversions are shown as a single histogram (solid gray grey). (Right) The same information but for S-wave arrival-time residuals.

Discussion and Conclusion

We present a simple and efficient multiple-earthquake location method that considers P- and S- wave arrival times and makes use of little prior information. The method avoids subjective assumptions about model parameters by applying a Bayesian hierarchical model that accounts for unknown seismic velocities and unknown arrival-time picking errors. These hierarchical/shared parameters are not replicated for multiple earthquakes which allow inversions of multiple earthquakes to better constrain seismic velocities and significantly reduced uncertainties in depth estimates for multiple-earthquake locations. However, the benefits of considering large numbers of earthquakes concurrently are likely limited as illustrated for the inversions of 2 smaller clusters of 10 and 18 earthquakes that produced similar reductions in uncertainty when compared to the inversion using the full catalogue of 47 earthquakes.

The velocity values that we invert for in the Canoe Reach area are consistent with regional values in the literature (e.g., Zelt and White, 1995; Kao et al., 2013; Bao et al., 2014; Chen et al., 2019).

In general, we observed depth estimates benefiting most from multiple-earthquake inversion, with

uncertainties reduced from 95% CI widths of ~18 km to ~9 km. This result is important for

subsequent tectonic interpretations, where earthquake depths provide important constraints (e.g.,

Jackson, 2002; Chen et al., 2019). Finding reduced uncertainties in earthquake depths due to

diminished uncertainties in seismic velocities in the multiple-earthquake inversions highlights the

importance of appropriate seismic models to obtain reliable earthquake depths.

Interestingly, the velocity estimates for inversions of the data set that included the full catalogue,

the northern cluster, and the southern cluster reveal similar values with significant overlap of 95%

CIs. Therefore, we conclude that the assumption of a homogeneous half-space velocity model is

reasonable for our purposes. However, for more general treatment of the velocity model, the

method will increasingly resemble the problem of a local earthquake tomography and require

more data (more earthquakes and more stations) to constrain complex velocity models.

Computational cost would also increase significantly in that case (Piana Agostinetti et al., 2015;

Zhang et al., 2016; Zhang et al., 2018).

To further analyse the results, we have identified that some of the parameters are either positively, negatively, or not correlated at all. For example, the latitude and longitude parameters at earthquakes in the southern cluster exhibit a positive correlation mainly due to the arrangement of the network which is elongated toward northwest-southeast (i.e., perpendicular to the southern cluster). This additional finding is demonstrated in electronic supplement Figure B-5.

The generality of a Bayesian model formulation and nonlinear treatment of the inverse problem resulted in pragmatic advantages. Importantly, hierarchical treatment of data errors accounts for both theory errors (due to errors and simplifications in the geophysical model) and measurement errors (due to noise in the environment and the recording process) and reduces the need for subjective assumptions being made in our analysis. The picking errors estimated by the inversion appear reasonable when considering the combination of picking uncertainty as well as theory errors due to the assumption of a uniform semi-infinite half-space.

We find that the multiple-earthquake location applied here is well-suited for applications involving modest data sets with little prior knowledge. In such situations, we show that employing a nonlinear inversion and treating data errors as uncertain results in significant advantages including reduced parameter uncertainty and that these uncertainties decrease when concurrently inverting for the locations of multiple earthquakes.

The method requires only modest computer resources and the concurrent location of 47 earthquakes requires ~20 CPU hours on a single core of a typical desktop computer. More details regarding algorithm convergence are in Figure B-6. Since interacting MCMC methods such as parallel tempering (e.g., Dettmer et al., 2013) scale well with the number of CPUs, this location is expected to scale as ~1/NCPU for computation time.

Chapter 3. Evolution of the Southern Rocky Mountain Trench using local seismicity

Summary: This study assesses the distribution of seismicity and the pattern of deformation of

the Southern Rocky Mountain Trench using data from a local network of seismometers around

Valemount, British Columbia, in western Canada. The Southern Rocky Mountain Trench hosts a series of hot springs that align with northwest-southeast trending thrust faults that accommodated shortening during the formation of the Canadian Cordillera. This study identifies the distribution of structures in the area surrounding Valemount based on a probabilistic earthquake catalogue for a twelve-month period spanning from September 2017 to August 2018. Together with results

from earlier geological and seismic studies, our new earthquake catalogue illuminates the extent

and geometry of faults in the subsurface. The westward dip of the Southern Rocky Mountain

Trench fault is one of the prominent subsurface structures that we quantify utilizing the rigorous

uncertainty estimates of the probabilistic earthquake catalogue. The boundaries of the Malton

Gneiss, which comprises the northern portion of the Shuswap metamorphic core complex, can

also be identified in the earthquakes detected here. We infer the underlying domelike shape of

the northern portion of the core complex based on the distribution of seismicity. Overall, the study

provides an interpretation of the local tectonic setting of the Southern Rocky Mountain Trench

using a distribution of local earthquakes near Valemount.

Key words: Earthquake dynamics, Continental tectonics, crustal structure, seismotectonics, North America

1. Introduction

The Canadian Cordillera in western Canada is structurally complex and one of the most prominent topographic and tectonic features on the North American continent. From subduction of the Pacific plate under the North America plate near the west coast, to deformation front at the North

American craton, the cordillera is the site of ancient and active zones of deformation. The formation of the Canadian Cordillera began as a result of the compressional orogeny of the rifted margin of western Canada during the collision and accretion of allochthonous terranes (Monger

& Price, 2002). The collisions themselves started in the Middle Devonian (~390 Ma) when oceanic lithosphere collided with, and subducted beneath, the North America plate, (e.g., Monger & Price,

2002; Monger & Gibson, 2019). The succession of collisions led to crustal thickening (Monger et al., 1982), faulting, folding, and metamorphism of the continent (Staples et al., 2014). The oblique nature of these collisional events led to a significant strike-slip component to the intraplate deformation (Monger & Price, 2002). Compressive forces associated with the collisional events gave way to an extensional environment in the Eocene (55-45 Ma) when the boundary on the western margin of the cordillera transitioned to a transform margin (Monger & Price, 2002; Monger

& Gibson, 2019). Today, the Canadian Cordillera can be subdivided into five morphogeographic belts, the Insular belt, Coastal belt, Intermontane belt, Omineca belt, Foreland Fold and Thrust belt (Figure 3-1; Monger & Price, 2002). The 750 Ma evolution of uplift and erosion of the

Canadian Cordillera is still preserved today in both the Canadian Cordillera itself and the sedimentary basins of western Canada.

Stretching from the British Columbia-Yukon border to Montana, the Rocky Mountain Trench

(RMT) is of scientific interest because of its exposure of a nearly linear valley that extends for

1600 km (Figure 3-1). Located between the Omineca and Foreland belts in the Canadian

Cordillera, the RMT is characterized by distinct northern, central, and southern segments (van der Velden & Cook, 1996). The linear shape of the RMT is likely controlled by basement structures

within the cordillera and was influenced by oblique convergence during the Late Cretaceous and

Paleocene (van der Velden & Cook, 1996).

The RMT is a U-shaped valley that is 5-13 km wide and 1-2 km deep. Exceptions to this general shape occur along the trench where it narrows and becomes more V-shaped (Armstrong, 1959;

Leech, 1966). The trench is highly asymmetric between Radium Hot Springs, B.C., and the

Canada-US border, with a steep valley wall on its east side and a gentle, gradual slope on the western side along the Purcell Mountains. The trench reaches its greatest width of 30 km near

Cranbrook, B.C. (van der Velden & Cook, 1996).

As described by van der Velden & Cook (1996), the RMT can be divided into three segments; the

northern RMT, which appears to be a significant strike-slip fault that only experienced minor

extension, the central RMT which is characterized by thrusting in the Jurassic to Early Cretaceous

and minor normal faulting, and the extension in the southern RMT dated back to the Early

Cenozoic. The northern RMT continues northward to the Tintina trench as a transcurrent fault

with ~450 km of dextral motion that occurred post-mid-Cretaceous (Gabrielse, 1985). While some

strike-slip motion may continue southward from the northern RMT (e.g., Lambert & Chamberlain,

1988; Murphy 1990; Pope & Sears, 1997), little or no strike-slip displacement has been identified

in the Southern RMT between 49°N and 50.25°N, which instead hosted extension and normal

faulting (e.g., van der Velden & Cook, 1996). The transition between these two regions has been

classified as the Central RMT (Figure 3-1), which is characterized by thrust faults that formed

during the Jurassic to Early Cretaceous and transitioned to minor normal faults in the Cenozoic

(McMechan, 2000). The lack of evidence for dextral faulting south of the northern RMT between

latitudes of ~54°N and ~52°N has been suggested to result from a north-south change in relative

plate motion during Late Cretaceous to Early Eocene (McMechan, 2000; Reid et al., 2002). The

geologic record of faulting and deformation along the RMT in the central and southwestern part

of the cordillera suggests that it was active the Eocene (~45 Ma; Monger & Price, 2002; Simony

& Carr, 2011; Monger & Gibson, 2019). Transitioning to the northern limit of the Southern RMT, extension occurred within the Shuswap Metamorphic Core Complex (MCC), which is as a series of north-south striking domelike structures comprised of high-grade metamorphic and plutonic rocks in southeastern British Columbia and north-eastern Washington (Parrish et al., 1988;

Vanderhaeghe et al., 1999; Platt et al., 2015). The Shuswap MCC is the most exhumed section of the southern Omineca belt (Figure 3-1; Johnson, 2006). The Southern RMT is characterized by moderate to high flow and possesses numerous hot springs. Hydrothermal fluids exploit the northwest-southeast trending thrust faults that formed during shortening in the Canadian

Cordillera (e.g., Allen et al., 2006).

