GPS inferred velocity and strain rate fields in eastern Canada

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GPS inferred velocity and strain rate fields

in eastern Canada

Thèse

Mohammad Ali Goudarzi

Doctorat en sciences géomatiques

Philosophiae doctor (Ph.D.)

Québec, Canada

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Résumé

La vallée du fleuve Saint-Laurent, dans l'est du Canada, est l'une des régions sismiques les plus actives dans l'est de l'Amérique du Nord et est caractérisée par de nombreux tremble-ments de terre intraplaques. Après la rotation rigide de la plaque tectonique, l'ajustement isostatique glaciaire est de loin la plus grande source de signal géophysique dans l'est du Canada. Les déformations et les vitesses de déformation de la croûte terrestre de cette ré-gion ont été étudiées en utilisant plus de 14 ans d’observations (9 ans en moyenne) de 112 stations GPS fonctionnant en continu.

Le champ de vitesse a été obtenu à partir de séries temporelles de coordonnées GPS quoti-diennes nettoyées en appliquant un modèle combiné utilisant une pondération par moindres carrés. Les vitesses ont été estimées avec des modèles de bruit qui incluent les corrélations temporelles des séries temporelles des coordonnées tridimensionnelles. Le champ de tesse horizontale montre la rotation antihoraire de la plaque nord-américaine avec une vi-tesse moyenne de 16,8±0,7 mm/an dans un modèle sans rotation nette (no-net-rotation) par rapport à l’ITRF2008. Le champ de vitesse verticale confirme un soulèvement dû à l'ajus-tement isostatique glaciaire partout dans l'est du Canada avec un taux maximal de 13,7±1,2 mm/an et un affaissement vers le sud, principalement au nord des États-Unis, avec un taux typique de −1 à −2 mm/an et un taux minimum de −2,7±1,4 mm/an.

Le comportement du bruit des séries temporelles des coordonnées GPS tridimensionnelles a été analysé en utilisant une analyse spectrale et la méthode du maximum de vraisemblance pour tester cinq modèles de bruit: loi de puissance; bruit blanc; bruit blanc et bruit de scin-tillation; bruit blanc et marche aléatoire; bruit blanc, bruit de scintillation et marche aléa-toire. Les résultats montrent que la combinaison bruit blanc et bruit de scintillation est le meilleur modèle pour décrire la partie stochastique des séries temporelles. Les amplitudes de tous les modèles de bruit sont plus faibles dans la direction nord et plus grandes dans la direction verticale. Les amplitudes du bruit blanc sont à peu près égales à travers la zone d'étude et sont donc surpassées, dans toutes les directions, par le bruit de scintillation et de marche aléatoire. Le modèle de bruit de scintillation augmente l’incertitude des vitesses

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estimées par un facteur de 5 à 38 par rapport au modèle de bruit blanc. Les vitesses esti-mées de tous les modèles de bruit sont statistiquement cohérentes.

Les paramètres estimés du pôle eulérien de rotation pour cette région sont légèrement, mais significativement, différents de la rotation globale de la plaque nord-américaine. Cette dif-férence reflète potentiellement les contraintes locales dans cette région sismique et les con-traintes causées par la différence des vitesses intraplaques entre les deux rives du fleuve Saint-Laurent.

La déformation de la croûte terrestre de la région a été étudiée en utilisant la méthode de collocation par moindres carrés. Les vitesses horizontales interpolées montrent un mouve-ment cohérent spatialemouve-ment: soit un mouvemouve-ment radial vers l'extérieur pour les centres de soulèvement maximal au nord et un mouvement radial vers l'intérieur pour les centres d'af-faissement maximal au sud, avec une vitesse typique de 1 à 1,6±0,4 mm/an. Cependant, ce modèle devient plus complexe près des marges des anciennes zones glaciaires. Basées se-lon leurs directions, les vitesses horizontales intraplaques peuvent être divisées en trois zones distinctes. Cela confirme les conclusions d'autres chercheurs sur l'existence de trois dômes de glace dans la région d'étude avant le dernier maximum glaciaire. Une corrélation spatiale est observée entre les zones de vitesses horizontales intraplaques de magnitude plus élevée et les zones sismiques le long du fleuve Saint-Laurent. Les vitesses verticales ont ensuite été interpolées pour modéliser la déformation verticale. Le modèle montre un taux de soulèvement maximal de 15,6 mm/an au sud-est de la baie d'Hudson et un taux d’affaissement typique de 1 à 2 mm/an au sud, principalement dans le nord des États-Unis. Le long du fleuve Saint-Laurent, les mouvements horizontaux et verticaux sont cohérents spatialement. Il y a un déplacement vers le sud-est d’une magnitude d’environ 1,3 mm/an et un soulèvement moyen de 3,1 mm/an par rapport à la plaque l'Amérique du Nord. Le taux de déformation verticale est d’environ 2,4 fois plus grand que le taux de déformation hori-zontale intraplaque.

Les résultats de l'analyse de déformation montrent l’état actuel de déformation dans l'est du Canada sous la forme d’une expansion dans la partie nord (la zone se soulève) et d’une compression dans la partie sud (la zone s'affaisse). Les taux de rotation sont en moyenne de 0,011°/Ma. Nous avons observé une compression NNO-SSE avec un taux de 3.6 à

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8.1 nstrain/an dans la zone sismique du Bas-Saint-Laurent. Dans la zone sismique de Char-levoix, une expansion avec un taux de 3,0 à 7,1 nstrain/an est orientée ENE-OSO. Dans la zone sismique de l'Ouest du Québec, la déformation a un mécanisme de cisaillement avec un taux de compression de 1,0 à 5,1 nstrain/an et un taux d’expansion de 1.6 à 4.1 nstrain/an. Ces mesures sont conformes, au premier ordre, avec les modèles d'ajuste-ment isostatique glaciaire et avec la contrainte de compression horizontale maximale du projet World Stress Map, obtenue à partir de la théorie des mécanismes focaux (focal me-chanism method).

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Abstract

The Saint Lawrence River valley (SLRV) in eastern Canada is one of the most seismically active regions in eastern North America, which is characterized by many intraplate earth-quakes. After its rigid plate rotation, the ongoing glacial isostatic adjustment (GIA) is by far the largest source of geophysical signal in eastern Canada. In this research, the current crustal deformation and strain rate field of this region was studied using more than 14 years (9 years on average) observations of 112 continuously operating GPS stations.

The velocity field was obtained from cleaned position time series of daily GPS solutions by applying a combined model using the weighted least-squares method. We estimated veloci-ty uncertainties by assuming advanced noise models to include the temporal correlation of the position time series. The horizontal velocity field shows the counter-clockwise rotation of the North American plate in the no-net-rotation model with the average of 16.8±0.7 mm/yr constrained to ITRF 2008. The vertical velocity field confirms the GIA-induced uplift all over eastern Canada with the maximum rate of 13.7±1.2 mm/yr and sub-sidence to the south mainly over north of the United States with a typical rate of −1 to −2 mm/yr and the minimum value of −2.7±1.4 mm/yr.

The noise behavior of the GPS position time series was explored by testing five different noise models of power-law, white, white plus flicker, white plus random-walk, and white plus flicker plus random-walk, using the spectral analysis and the maximum likelihood methods. The results show that combination of white plus flicker noise is the best model for describing the stochastic part of the position time series. Furthermore, amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of the white noise model are almost equal across the study area, they are pre-vailed by the flicker and the random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model, while the estimated velocities from all noise models are statistically consistent.

The estimated Euler pole parameters for this region are slightly but significantly different from the overall rotation of the North American plate. This difference potentially reflects

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local stress in this seismic region, and the difference in intraplate velocities between the two sides of the SLRV accumulates stress in the faults located along the river.