Following the transition from compressional boundary forces, the Shuswap MCC formed due to extensional forces as the thickened orogen began to collapse (Monger et al., 1982; Brown et al.,

1986; Brown & Journeay, 1987). The Malton Gneiss (MG) marks the northern extent of the

Shuswap MCC, which widens to the south (Figures 3-1 and 3-2; see location of Valemount for

geographic reference). The MG and Shuswap MCC are examples of domelike structures of

exhumed lower and middle crustal material in the eastern cordillera (Simony et al., 1980; Struik,

1988; McDonough & Parrish, 1991; Whitney et al., 2013). The MG consists of several bodies of

crystalline Precambrian rocks exposed over an area extending 40 km by 80 km (e.g., McDonough

& Parrish, 1991). The Southern RMT, Purcell Trench, Columbia River, North Thompson-Albreda

(NTA), and Okanagan faults (OF) all accommodated significant normal faulting during exhumation

of the Shuswap MCC and extensional collapse of the Omineca belt beginning in the Eocene

(Parrish et al., 1988; van der Velden & Cook, 1996). To the west of the Shuswap MCC lies the

Wells Gray volcanic field, which is a site of late Cenozoic volcanism in eastern B. C. (Hickson and

Souther, 1984). Holocene eruptions in the Wells Gray volcanic field were generally small volume

(<1 km3), suggesting that the magmas were aided in their assent to the surface by extensional

tectonics and thin crust (Hickson and Vigouroux, 2014).

Figure 3-1. Regional map of the RMT (Rocky Mountain Trench) within the Canadian Cordillera and bordering southeastern Alaska and northwestern Montana (modified after Wheeler et al., 1991). Five morphogeographic belts: Foreland Fold and Thrust belt, Omineca belt, Intermontane belt, Coastal belt, and Insular Belt. Red line is showing the central RMT, that extends from latitude ~52o to 54o and marks the transition between the southern and northern RMT. The black box shows the location of our study area. NRMT, Northern Rocky Mountain

Trench; SRMT, Southern Rocky Mountain Trench; MG, Malton Gneiss; Shuswap MCC, Shuswap Metamorphic Core Complex; PA, Purcell Anticlinorium; V, Valemount; WG, Wells Gray volcanic field; R, Radium Hot Spring; C, Crambrook; PT, Purcell Thrust; R, Radium; NTA, North-Thompson Albreda; CF, Canal Flats; FL, Flathead Lake; MT, Montana.

We detect and locate seismic activity near the junction of the Southern RMT and the NTA fault using data recorded by a temporary network of seismometers. There has been a lack of seismic studies that focus on the RMT between latitudes ~52°N to ~54°N. Accordingly, little is known

about the level of activity on faults in that area. We gain insight into the structure of the faults by

examining seismicity in the area of the RMT during the one-year deployment of the Canoe Reach

seismic network (Figure 3-2). Using the distribution of local seismicity, we study the subsurface

structure of Canoe Reach at the northern end of the MG, which is bounded by the RMT to the

east and the NTA to the west. The nonlinear method we used to locate this seismicity was

developed in earlier work by Purba et al. (2020). A strength of this Bayesian nonlinear approach

is that it fully quantifies uncertainty of the earthquake locations, which allows us to confidently

identify active structures and differentiate between locations of nearby earthquakes.

Figure 3-2. Map of the Canoe Reach network and the seismicity (modified after Cui et al., 2018). Stations are indicated by black triangles. The RMT, Rocky Mountain Trench; PT, Purcell Thrust; NTA, North Thompson Albreda; CM, Cariboo Mountains; RM, Rocky Mountains; Kinbasket Lake; Shuswap MCC, Shuswap Metamorphic Core Complex; MG, Malton Gneiss (modified after McDonough & Parrish, 1991). Four transect lines are drawn according to seismicity; red shaded zone indicates the earthquake included in corresponding transect line. Colour bar indicates earthquake locations at depth. The northwestern and southern earthquake clusters are outlined inside black ellipses. Three repeating events are located inside black dashed line.

1.a Previous Geophysical and Geological Studies

Seismic studies and the exposed geological information constrain the subsurface geometry of the

RMT. To the south of Valemount, near ~50oN, early refraction seismic studies show large-scale

variations in crustal thickness in the Southern RMT (Chandra & Cumming, 1972; Cumming et al.,

1979). Still around this latitude, crustal thickness varies from about 40-45 km east of the Rocky

Mountains, to 45-50 km beneath the RMT and Purcell anticlinorium, to ~35 km just west of the

Purcell anticlinorium (Cook & van der Velden, 1995; van der Velden & Cook, 1996). The

Lithoprobe project used seismic-reflection data to image the crust across the RMT near Canal

Flats, and across the Purcell anticlinorium (Figure 3-1; Cook et al., 1988). The reflection data revealed that North American crust and its deformed cover rock can be traced to the west of the

Rocky Mountain thrust and fold belt, beneath the RMT and Purcell anticlinorium (Cook 1988). The basement below the western Rocky Mountains and Purcell anticlinorium north of 49.25°N dips to the west at ~2° below the Rocky Mountains and steepens to ~13° on the west side of the trench

(Eaton & Cook, 1988; Cook et al., 1988).

The formation of the RMT has been examined based on structures exposed at the surface and presented on geologic maps (Wheeler et al., 1991, Cowan et al., 1997). However, underlying structures cannot be accurately unravelled based on the exposed geology alone. Therefore, incorporating observations from our local seismic study with previous investigations of the RMT will refine our understanding of its structure at depth.

2. Canoe Reach Earthquake Catalogue

2.a The Deployment, Instruments, and Network

Our study used a deployment of 10 three-component broadband seismic stations near the town

of Valemount and the Canoe Reach geothermal field. The network configuration spans 30 km

east-west and 35 km north-south and is centred around the northern end of Kinbasket Lake

(Figure 3-2). The average spacing between each station is ~5 km and varies from 3 to 12 km due to the mountainous terrain of the region. We consider detections over one year between 1

September 2017 and 31 August 2018.

2.b Earthquake Detection

Before carrying out earthquake detections in the Canoe Reach dataset, we remove the instrument response of the seismic time series and convert the waveforms to units of velocity. This time series analysis is accomplished using the Obspy instrument response function (Beyreuther et al.,

2010) and a water level of 60 during deconvolution. After removing the instrument response, we decimate the data to a common sampling rate of 50 Hz. To study local earthquakes with our station configuration, we anticipate the lower end of the detectability threshold of the network to be limited to smaller events with magnitudes > 0. Thus, it is reasonable to expect the frequency of the signals from these earthquakes to be lower than the 25 Hz Nyquist frequency of the data after filtering and decimating to a sampling interval of 50 Hz. To reduce the effects of unwanted noise, including from anthropogenic sources, we apply a 4th-order Butterworth filter between and

1-24 Hz to the decimated data. These processed waveforms are then input for two detection algorithms that we employ to identify local seismicity: (1) kurtosis-based detection and (2) short- term average to long-term average (STA/LTA) detection.

The kurtosis of a time series is a measure of the statistical distribution of the amplitudes of the signal. Sharp changes in amplitude associated with the abrupt onset of seismic arrivals affect the kurtosis value of the time series. Our detection method is like earlier investigations that identified seismic signals based on the kurtosis of a function (e.g., Baillard et al., 2014; Akram & Eaton,

2016). In this detection method, we calculate the kurtosis of the seismic time series in a five- second time window. By sliding the five-second time-window along the entire seismic time series for each channel, we calculate the continuous characteristic function (CF) for the entire network.

We dynamically define the kurtosis threshold by calculating it for the running kurtosis window as

the mean of the characteristic function (CF) added to the multiplication of standard deviation (std)

of the CF and a scaling factor (SCL) [kurtosis threshold = mean (CF) + std (CF) * SCL]. By using

a dynamic threshold, we require the CF exceed a higher value during noisy periods when the

standard deviation of the CF would be expected to be high. Based on testing a range of scaling

factors, we found that using a SCL value of 10 detected signals that appeared to be associated

with earthquakes without including too many spurious detections (Table 3-1).

In addition to the kurtosis method, we employ a standard STA/LTA detection algorithm (e.g., Allen,

1978). The STA/LTA ratio is sensitive to rapid fluctuations in signal energy. We use window lengths of 2 and 60 s, for the STA and LTA, respectively (Table 3-1). Unlike the kurtosis method, the STA/LTA trigger level is static with a value of 10. For a detected signal to be counted as an arrival and linked to a potential earthquake, it needs to be associated with a minimum of seven other detections by other channels in the Canoe Reach network within a 30-s window. Once triggered detections occur on at least eight channels within a 30 s time window, a potential earthquake is declared.