The surface deformation of the region was studied using least-squares collocation. Interpo-lated intraplate horizontal velocities show a spatially coherent radially outward motion from the centers of maximum uplift to the north and inward motion to the centers of maxi-mum subsidence to the south with a typical velocity of ~1–1.6±0.4 mm/yr. This pattern, however, becomes more complex near the margins of the formerly glaciated areas. Based on their directions, the intraplate horizontal velocities can be divided in three distinct zones. This confirms the existence of three ice domes in the study region before the last glacial maximum. A spatial correlation is observed between areas with higher magnitude of the intraplate horizontal velocity and the seismic zones along the SLRV. The vertical velocities were interpolated to model the ongoing vertical deformation. The model shows maximum uplift rate of 15.6 mm/yr to southeastern of Hudson Bay and a typical subsidence rate of 1– 2 mm/yr to the south mainly across the north of the United States. Along the SLRV, hori-zontal and vertical motions are spatially coherent toward southeast with the typical magni-tude of ~1.3 mm/yr relative to North American plate and the average uplift rate of 3.1 mm/yr, respectively. In general, the rate of vertical deformation is typically ~2.4 times larger than the rate of the intraplate horizontal motion in this area.

Results of strain analysis show the present-day straining of eastern Canada in the form of extension to the north (the area under uplift) and shortening to the south (the area under subsidence). On average, rotational rates are at the level of 0.011°/Myr. A NNW-SSE shortening with a typical rate of ~3.6–8.1 nstrain/yr is observed over the Lower Saint Law-rence seismic zone. In the Charlevoix seismic zone, an extension with a typical rate of ~3.0–7.1 nstrain/yr is oriented about ENE-WSW. In the western Quebec seismic zone, the deformation has a shear straining mechanism with a typical shortening rate of ~1.0– 5.1 nstrain/yr and extension rate of ~1.6–4.1 nstrain/yr. These results are consistent, to the first order, with GIA models and with the maximum horizontal compressional stress of the World Stress Map resulted from focal mechanism method.

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Résumé ... III Abstract ... VII Contents ... IX List of tables ... XIII List of figures ... XV List of abbreviations ... XIX Dedication ... XXIII Acknowledgements ... XXV Foreword ... XXVII Chapter 1. Introduction ... 1 1.1. Introduction ... 1 1.2. Study area ... 5 1.2.1. Geological settings ... 6 1.2.2. Seismicity ... 8 1.3. Previous works ... 9

1.4. Motivation for this research ... 11

1.5. Research problems ... 11

1.5.1. Campaign data ... 12

1.5.2. GIA horizontal motions ... 12

1.5.3. Assumption about the noise model ... 12

1.5.4. Resolution of the geodetic methods ... 13

1.5.5. Other considerations ... 13

1.6. Research objectives ... 14

1.6.1. General objective ... 14

1.6.2. Specific objectives ... 14

1.7. General methodology ... 16

1.8. Thesis contribution and outline ... 17

1.9. References ... 21

Chapter 2. The three dimensional velocity field ... 27

2.1. Abstract ... 28

2.2. Introduction ... 28

2.3. Region of study, the GPS network and observations ... 31

2.4. GPS Data analysis ... 33

2.4.1. Data processing ... 33

2.4.2. Position time series and data editing ... 34

2.4.3. Estimating uncertainties of station velocities ... 38

2.5. Results and discussion ... 43

2.5.1. Three-dimensional velocities and their uncertainties ... 43

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2.5.3. Intraplate horizontal velocities ... 50

2.5.4. Ecological impacts and hazards ... 54

2.6. Conclusion ... 55

2.7. Acknowledgements ... 56

2.9. Appendix A: Figures ... 61

2.10. Appendix B: Tables ... 65

Chapter 3. Noise analysis of the position time series ... 67

3.1. Abstract ... 67

3.3. Region of study ... 71

3.4. GPS network and observations ... 72

3.5. Methods and data analysis ... 76

3.5.1. GPS data processing and velocity field ... 76

3.5.2. Estimating spectral indices ... 79

3.6.1. Spectral indices ... 82

3.6.1.1. Spectral analysis ... 83

3.6.1.2. Maximum Likelihood Estimation ... 86

3.6.2. Spatial correlation of estimated amplitudes ... 94

3.6.3. Stability of monuments ... 96

3.10. Appendix A: Figures ... 105

Chapter 4. Methodology for estimating the Euler pole ... 109

4.1. Abstract ... 109

4.3. Mathematical background ... 111

4.3.1. Models and the least-squares adjustment ... 112

4.3.1.1. Direct Euler pole problem in ECEF CCS ... 112

4.3.1.2. Direct Euler pole problem in LG CCS ... 115

4.3.1.3. Inverse Euler pole problem in ECEF CCS ... 116

4.3.1.4. Inverse Euler pole problem in LG CCS ... 118

4.3.2. Discussion of models ... 118

4.3.2.1. Ellipsoid to sphere simplification ... 119

4.3.2.2. Simplification of the weight matrix ... 120

4.3.2.3. Effect of the vertical component of the velocities ... 121

4.3.2.4. Comparing ECEF CCS and LG CCS ... 121

4.3.3. Statistical tests ... 122

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4.3.3.2. Pearson’s correlation coefficient ... 122

4.3.3.3. Baarda’s data snooping ... 123

4.3.3.4. The tau test ... 124

4.4. The software functionality ... 125

Chapter 5. Estimating the rotation pole for eastern Canada... 131

5.1. Abstract ... 131

5.3. The Euler’s theorem ... 133

5.4. Region of study ... 134

5.5. CGPS network and observations ... 136

5.6. Estimating Euler pole parameters ... 140

5.7. Discussion ... 141

5.8. Conclusion... 147

Chapter 6. Methodological aspects of calculating crustal strain rates ... 155

6.1. Abstract ... 155

6.3. Strain modelling methodology ... 157

6.3.1 Segmentation approaches ... 157

6.3.2. Inversion approaches ... 158

6.3.3. Gridding or interpolation approaches ... 159

6.4.1. Spherical model of the strain rate tensor ... 164

6.4.2. Representation of the strain rate tensor ... 164

6.4.3. Specifications of the strain rate tensor ... 166

6.4.4. Effect of the vertical velocity on the strain rate tensor ... 167

6.5. Least-squares collocation ... 168

6.5.1. Trend surface ... 171

6.5.2. Covariance function ... 172

6.5.3. Multidimensional covariance functions ... 175

6.6. GeoStrain software description ... 176

6.7. Computational performance analysis ... 178

6.8. Conclusion... 179

6.11. Appendix: calculating the strain rate tensor ... 185

Chapter 7. Crustal strain rate field ... 189

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7.4. Methodology ... 196

7.5. Data set ... 198

7.6.1. Vertical velocities ... 198

7.6.2. Intraplate horizontal velocities ... 203

7.6.3. Strain rates ... 206

7.6.4. Saint Lawrence River valley ... 208

7.10. Appendix ... 219

Chapter 8. Conclusion and recommendation ... 221

8.1. Conclusion ... 221 8.1.1. Velocity field ... 221 8.1.2. Noise analysis ... 224 8.1.3. Strain analysis ... 226 8.2. Limitations ... 227 8.3. Recommendations ... 228 8.4. References ... 230

Appendix 1. List of software ... 233

Appendix 2. Author’s curriculum vitae ... 235

Appendix 3. Author’s publications ... 237

Appendix 4. Reprint permissions ... 239

A4.1. Reprint permission for Chapter 3 ... 239

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List of tables

Table 2.1. Station velocities and their uncertainties estimated using white and white

plus flicker noise models as well as intraplate horizontal velocities. ... 41

Table 2B.1. Description of CGPS stations. ... 65

Table 3.1. Selected CGPS stations. ... 74

Table 3.2. Estimated spectral indices and velocity uncertainties. ... 91

Table 3.3. Summary of the estimated amplitudes for the different noise models and their velocity uncertainties. ... 94

Table 3.4. Random-walk noise amplitude and minimum length of time series necessary to detect the corresponding noise amplitude. ... 97

Table 4.1. The estimated Euler pole parameters and their sigma values from the velocity vectors in the earth-centered earth-fixed Cartesian coordinate system. ... 121

Table 5.1. The selected CGPS stations in eastern Canada for estimating the Euler’s pole of rotation. ... 139

Table 5.2. Estimated absolute Euler poles of rotation. ... 140

Table 7.1. Estimated parameters of the covariance functions for the Saint Lawrence River valley area. ... 210