Table 3-1. Detection parameters for the kurtosis and STA/LTA methods in this study.

Detection methods Detection Parameters Kurtosis STA/LTA SCL (Scaling Factor for dynamic threshold) 10 n/a Static threshold n/a 10 STA time window n/a 2 s LTA time window n/a 60 s Kurtosis time window 5 s n/a Min. # of channels for declaration 8 8 Normal moveout window 22 s 22 s Low corner frequency 1 Hz 1 Hz High corner frequency 24 Hz 24 Hz

Using both kurtosis measurements and STA/LTA detections, our study of local seismicity identified 42 earthquakes before manually reviewing the triggered signals. We then manually reviewed the waveforms to refine the detections to those that we can confidently attribute to a local earthquake. Although both methods detected 37 overlapping earthquakes, kurtosis and

STA/LTA detection each identified five additional earthquakes. Following manual inspections for all detections, the final catalogue includes 47 earthquakes, (Table 2). Examples of waveforms from earthquakes that both methods detected are shown in Figure 3-3. The supplementary material also presents the waveforms for one example that was detected only by kurtosis detection (Figure C-2) and one example that was only identified by STA/LTA detection (Figure C-

3).

The Canoe Reach network was operated jointly with Nanometrics, who calculated local magnitudes (Ml) for a subset of 23 of the earthquakes detected here (Table S-2). The average Ml of those earthquakes is 0.7 and ranges between -0.14 and 1.79. The small magnitude of these earthquakes highlights why they are difficult to detect and locate. These earthquakes generally exhibit low-amplitude and subtle first arrivals (Figure 3-3). In addition to the arrival times of these low-amplitude phases being difficult to pick, their small and limited number of signals make calculating focal mechanisms difficult and not attempted here.

Using a nonlinear multiple-earthquake location method, we estimated locations and uncertainties with a Bayesian approach. Obtaining locations was hindered by the study being in an area with little prior knowledge of local structure. Using an earthquake location approach that does not depend on possessing a detailed model of the seismic velocities was critical to being able to locate these earthquakes without making assumptions of the regional structure. Further details of the Bayesian approach that we employed, which solves for earthquake hypocentre parameters as well as P-wave velocity (Vp), the ratio of P-wave to S-wave velocity (Vp/Vs), and the standard deviations of the error in arrival pickings can be found in Purba et al. (2020).

Figure 3-3. Three-component seismograms presenting earthquake number 21 in our catalogue. This earthquake occurred on 2018-01-21 at 04:26:12 UTC. Waveforms are filtered between 10 - 20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals. Both STA/LTA and kurtosis detections declared this as a potential earthquake because of detections in all channels. Traces of plotted for all 10 Canoe Reach stations arranged in numeric order CRG01-CRG14 from top to bottom. Left column – east-west channel; centre – north-south channel; and right – vertical channel.

The location of 47 earthquakes also provided seismic-wave velocities in a homogenous half- space. We choose 95% Credibility Intervals (CIs) to represent the highest probability density intervals that contain 95% probability of the location parameters (Purba et al., 2020). The 95%

CIs for Vp are 5.9 to 6.1 km/s and for Vp/Vs ratio 1.67 to 1.70 (Purba et al., 2020). This compressional-wave velocity agrees with the result of the Lithoprobe refraction study (Clowes et al., 1995) which found seismic velocity between 6.0 – 6.3 km/s in the upper crust of the Omineca

belt to the south of our study area. Attaining reliable earthquake locations and estimates of seismic velocities reveals the distribution of subsurface structures in this part of the cordillera and where they are active today. Identifying these structures can then be used to constrain the tectonic processes that may have shaped this portion of the Canadian Cordillera.

3. Description of Earthquake Locations

The distribution of 47 earthquakes in our catalogue can be divided into three groups. A cluster of

17 closely spaced earthquakes at a depth near 11 km is located in the northwestern portion of the study area. This northwestern cluster is located between the Purcell Thrust and the RMT (top- left ellipse in Figure 3-2). A second cluster of earthquakes is more diffuse, deeper, and is comprised of ten earthquakes that lie in the southern portion of our study area to the west of the

NTA at an average depth of 13 km (bottom-left ellipse in Figure 3-2). The remaining earthquakes are more sparsely distributed and extend along the strike of the RMT. These sparsely distributed earthquakes constitute the third group of earthquakes.

The effect of the distance between the earthquakes and the network of stations on earthquake location is seen in the range of uncertainties in earthquake depths. The depth uncertainty extends from 3- to 6-km for the earthquakes in the northwestern cluster, and from 10- and 14-km for the earthquakes in the southern cluster. The smaller uncertainties in the northwestern cluster results from these earthquakes being located closer to the network; Figure C-1 in electronic supplement shows a comparison of earthquake location uncertainties in a map view (Purba et al., 2020). The results in computing location parameters (e.g., latitude, longitude, depth, origin time) show non-

Gaussian shapes of the prior probability density, which are plotted as the 95% CIs (Figure 4 in

Purba et al., 2020).

3.a Transect A

Transect A is perpendicular to the RMT and crosses through the densest distribution of seismicity detected here. This transect includes the 17 earthquakes in the northwestern cluster, and five shallower earthquakes to the northeast (Figure 3-4a). Along this profile, earthquakes gradually deepen from less than 5-km in the east to nearly 15-km depth to the west. On this transect, the zone of active seismicity extends 10 km to the east of the RMT and 8 km to the west. The average depth uncertainty in this earthquake cluster is 4.1 km (Figure 3-4a).

3.b Transect B

Transect B, also perpendicular to the RMT, is to the south of Transect A (Figure 3-2). From the eight earthquakes located along Transect B, we observe that the pattern of deformation changes from north to south along this portion of the RMT. On this transect the zone of active seismicity extends for only 8 km to the east of the RMT and 17 km to the west (Figure 3-4b). The average depth is 14 km for the three earthquakes on the western half of this transect, one earthquake occurs in the centre of the transect at a depth near 5 km, and four earthquakes occur to the east and lie at an average depth of 8 km. The average depth uncertainty in this earthquake cluster is

3.6 km (Figure 3-4b).

3.c Transect C

Transect C is oriented perpendicular to the NTA and further south of the seismic network (Figure

3-4c). The transect includes seven earthquakes that are west of the surface position of the NTA, which lies about 6 km to the east of the easternmost earthquake along the transect. The distribution of seismic activity along this transect dips to the northwest, which differs from the two transects to the north. The earthquakes along this transect appear to lie along the NTA on the west side of the MG. At the latitude of this transect, which is located at the southern end of our

study area, the zone of seismicity extends 34 km to the west of the RMT, and we detect no seismicity to the east of the RMT. The average depth uncertainty in this earthquake cluster is 12.1 km (Figure 3-4c).

3.d Transect D

Viewing seismicity along a transect that parallels the RMT emphasizes the changing level of earthquake activity from north to south along the fault (Figure 3-4d). Seismicity along Transect D includes 24 earthquakes, most of which correspond to the closely spaced earthquakes in the northwestern cluster. The level of activity diminishes away from the northern portion of this transect. The more frequent earthquakes in the northern portion of this profile occur at an average depth of 11 km depth and less frequent earthquakes in the south occur at an average depth of 14 km. This transect clearly illustrates the higher level of active deformation towards the northern portion of the study area compared to the south. The average depth uncertainty in this earthquake cluster is 3.2 km (Figure 3-4d).

3.e Earthquake Location Uncertainties

The lack of uncertainty knowledge in earthquake locations hinders attributing deformation to specific structures and can lead to over-interpretation or erroneous conclusions. Quantifying uncertainties is particularly challenging while investigating regions such as Canoe Reach, where little prior information exists about crustal seismic velocities. The Bayesian approach employed here addresses this lack of prior information on crustal structure by simultaneously solving for event locations and seismic velocities within the range of 4 and 7 km/s for Vp and between 1.42 and 2 for the Vp/Vs ratio (see Purba et al., 2020 for further details). Our inversion solves for best fitting Vp and Vp/Vs values for a half-space encompassing the events. In addition to limiting subjective assumptions about seismic velocities, this approach provides a measure of uncertainty by reporting the range in seismic velocities and event locations that can match the observed

arrival times of our P- and S-wave picks (Purba et al., 2020). These assessments of uncertainties are especially useful in considering earthquakes along transect B (Figure 3-4b). We can see from the distribution of earthquakes and their depth uncertainties, that earthquakes towards the western and eastern margins of this transect are deeper than the earthquake near the centre.

This difference in depth is clearly resolved given the depth uncertainties.

Figure 3-4. Depth profile of the earthquake catalogue with error bars included. The error bars indicate the lower and upper 95% CIs, and dotted circles for the modes of earthquake depth distributions from the catalogue (Table 2). (a) Transect A consists of 22 earthquakes. Each earthquake is presented as a circle with a colour according to its depth. The elevation profile is provided above the depth profile. The inverted triangles denote the location of the seismic stations projected to the transect line; red dot for PT, Purcell Thrust; black dot for SRMT, Southern Rocky Mountain Trench. (b) Transect B includes eight earthquakes. Blue dot marks NTA, North-Thompson Albreda, projected to the transect line. (c) Six earthquakes are included under transect C, west of the NTA. Blue dot on the elevation profile marks the projected NTA to the transect line. (d) Transect D is comprised of 22 earthquakes under transect D, along the SRMT. A cluster of 17 earthquakes in the north located under station CRG10 and other five earthquakes to the south of the depth profile.

4. Discussion and Conclusion

We analyse 47 probabilistic earthquake locations to interpret the distribution of deformation within an area in the southeastern Canadian Cordillera with little previous knowledge on seismicity.

Comparing the distribution of seismicity in Transects A-D, we can infer the pattern of deformation on this portion of the RMT and the area surrounding the MG. The location of the northern cluster lies near the intersection of the RMT, NTA, and the Purcell Thrust (PT). This cluster represents the most active region of the faults investigated here. In Figure 3-4a, Transect A combines the northwestern cluster with five shallower earthquakes to the east of the transect. The depth of seismicity in this area increases from east to west on west-dipping faults that intersect the RMT at depth (e.g., Mountjoy 1980; Pana & van der Pluijm, 2014). The location of the northwestern cluster near the coalescence of multiple faults makes identifying the forces responsible for driving deformation in the region challenging. These earthquakes may mark strike-slip faulting on the

RMT or normal faulting on the NTA. Alternatively, they could be driven by compressive forces and shortening on the PT. Attaining focal mechanisms from these events will provide additional information needed to further constrain our interpretation. However, the limitations of this dataset have prevented determining mechanisms for these events to date.

Further south from transect A, transect B reveals a different pattern of seismicity, that aligns with the fault boundaries of the Shuswap MCC. The northern tip of where the MG is exposed at the surface, lies to the south of where the PT crosses the NTA and the RMT, which is located 5 km to the south of Transect B. The shape of the MG has been suggested to exhibit domelike structure

(e.g., Simony & Carr, 2011; Pana & van der Pluijm, 2014). Transect B includes one shallow earthquake near the centre of the transect line, three deep earthquakes in the west, and four earthquakes in the east with intermediate depth compare to the earthquakes in the west. All earthquakes are located with depth uncertainties that support their depths to be distinct between these three groups. The deeper seismicity to the east and west of the shallower earthquake in the middle supports a domelike structure of the MG in the subsurface. Based on this interpretation, the seismicity along Transect B would occur along the boundary between the exhuming MG and overlying hanging blocks. The exhumation of the MG would be consistent with the RMT and NTA acting as normal faults. In a deforming region, we would expect seismicity to primarily be located on existing faults, rather than within the block separating the faults.

The pattern of deformation in the southern portion of the study area spreads away from the RMT to the west of the NTA. The north-to-south broadening of the zone of seismicity tracks the NTA, which forms the western boundary of the MG and the Shuswap MCC. Assuming that the earthquakes in transect D lie along the NTA (Figure 3-4b & c), the westward dip to their distribution indicates the broadening of the dome shape of the MG with depth. The prevalence of seismicity to the west of the NTA and to the east of the RMT highlights that most of the earthquakes occur in the area surrounding the MG, rather than within it. This pattern of earthquakes may simply be due to the timing of deformation within the MG not coinciding with the one-year of monitoring that we consider here or that it is no longer an active structure. Alternatively, the lack of earthquakes within the MG may indicate that it deforms in an aseismic manner. The observed pattern of earthquakes that surrounds gneiss domes in the Pamirs similarly lies outside their surface

exposure (e.g., Schurr et al., 2014). Whitney et al. (2013) described ductile deformation zones within the MCCs to the south of the Transect D during the Eocene. We suggest that the seismic activity to the west of the NTA in transect C (Figure 3-4c), shows a clear boundary from ductile deformation within the MG to active brittle deformation on the hanging wall of the NTA.

The NTA has previously been identified as a normal fault (e.g., McDonough & Parrish, 1991), accordingly, the seismicity observed here would correspond to the block on the western side of the NTA moving downward and to the northwest. North-westward motion of the block along the western side of the NTA normal fault is compatible with dextral motion along the RMT to the north.

Extensional collapse of the southeastern portion of the Canadian Cordillera would contribute to normal faulting on the NTA. The change in the distribution of seismicity around the RMT and NTA at the northern limit of the MG and the Shuswap MCC may mark the transition in the style of deformation along the Canadian Cordillera from an extensional environment in the southeastern portion of the cordillera to a dextral shear zone further north. Seismicity is confined to a region that extends less than 20 km around the RMT to the north of Valemount. However, to the south of Valemount seismicity extends across a broader region that is more than 30 km wide and lies primarily to the west of the RMT. This difference in the distribution of deformation around the RMT may reflect a transition from a narrow fault zone to the north of Valemount and a broader region of extension to the south. Our data exhibit a zone of focused deformation at the intersection of the RMT and NTA normal faults to the north of the MG.

The migration of crustal fluids may also contribute to the distribution of seismicity observed across the Canoe Reach study area. The numerous hot springs present within the Southern RMT highlight the presence of warm crustal fluids in the shallow crust (Allen et al., 2006). The neighbouring Wells Gray volcanic field, which has been active in the Holocene (Hickson &

Vigouroux, 2014), also indicates that warm magmatic material is likely present in the shallow crust of the region. Further evidence for fluids influencing the crustal seismicity observed here comes

from some of the earthquakes observed here producing signals with highly similar waveforms

(Figure 3-5). Repeating clusters of earthquakes, with highly correlated waveforms, have been attributed to transient pressure gradients produced by the exsolution of fluids from magmas at depth (Shelly et al., 2015).

Figure 3-5. Vertical waveforms from three earthquakes that occurred on June 26th, 2018 recorded by station CRG04 (earthquake numbers 41 - bottom, 42 - middle, and 43 - top). These signals have been filtered from 5 to 15 Hz. In addition to similar P- and S-waves recorded near relative times of 1 and 2.5 s respectively, the waveforms also exhibit similar signals in their coda out to times of 8 s and later. Refer to Figure 3-2 for epicentre location of these three earthquakes.

The crustal velocities of the area reflect the presence of metamorphic rocks. Our inversion (Purba et al., 2020) that solved for the locations of earthquakes discussed here and for the seismic properties of a half-space encompassing these earthquakes found 5.9 - 6.1 km/s and 1.67 - 1.70

for Vp and Vp/Vs respectively. These seismic velocities are consistent with expectations for

metamorphic rocks, which generally possess lower values of Vp and Vp/Vs than igneous rocks

(Christensen, 1996; Hyvönen et al., 2007). Because the minerals that comprise the rocks within the Malton Gneiss and surrounding area contain a large amount of quartz (McDonough and

Parrish, 1991), their felsic composition also contributes to the observed low Vp/Vs values

(Christensen, 1996). Based on these seismic velocities, and the distribution of seismicity surrounding the MG, the portion of the southern RMT investigated here appears as a transition from a region characterized by narrowly focused brittle deformation to the north of Valemount and a wider zone of deformation to the south.

Chapter 4. Conclusions and recommendations

I studied local earthquakes near the Valemount, British Columbia, to answer questions about the tectonic evolution of the area. The study included deploying 10 seismic stations in August 2017 for a one-year recording period. Three maintenance field visits were conducted during this time span. Recorded data in this study extend from September 1st, 2017 to August 31st, 2018.

The seismic data include significant noise from traffic, logging and other sources, presenting challenges in distinguishing earthquake signals from noise. To address this, I applied two independent detection methods based on signal kurtosis and STA/LTA. Both methods led to an earthquake catalogue of 47 earthquakes and a high confidence that significant earthquakes were detected. However, further improvement in the completeness of the catalogue may be achieved in future studies by applying these 47 earthquakes as the parent earthquakes/templates in matched filtering technique, by applying exhaustive cross-correlation search, or more efficient

matrix-profile methods (Senobari et al., 2018).

The 47 detected earthquakes were studies by manually picking P- and S- arrival times for subsequent location. A limitation in the manual picking approach is human error which can result in inconsistencies. In future work, the picking may be improved by waveform cross-correlation methods of signals for earthquake pairs and/or station pairs (Shearer, 1997; Waldhauser and

Ellsworth, 2000).

Probabilistic (Bayesian) earthquake location was applied via Metropolis-Hastings sampling, a

Markov-chain Monte Carlo method. This algorithm solves the nonlinear inverse problem and provides earthquake locations and their uncertainties while relying on some prior assumptions.

Importantly, location requires knowledge about seismic velocities in the study area. Surrounding

Valemount, little such knowledge is available and led me to assume seismic velocities as unknown. While this approach can cause large uncertainty when locating earthquakes with only

a few seismic stations, the issue was overcome by concurrent location of the whole catalogue.

Compared to the single-earthquake case, our multiple-earthquake location defines a hierarchical

model where each earthquake is assigned unknowns for its location but shared parameters ( p,

s, Vp, Vp/Vs) describe data noise and seismic velocities. This multiple-earthquake location𝜎𝜎

𝜎𝜎substantially improves the parameter solutions by reducing uncertainties. Depth estimates

improved drastically from 18-km uncertainty when locating single earthquakes to 5-km uncertainty

for multiple-earthquake location. Similarly, the uncertainty for the half-space Vp improved from 5.3

– 6.7 km/s to 5.9 – 6.1 km/s and for Vp/Vs improved from 1.43 – 1.85 to 1.67 – 1.70 after applying

the multiple-earthquake inversion.

The hierarchical model made the significant assumption of a uniform half-space. This assumption

was examined by considering inversions for sub-sets of earthquakes and was found to be

reasonable. However, considering a velocity model with multiple layers would present a more

complete solution. Achieving this treatment would be a non-trivial extension to the existing

algorithm in both methodology and computational cos t. It could be addressed by treating the

number of layers as well as velocity parameters within the layers as unknowns (a trans-

dimensional model; e.g., Malinverno, 2002; Dettmer et al., 2010).

The nonlinear location method I present is associated with significantly higher computational cost

than traditional linearized methods. However, a solution for 47 earthquakes was obtained in ~20

hours on a single core of a personal computer. Therefore, the approach appears feasible in many

research settings. Parallel implementation is possible on both parallel computers and graphics

processing units which would permit treating much larger numbers of earthquakes. In addition, I

showed that the advantages of multiple-earthquake location diminish after a few 10s of

earthquakes. Therefore, clustering of earthquakes may help reduce the computational cost of

inversions.

The distribution of seismicity shows a distinct pattern, from a dense cluster that aligns with the

northern limit of MG to the north of Valemount to a broader zone of diffuse deformation to the

south that extends to the west of the NTA. The active seismicity pattern in the north has occurred

near the coalescence of multiple faults, which makes identifying the forces responsible for driving

deformation in the region challenging without focal mechanisms. Since focal mechanism solutions

can interpret the style of faulting in this region, the limitations of this dataset (comprised of only

small earthquakes) prevented their analysis here.

The presence of metamorphic bodies in this study, such as Shuswap MCC and MG, may be

affecting the calculated seismic velocities. From the hierarchical parameters in the location method, I obtained the range in the P-wave velocity and the P- to S- ratio to be between 5.9 - 6.1

km/s and 1.67 – 1.70, respectively. Perhaps, another constraint in measuring the seismic

velocities can be obtained from collecting rock samples in the area. These low seismic velocities

likely reflect the prevalence of metamorphic rocks in the portion upper crust sampled here

(Christensen, 1996; Hyvönen et al., 2007). In addition, the abundance of high anisotropic

metamorphic mineral sillimanite would likely be a source of seismic anisotropy (Digel et al., 1998;

Yang et al., 1996; van der Berg et al., 2005). Thus, future study can be directed to understand

the two types of anisotropy in the region (vertical and horizontal transverse isotropy) based on

variations in seismic wavespeed with direction.

In addition to investigating anisotropy in the study area, another suggestion is to perform an

earthquake magnitude study. Although I include local magnitude information from Nanometrics

(described in Chapter 3), having moment magnitude Mw can provide more objective magnitude

measurements for these earthquakes. Another suggestion is to apply coda and energy methods for moment magnitude estimation of these lower magnitude earthquakes (Aki, 1969; Rodríguez‐

Pradilla & Eaton, 2019). The method has been used in micro-seismic data, which tend to result in

lower magnitude earthquakes (Mw < 1).

From detecting local earthquakes near the southern RMT, I conclude that the region exhibits some active zones of deformation in the southeastern cordillera. Although previous tectonic studies have indicated the active deformation in this part of cordillera occurred in the Eocene (~45

Ma; Monger & Price, 2002; Simony & Carr, 2011; Monger & Gibson, 2019), this local earthquake study has revealed that the deformation is still currently active until today. Since the seismicity is focused in the northwestern cluster from the earthquake catalogue, one suggestion for future network configuration is to centre it around the northwestern cluster, then obtain focal mechanism solutions from a complete station azimuthal coverage to understand faulting style for each detected earthquake.

Data and Resources

Data in this study were recorded by the University of Calgary and are available from the authors upon request. The algorithm is available at https://gitlab.com/dettmer-jan/location-pt. Data

processing employed Obspy (Beyreuther et al., 2010) and Pyrocko (Heimann et al., 2017). The

earthquake location catalogue for Canoe Reach data is available in the electronic supplemental

material.

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Appendix A copyright permissions

https://www.seismosoc.org/publications/bssa-submission-guidelines/

Appendix B supplemental information for “Nonlinear Multiple Earthquake Location and Velocity Estimation in the Canadian Rocky Mountain Trench”

This supplement contains the probabilistic earthquake catalogue for the Rocky mountain

trench as a separate table and several additional figures that provide further information to

complement the figures in the main text. This Section Discussion presents additional insights that

some readers may find useful.

Discussion

Figure B-1 shows simulation results in terms of total error marginal densities, sorted

according to hypocentre distance from the network centroid. The marginals are obtained by

subtracting the true model parameter values from the posterior marginals of the solution. Results

from 2 simulations are shown. In simulation 1 the true model is consistent with the assumed model in the inversion (no theory error). In simulation 2 data are computed based on a velocity model with a single layer over a half space. The inversion is carried out under the assumption of a uniform half space (theory error exists). The first 10 rows are reproduced from the main text.

Figure B-2 shows simulation results in terms of marginal densities of shared parameters. The results for simulation 2 indicate that the inversion approximately resolves the average of the layered Vp model.

Figure B-3 shows the epicentre marginal distribution (i.e., latitude and longitude parameters) for earthquake 37 via single-earthquake inversion. Earthquake 37 is part of the northwestern cluster.

Figure B-4 summarizes the results of our study in terms of marginal distributions for hypocentre locations with parameters latitude, longitude, depth, and origin time. Results are for both multiple- earthquake inversions of 47 earthquakes and single-earthquake inversion of corresponding earthquakes. The marginals of the multiple-earthquake inversion are significantly narrower than

those of single-earthquake inversions. The narrower distributions correspond to solving a better determined problem, where a greater number of data are available to constrain the parameters.

In this case, for 47 earthquakes, there are 313 P and 375 S arrival-times available and the number of parameters is 192. For single-earthquake inversions, at most 20 arrival-time picks are available, and the number of parameters is 8. These 1D marginals exhibit significant nonlinear effects similar to those observed in the inversion of event 37 (Fig. 2-4, main text). These features emphasize the importance of employing a nonlinear inversion method for this problem. Table E-1 summarizes the 95% CI information.

Figure B-5 shows the posterior model correlation matrix for the multiple-earthquake location of 47

earthquakes. The correlation matrix is defined as = / , where are elements of

𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 the posterior model covariance matrix. Note that the𝑅𝑅 correlation𝐶𝐶 � 𝐶𝐶ma𝐶𝐶trix is symmetric.𝐶𝐶 The first 188

rows and columns of the matrix correspond to hypocentre parameters for 47 earthquakes. The

block-structure appearance is largely due to correlation patterns that repeat for various

earthquakes. For example, positive correlations between latitude and longitude are observed for

many earthquakes that are located in the southwest or northeast of the network. For example,

Figure B-3 (b) shows a portion of the correlation matrix of the 4 hypocentre parameters of earthquake 37. Latitude and longitude are positively correlated, while origin time and depth (third

row down) are negatively correlated.

The last 4 rows and columns of R correspond to the shared parameters Vp, Vp/Vs, p, s. More

detail about the correlations for these parameters is shown in Figure B-5 (c) for 11 earthquake𝜎𝜎 𝜎𝜎 s.

Earthquake 37 is highlighted by a black box and these correlations can be linked to the display of

Figure B-5 (b). A clear negative correlation exists between depth and both velocity parameters.

This is true for all earthquakes in the catalogue. The negative correlation means that higher velocity is required to locate an earthquake and more shallow depth. Therefore, this correlation explains the significant reduction in depth uncertainty when constraints on velocity are improved.

In addition, the origin time parameter and seismic velocity exhibit a positive correlation for all earthquakes.

Figure B-6 presents the algorithm history in terms of the convergence parameter γ for the multiple- earthquake location of 47 earthquakes. During the inversion, the algorithm samples from two independent Markov chains. That is to say, each chain samples all parameters of the model (e.g.,

8 parameters in the single-earthquake case, 192 parameters for the full catalogue). The convergence is evaluated in terms of 1D marginal distributions that are normalized to unity. The convergence parameter γ is defined as the maximum difference between marginal distributions for the two independent chains. The maximum is taken over all parameters. A subjective threshold for δ is set to evaluate convergence. In Figure B-6, the γ threshold was set to 0.01, far smaller than would typically be deemed sufficient. We observe, that meeting small threshold levels requires significant computational time with limited benefit for improved inferences. In this case, a threshold value of 0.05 was achieved after ~100,000 recoded samples. The total computation time was 21 hours a single core of a typical personal desktop computer. Further inspection of

Figure B-6 suggests that useful results can be achieved with significantly less cost (<1/2 that time).

Figure B-7 shows uncertainty-quantification results for single versus multiple-earthquake location.

The goal of this figure is to study how hypocentre and shared-parameter uncertainties change as data for additional earthquakes are included in the multiple-earthquake location. Results for 1, 2,

4, 8, and 18 earthquakes are shown. All earthquakes are located in the northwestern cluster, and we consider the effect on uncertainty for earthquake 37. Uncertainties for earthquake 37 are reduced substantially for all parameters. The most significant reduction in uncertainty occurs when adding a second earthquake to the location procedure. However, uncertainties continue to decrease as additional events are added to the inversion, suggesting that it is advantageous to carry out multiple-earthquake location with significant numbers of events.

Note that some other events in the catalogue saw more significant reduction in uncertainty and others less significant reduction, depending on hypocentre location with respect to the network.

Importantly, depth and origin time in Fig. B-7 show significant improvements as the number of events increases. A significant reduction is also visible for all shared parameters, once the number of events reaches 8 or higher.

Figure B-1. Results of two simulation studies in terms of absolute error marginal distributions, where true parameter values correspond to values of 0. Earthquakes sorted according to increasing distance from the network centroid from top to bottom. Black lines represent simulation 1 (data simulated with uniform half space and inverted with uniform half space) and gray lines simulations 2 (data simulated with layered half space and inverted with uniform half space).

Figure B-2. Results of two simulation studies in terms of marginal distributions for shared parameters. Black lines represent simulation 1 (data simulated with uniform half space and inverted with uniform half space) and gray lines simulation 2 (data simulated with layered half space and inverted with uniform half space). Dashed lines represent true parameter values for simulation 1.

Figure B-3. Epicentre map for 2D marginal distributions of catalogue earthquake 37. Red is a higher probability, whereas blue is lower probability. The earthquake is a part of the northwestern earthquake cluster.

Figure B-4. Histogram PPDs of parameter latitude, longitude, origin time, and depth between multiple-earthquake (blue) and single-earthquake inversions (black) for 47 earthquakes. Dashed lines are the lower and upper 95% CIs for each parameter. Earthquakes are sorted according to increasing depth from the network centroid. The extent of the depth axis is limited to 20-km depth for better display of results. However, the prior extends to 35-km depth.

Figure B-4. Continued.

Figure B-5. (a) Posterior model correlation matrix for multiple-earthquake location with 47 earthquakes. Since the matrix is symmetric, only the upper triangular matrix needs to be considered. The first 188 rows and columns correspond to hypocentre parameters for 47 earthquakes. The last 4 rows and columns correspond to the shared parameters. The colour scale is from red for perfect positive correlation, to white for neutral correlation, to blue for perfect negative correlation. (b) Magnified portion of the correlation matrix for earthquake 37. (c) Magnified portion of the correlation matrix for the 4 shared parameters and the last 11 earthquakes in the catalogue. The black box highlights the portion for earthquake 37.

Figure B-6. Convergence parameter γ as a function of MCMC step during the inversion. The dashed line marks the converge value of 0.05. Convergence times in the main text refer to achieving a value of γ = 0:05.

Figure B-7. Multiple-earthquake inversion uncertainty scaling with number of earthquakes studies. Uncertainties for earthquake 37 are considered in multiple-earthquake inversion while increasing the number of earthquakes in the inversion: single earthquake (green), 2 earthquakes (gray), 4 earthquakes (blue), 8 earthquakes (red), and18 earthquakes (black).

Appendix C supplemental information for “Evolution of the Southern Rocky Mountain Trench using local seismicity”.

This supplement contains earthquake location uncertainties produced by nonlinear multiple-

earthquake location method from Purba et al., 2020 and earthquake waveforms detected by two

detection methods. Viewing the epicentre marginal distributions of 47 events from the earthquake

catalogue reveals that the distributions exhibit varying degrees of correlation that are consistent

with our network shape (Figure C-1; elongated in the northwest-southeast direction). Epicentre

location uncertainties are elongated perpendicular to the trend of the network orientation. Events

farther away from the network centroid tend to have larger uncertainties, whereas events near

the network centroid possess lower uncertainty. Further explanation regarding the earthquake

location method and their uncertainties can be found in Purba et al. (2020).

This supplement also includes earthquake waveforms that have been detected by the kurtosis

and STA/LTA methods. The kurtosis method has triggered detections on 11 channels, four of

which appear on the vertical channels and seven on the horizontal components for event number

15 (Figure C-2). The detection number is different for the STA/LTA, where only six channels

triggered, two of which are vertical and the other four are horizontal. Because we set a minimum

declaration number of channels to be eight, only the kurtosis method declared this signal as a

potential earthquake signal.

For event number three, 12 channels have been triggered by the STA/LTA detections (Figure C-

3). Six detections appear on the vertical channels, and the other six are on the horizontal

components. For the kurtosis method, detections occur only in seven channels. Since the

minimum number of channels for a declaration is eight, only the STA/LTA declared this as a

potential earthquake signal. Using separate approaches for detecting earthquakes allowed us to

identify subtle, and often emergent, signals associated with the small magnitude events identified here.

Figure C-1. (Figure 1 in Purba et al., 2020) Map of the study area along the RMT. The locations of 10 seismic stations are shown by triangles. Known fault locations are indicated for normal faults (solid) and thrust faults (dashed). Probabilistic epicentre locations for the 47 events located in this study are shown by the gray scale (white - low probability, black - high probability). Note that some probability density functions for location overlap each other. Ellipses outline the northwestern and southern event clusters.

Figure C-2. Three-component seismograms presenting earthquake number 15 in our catalogue. This earthquake occurred on 2017-12-02 at 15:12:47 UTC. Waveforms are filtered between 10 - 20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals. Only kurtosis detection declared this as a potential earthquake because of sufficient number of detections in 11 channels (4 vertical and 7 horizontal channels). Traces of plotted for all 10 Canoe Reach stations arranged in numeric order CRG01-CRG14 from top to bottom. Left column – east- west channel; centre – north-south channel; and right – vertical channel. Black indicates both kurtosis and STA/LTA have triggered a detection; red for the kurtosis; and green for neither of them.

Figure C-3. Three-component seismograms presenting earthquake number 3 in our catalogue. This earthquake occurred on 2017-09-23 at 18:27:05 UTC. Waveforms are filtered between 10 - 20 Hz and then normalized. Some stations exhibit both clear P- and S- or either P- or S- arrivals. Only STA/LTA detection declared this as a potential earthquake because of sufficient number of detections in 12 channels (6 vertical and 6 horizontal channels). Traces of plotted for all 10 Canoe Reach stations arranged in numeric order CRG01-CRG14 from top to bottom. Left column – east- west channel; centre – north-south channel; and right – vertical channel. Black indicates both kurtosis and STA/LTA have triggered a detection; blue for the STA/LTA; and green for neither of them.

Appendix D review for MCMC method

Markov Chain Monte Carlo (MCMC) method is a random-walk generation used to sample from a posterior probability density (PPD). Sampling with MCMC in geophysical inversion employs the forward model and associated likelihood function to predict data and evaluate the fit with observed data. The method has significant computational cost and is applied to nonlinear inverse problems, where closed-form expressions cannot be found for the PPD. In my study, I apply MCMC sampling to locate earthquake hypocentres. The PPD is approximated by a sequence of dependent samples from random-variable vectors

X , X , X , . . . , (D.1) 0 1 2

where the probability distribution of X is dependent on the previous value, X , and not on earlier n+1 n values of random variables in the sequence (i.e., Aster et al., 2019). Hence,

P(X | X , X , . . . , X ) = P(X | X ). (D.2) n+1 0 1 n n+1 n

The ensemble of samples approximates the solution of a Bayesian inverse problem following

Bayes’ rule. For M model parameters m and N observed data d, Bayes’ theorem is

( | ) ( ) ( | ) = , (D.3) ( ) 𝑃𝑃 𝐝𝐝 𝐦𝐦 𝑃𝑃 𝐦𝐦 𝑃𝑃 𝐦𝐦 𝐝𝐝 𝑃𝑃 𝐝𝐝 where P(m|d) is the PPD, P(d|m) is the probability of data given proposed model, P(m) is the

prior, here assumed to be uniformly distribute. Probability P(d) is the normalizing constant and is

difficult to compute for nonlinear problems but can be ignored for inferences on m.

The choice of m is specific to every study. For this location study = [ , , , T , Vp, Vp/Vs, p,

𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 s], where is the station index. The first four parameters are the hypocentre𝐦𝐦 𝜆𝜆 𝜑𝜑 parameters𝑧𝑧 latitude,𝜎𝜎

𝜎𝜎 𝑖𝑖

longitude, depth, and origin time. The latter four parameters are P-wave velocity, P- to S-velocity ratio, noise standard deviation of P arrival times, and noise standard deviation of S arrival times.

Observed data ( ) are the arrival time picks from every seismic station. The observed data are 𝒐𝒐𝒐𝒐𝒐𝒐 𝑖𝑖 measured as 𝐝𝐝 = T + , where T is the travel time of an earthquake signal. The physical 𝒐𝒐𝒐𝒐𝒐𝒐 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 assumption made𝐝𝐝 here for 𝝉𝝉predicted times are straight ray paths, assuming a homogenous half- space Earth model. Therefore, data predictions are calculated as 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝐝𝐝𝑖𝑖 ( ) + ( ) + ( ) (D.4) = , + 2 2 2, 𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒 𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒 𝑠𝑠𝑠𝑠 𝑒𝑒𝑒𝑒 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 � 𝑥𝑥 − 𝑥𝑥 𝑦𝑦 − 𝑦𝑦 𝑧𝑧 − 𝑧𝑧 𝐝𝐝𝑖𝑖 𝝉𝝉𝑖𝑖 𝑉𝑉 where subscripts eq denote earthquake locations, subscripts st denote station locations, and V is

the seismic velocity for P- and S-waves depending on the phase considered.

For inference on a fixed model parametrization, the normalizing constant P(d) in the Bayes’

theorem can be ignores. In addition, for observed (fixed) data dobs, P(m|d) becomes the likelihood

function ( ) and Bayes’ rule can be written

𝐿𝐿 𝐦𝐦 ( ) ( ). (D.5) 𝐨𝐨𝐨𝐨𝐨𝐨 𝑃𝑃�𝐦𝐦�𝐝𝐝 � ∝ 𝐿𝐿 𝐦𝐦 𝑃𝑃 𝐦𝐦 The likelihood function ( ) is a measure of the probability that gave rise to dobs. The likelihood

function ( ) is formulated𝐿𝐿 𝐦𝐦 based on the assumption of Gaussian𝐦𝐦 -distributed noise,

𝐿𝐿 𝐦𝐦 1 1 ( ) = ( ) ( ) = 2 exp , (D.6) 2 ( ) 𝑇𝑇 𝑃𝑃 𝑆𝑆 𝑗𝑗 𝑗𝑗 𝑁𝑁𝑗𝑗⁄2 𝑁𝑁 2 𝑗𝑗 𝐿𝐿 𝐦𝐦 𝐿𝐿 𝐦𝐦 𝐿𝐿 𝐦𝐦 � �− 𝑗𝑗 𝐫𝐫 𝐫𝐫 � 𝑗𝑗=1 2π 𝜎𝜎𝑗𝑗 𝜎𝜎 which assumed that the noise on P and S picks are independent. Equation (D.6) assumes that standard deviations represent the data covariance matrix = I. Further, data residuals = 2 𝑗𝑗 𝑖𝑖 𝑖𝑖 𝒋𝒋 ( ) are the𝜎𝜎 difference of observed and predicted data𝐂𝐂 𝜎𝜎( ). 𝐫𝐫 𝐨𝐨𝐨𝐨𝐨𝐨 𝐝𝐝𝑗𝑗 − 𝐝𝐝𝑗𝑗 𝐦𝐦 𝐝𝐝𝑗𝑗 𝐦𝐦

The MCMC sampling simulates a random walk in the parameter space for m. To improve acceptance rates in the random walk, I apply the Metropolis Hasting (MH) algorithm with principal axes proposal distributions. In standard MH, a new state m’ is proposed based on m and a proposal distribution . The new state is then accepted or rejected based on the MH acceptance criterion 𝑄𝑄

( ) ( ) ( | ) = min 1 , , (D.7) ( ′) ( ′) ( | ′) 𝐿𝐿 𝐦𝐦 𝑃𝑃 𝐦𝐦 𝑄𝑄 𝐦𝐦 𝐦𝐦 𝛼𝛼 � ′ � 𝐿𝐿 𝐦𝐦 𝑃𝑃 𝐦𝐦 𝑄𝑄 𝐦𝐦 𝒎𝒎 where = 1 would correspond to accepting the proposed model, while < 1 means there is a probability𝛼𝛼 of of the proposed model being accepted. The term after 1 indicates𝛼𝛼 the ratio of the

𝛼𝛼 likelihood between the proposed model and the current model ( ′) , multiplied by the ratio in the 𝐿𝐿�𝐦𝐦 � 𝐿𝐿 𝐦𝐦

prior probability for the proposed model to the current model ( ′) (always one for the uniform 𝑃𝑃�𝐦𝐦 � 𝑃𝑃 𝐦𝐦 prior assumption), multiplied by the ratio in the proposal distribution of the proposed model vs.

the current model (unity when assuming a Gaussian proposal). Under our assumptions, equation

D.7 reduces to:

( ) = min 1 , . (D.8) ( ′) 𝐿𝐿 𝐦𝐦 𝛼𝛼 � � 𝐿𝐿 𝐦𝐦 The MH algorithm is summarized in pseudocode below:

1. Specifying upper & lower bounds for all parameters. 2. Choose a starting model. 3. Perturb model parameters via , calculate with eq. (D.8).

4. Accept or Reject as a new state𝑄𝑄 of algorithm:𝛼𝛼 (a) if 1 accept ′ (b) if 𝛼𝛼 ≥1 draw random𝐦𝐦 ← 𝐦𝐦 number ~ (0,1) 𝛼𝛼 i.≤ if accept 𝜉𝜉 𝑈𝑈 ′ ii. if 𝜉𝜉 ≤ 𝛼𝛼 reject 𝐦𝐦 (return← 𝐦𝐦 to ) ′ 5. Repeat steps 3 𝜉𝜉an≥d 𝛼𝛼4 many times𝐦𝐦 and periodically𝐦𝐦 examine convergence.

The performance of MH sampling depends strongly on the tuning of . Here, proposing a new state m’ is based on rotating the parameter vector into principal axes𝑄𝑄 (PA) space to reduce the negative impact of correlated parameters on sampling efficiency. As mentioned in Chapter 2, the rotation to PA requires the estimation of the model parameter covariance matrix. In my work, this estimation is carried out in two phases: (1) a linearized approximation, and (2) a numerical, nonlinear approximation (Dosso et al., 2014). The model covariance matrix estimate is then

( ) employed in a singular value decomposition = which provides the rotation matrix 𝒎𝒎 𝐓𝐓 𝒆𝒆𝒆𝒆𝒆𝒆 for efficient proposal direction and for efficient𝐂𝐂 proposal𝐔𝐔𝐔𝐔𝐔𝐔 standard deviation, shown in Figure D𝐔𝐔-

1. Importantly, the proposal is not treated𝚲𝚲 as multivariate since high-dimensional proposals result

in poor acceptance rates (MacKay, 2003). Rather, m is rotated into PA space and then perturbed

by a univariate Cauchy distribution with scale parameter given by the appropriate singular value

from . In particular, the steps in the rotation sampling algorithm are as follows:

1. To𝚲𝚲 propose new model for the Markov chain, rotate

( ) = . (D.9) 𝑟𝑟 𝐓𝐓 𝐦𝐦 𝐔𝐔 𝐦𝐦 Since proposed parameter m' exhibit reduced correlation, perturbations are efficient.

Parameters j can be perturbed (one at a time) as

( ) = ( ) + , (D.10) ′ 𝑟𝑟 𝒓𝒓 𝐦𝐦 𝐦𝐦 𝐠𝐠 T where g = [0, … , 0, gj, 0, … ,0] and gj ~ CA(0, j) and j is the scale parameter of the Cauchy

proposal, determining the step size. The Cauchy𝜎𝜎 proposal𝜎𝜎 distribution is applied here rather

than a Gaussian proposal to allow occasional large steps which can lead to modest

performance increases: In comparison to a Gaussian distribution, the Cauchy distribution has

higher central probability and heavier tails (Figure D-2).

2. Obtain by rotating it back, ′ 𝐦𝐦 = ( ) . (D.11) ′ ′ 𝒓𝒓 𝐦𝐦 𝐔𝐔 𝐦𝐦 3. The likelihood function of the proposed model ( ) is then evaluated. Determination of the ′ proposal will apply the acceptance criterion in Metropolis𝐿𝐿 𝐦𝐦 -Hasting, as discussed earlier.

After a model proposal is accepted, record the “random walk” direction of the accepted model parameters, as the marginal probability distribution. Due to complexity of the model parameters, they are sometimes reduced to M 1D distributions by integrating (averaging) over M – 1 parameter,

( ) = … ( ) … … = 1, … , . (D.12)

𝑖𝑖 1 2 𝑖𝑖−1 𝑖𝑖+1 𝑀𝑀 𝑃𝑃 𝑚𝑚 �𝑚𝑚1 �𝑚𝑚2 �𝑚𝑚𝑖𝑖−1 �𝑚𝑚𝑖𝑖+1 �𝑚𝑚𝑀𝑀𝑃𝑃 𝐦𝐦 𝑑𝑑𝑚𝑚 𝑑𝑑𝑚𝑚 𝑑𝑑𝑑𝑑 𝑑𝑑𝑚𝑚 𝑑𝑑𝑑𝑑 𝑖𝑖 𝑀𝑀 An example is displayed in Figure 2-4 (or Figure D-3 in this Appendix), where 1D marginals of

every parameter in single-earthquake inversion are presented by collapsing marginal distributions

in 8-parameter space. Further analyses are conducted by calculating the 95% credibility intervals

in the posterior probability densities, which summarize the upper and lower error bars for non-

Gaussian distributions. In addition, examples of 2D marginals are shown on an epicentre map

view in Figure D-4.

Figure D-1. (a) random walk without rotation, and (b) with rotation. A more efficient step direction and size is achieved through applying rotation. Red dashed line on the right represents the marginal distribution in the rotated axes, which also shows high probability distribution given only few samples.

Figure D-2. Cauchy (dashed) versus Gaussian (solid) distribution. Note the higher central peak and heavier tails of the Cauchy distribution.

Figure D-3. (Same as Figure 2-4). Inversion results for earthquake 37 in terms of 1D marginals of longitude, latitude, depth, and origin time (top), and Vp, Vp/Vs, p, and s, (bottom). Dashed lines represent 95% credibility intervals. The plot boundaries represent the width of the uniform prior 𝜎𝜎 𝜎𝜎 distributions, except for latitude and longitude, where bounds were significantly wider than shown to span the full study area. Solid lines show Gaussian distributions with means and standard deviations taken from the marginals for comparison.

Figure D-4. (Same as Figure B-3). Epicentre map for 2D marginal distributions of catalogue earthquake 37. Red is a higher probability, whereas blue is lower probability. The earthquake is a part of the northwestern earthquake cluster.

Appendix E Canoe Reach Earthquake Catalogue

The earthquake catalogue generated in this study is shown in Table E-1.

Table E-1. Canoe Reach earthquake catalogue from September 2017 – August 2018. The catalogue consisted of 47 earthquakes that have been manually inspected. For every inversion parameter, the mode, lower and upper bound of 95%CI are written as mo, x1, and x2. Local magnitude (Ml) is included from Nanometrics.

EVID Origin_time P det S det Ml lon_mo lon_x1 lon_x2 lat_mo lat_x1 lat_x2 z_mo z_x1 z_x2 1 2017-09-01T01:14:43.24 4 6 n/a -119.2351 -119.2529 -119.2201 52.9949 52.9749 53.0062 2.9 0 7.9 2 2017-09-23T15:18:29.89 10 7 n/a -119.2016 -119.2204 -119.1837 52.4786 52.4677 52.4926 14.4 12.2 16.2 3 2017-09-23T18:26:59.53 10 7 n/a -119.2016 -119.2258 -119.1817 52.4773 52.4624 52.4896 15.3 12.7 17.5 4 2017-09-28T19:53:00.95 8 8 1.17 -119.4553 -119.4734 -119.4401 52.7612 52.7531 52.7698 13.8 12.1 15.4 5 2017-10-01T11:16:22.21 8 8 0.98 -119.4152 -119.4316 -119.3957 52.8859 52.8785 52.8988 11.8 10.6 13.1 6 2017-10-04T23:36:54.84 7 8 n/a -119.2542 -119.2793 -119.2299 52.3932 52.3775 52.41 12.1 4.9 16.3 7 2017-10-07T11:24:18.08 7 7 n/a -119.2552 -119.2821 -119.2248 52.4061 52.3913 52.4238 14.2 8.1 18 8 2017-10-10T23:00:03.87 9 10 1.13 -119.4635 -119.478 -119.4448 52.7608 52.7524 52.7696 15 13.4 16.4 9 2017-10-16T19:37:24.65 10 8 n/a -119.3052 -119.3311 -119.2782 52.3451 52.3294 52.3625 18.9 14.1 23.1 10 2017-10-20T04:45:47.33 10 7 n/a -119.4421 -119.4692 -119.4109 52.2609 52.2428 52.2787 13.5 0 18.5 11 2017-10-30T04:54:02.64 7 8 0.32 -119.0955 -119.1065 -119.0854 52.6921 52.6841 52.6983 13 11.5 14.4 12 2017-11-18T05:30:17.30 7 7 0.55 -119.1598 -119.1699 -119.1482 52.9384 52.9294 52.9494 0.1 0 4.3 13 2017-12-01T12:38:26.26 5 9 1.14 -119.4296 -119.4468 -119.4062 52.9172 52.9059 52.9282 12 10.6 13.4 14 2017-12-02T00:32:34.21 6 9 n/a -119.4269 -119.4476 -119.4092 52.9195 52.9086 52.9324 10.5 9.2 11.8 15 2017-12-02T15:12:53.41 6 9 0.12 -119.426 -119.4454 -119.4041 52.9273 52.91 52.9365 10.9 9.5 12.2 16 2017-12-02T20:36:10.64 6 9 n/a -119.5704 -119.5911 -119.5467 52.9236 52.913 52.9354 0.1 0 3 17 2017-12-19T02:03:21.60 6 6 n/a -118.9348 -118.9587 -118.9172 52.586 52.5783 52.5972 13.8 12.4 15.3 18 2017-12-21T20:42:36.95 5 7 0.44 -119.4223 -119.4462 -119.4016 52.9727 52.9597 52.9921 9 6.4 11.2 19 2017-12-23T04:54:55.96 5 6 n/a -119.3003 -119.3273 -119.2669 52.41 52.3927 52.4316 10.7 0.8 14.8

20 2018-01-05T05:23:51.80 6 7 n/a -119.4477 -119.4779 -119.428 52.8809 52.8697 52.8924 10.7 8.1 12.9 21 2018-01-21T04:26:09.25 10 9 1.79 -119.2873 -119.3058 -119.272 53.0527 53.0417 53.0643 1.6 0 7.8 22 2018-02-04T10:34:38.31 5 7 n/a -119.5217 -119.5525 -119.4981 52.8799 52.8625 52.8987 12.4 8.9 15.2 23 2018-02-28T15:13:21.78 6 9 0.54 -119.4394 -119.4592 -119.4199 52.8827 52.8729 52.8949 10.2 7.7 12.1 24 2018-03-03T17:08:44.01 4 9 n/a -119.111 -119.1239 -119.0988 52.7135 52.7041 52.7218 16.1 15 17.3 25 2018-03-06T05:17:15.88 5 7 -0.05 -119.4205 -119.4443 -119.404 52.8881 52.8771 52.9036 10.9 9.4 12.4 26 2018-03-06T11:14:27.29 5 7 0 -119.4958 -119.5217 -119.4696 52.7465 52.7328 52.7629 13.4 10.9 15.5 27 2018-03-11T17:59:44.70 10 10 0.94 -119.383 -119.3966 -119.3685 52.6626 52.6554 52.6702 11.4 9.4 13 28 2018-03-17T14:29:40.95 10 10 1.33 -119.3026 -119.3199 -119.2893 53.0093 52.9991 53.0233 6.8 0.7 9.5 29 2018-03-29T04:47:12.03 8 9 0.38 -119.2473 -119.2549 -119.2397 52.7839 52.7789 52.7884 4.7 3.4 5.8 30 2018-04-09T22:23:06.61 4 8 n/a -119.4664 -119.4907 -119.4442 52.9165 52.8995 52.9297 12.8 11.3 14.4 31 2018-04-22T17:32:23.02 8 8 n/a -119.2783 -119.2896 -119.2642 53.0115 53.0013 53.0246 1 0 6.9 32 2018-05-03T02:28:30.16 9 10 n/a -119.3471 -119.3759 -119.327 52.3902 52.3757 52.4048 13.8 6.5 18.2 33 2018-05-08T04:10:06.26 6 8 n/a -119.2481 -119.2695 -119.2157 52.3966 52.385 52.4144 9.6 1.1 13.8 34 2018-05-14T14:01:06.61 7 7 n/a -119.2496 -119.2733 -119.2189 52.3656 52.3543 52.3844 9 0.1 12.8 35 2018-05-21T07:53:22.68 6 8 1.11 -119.4618 -119.4827 -119.4421 52.8847 52.8711 52.8943 13.3 11.8 14.6 36 2018-05-28T22:29:20.26 5 8 0.68 -119.4154 -119.4318 -119.3954 52.8883 52.8762 52.8987 10 8.5 11.5 37 2018-05-29T17:58:05.93 6 7 0.92 -119.4411 -119.4635 -119.4181 52.8846 52.8735 52.8984 10.8 9.4 12.3 38 2018-05-30T00:18:10.20 5 9 n/a -119.4354 -119.4521 -119.4124 52.8957 52.8841 52.9071 12.4 11 13.8 39 2018-05-30T19:56:10.93 5 9 n/a -119.4244 -119.4452 -119.3988 52.9003 52.8891 52.9128 11.3 9.6 12.8 40 2018-05-31T16:19:59.65 8 9 1.47 -119.4316 -119.4493 -119.4114 52.9217 52.9112 52.9352 11.8 10.6 13.1 41 2018-06-26T03:31:45.15 6 7 0.32 -119.1491 -119.1619 -119.1332 52.8714 52.8597 52.8822 7.1 4.4 9.2 42 2018-06-26T03:35:28.52 6 7 0.29 -119.1445 -119.1561 -119.1279 52.8665 52.8576 52.8768 9.2 7.4 10.9 43 2018-06-26T03:53:47.37 6 7 0.66 -119.1466 -119.1589 -119.1323 52.8623 52.8549 52.8727 9.1 7.5 10.7 44 2018-07-29T10:28:30.07 6 7 -0.14 -119.2026 -119.2125 -119.1886 52.6713 52.6657 52.6783 11.7 10.2 13 45 2018-08-01T11:50:44.00 8 9 n/a -119.1202 -119.1288 -119.1074 52.8252 52.8181 52.8319 7.4 6 8.9 46 2018-08-06T02:46:17.18 5 9 n/a -119.4221 -119.4403 -119.4035 52.8862 52.8763 52.8978 10.8 9.3 12.2 47 2018-08-13T09:49:31.35 6 9 n/a -119.4428 -119.4621 -119.425 52.8914 52.8793 52.9018 10.8 9.4 12.2