Table 7A.1. Station velocities and their 1-σ uncertainties. ... 219

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List of figures

Figure 1.1. Observed vertical rates from the Canadian base network (black dots) show a spatially coherent pattern of uplift consistent with the expected glacial

isostatic adjustment signal (Henton et al., 2006). ... 2 Figure 1.2. Historical and instrumental earthquakes in or near Canada between 1627

and 2012 (source:

http://www.earthquakescanada.nrcan.gc.ca/historic-historique/caneqmap-eng.php, accessed: June 18, 2015). ... 3 Figure 1.3. Instrumental earthquakes in eastern Canada with M ≥ 3 from 1945 until

mid-2014 as well as historical earthquakes since 1663 (data source:

Earthquake Canada and the US Advanced National Seismic System). ... 4 Figure 1.4. Geological setting of the Saint Lawrence River valley (Mazzotti et al.,

2005). ... 7 Figure 1.5. The workflow of the dissertation. It shows the interrelationship among

different processing or analysis sections (blue boxes) are and where the

intermediate (green boxes) and final results (yellowish boxes) come from. ... 19 Figure 2.1. Instrumental earthquakes in eastern Canada with M ≥ 3 from 1945 to

mid-2014 as well as historical earthquakes since 1663 (data source:

Earthquake Canada and the US Advanced National Seismic System). ... 32 Figure 2.2. Spatial distribution of the selected CGPS stations. Stations have

maximum spatial density over the Saint Lawrence River valley and are

shown with a larger scale in the lower-left inset. ... 33 Figure 2.3. Position time series for station CHIC as well as the estimated parameters.

Continuous and dashed vertical lines show estimated offsets and their

corresponding epochs, respectively. ... 38 Figure 2.4. (A) Horizontal and (B) vertical velocities and their uncertainties estimated

by assuming white and white plus flicker noise models. Error ellipses in

A are plotted 3 times larger. ... 45 Figure 2.5. (A) The GPS-derived model of the vertical deformation for eastern North

America and (B) corresponding one-sigma uncertainties, (C) the misfit of the GPS-derived model with respect to the ICE-5G VM2 model,

(D) representation of the interpolated vertical velocities in the form of

contour map as well as major water bodies. ... 47 Figure 2.6. Intraplate horizontal velocities overlaid on (A) the GPS-derived and

(B) the ICE-5G VM2 vertical deformation models. ... 51 Figure 2.7. (A) Interpolated magnitudes of intraplate horizontal velocities,

(B) profiles of the interpolated magnitudes from KUUJ with the

maximum rate of uplift toward the collapsing peripheral forebulges. ... 53 Figure 2A.1. Graphical representation of the CGPS observations. ... 61 Figure 2A.2. Percentage of the cleaned CGPS observations. ... 62 Figure 2A.3. Comparing velocities and their uncertainties estimated by white and

white plus flicker noise models. The grey horizontal line shows Ratio = 1. Stations are sorted according to the number of epochs in their time series from shortest in the left to the longest in the right side of the graph. ... 63

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Figure 2A.4. Variogram of the vertical velocity field for the transformed coordinates. ... 64 Figure 3.1. Noise spectrum in geophysical phenomena. ... 70 Figure 3.2. Spatial distribution of the selected CGPS stations. Stations have highest

spatial density over the Saint Lawrence River valley, and are shown with a larger scale in the lower-left inset. ... 73 Figure 3.3. The Lomb-Scargle periodogram and the estimated spectral indices for

station SCH2. ... 85 Figure 3.4. Histogram of the spectral indices estimated by (A) the spectral analysis,

and (B) the Maximum Likelihood Estimation methods. ... 86 Figure 3.5. (A–E) Graphical representation of the estimated noise amplitudes in

different models, (F) correlation of white noise versus flicker noise

amplitudes for all stations except LOZ1. ... 89 Figure 3.6. Flicker noise amplitudes as a function of (A) station latitude, and

(B) station longitude for the north (n), east (e) and up (u) directions as well as their one-sigma uncertainties and the quadratic trend in the

least-squares sense. ... 96 Figure 3.7. Spatial distribution of the stations with non-zero random-walk amplitude.

The scale for SASK is 1/20. ... 98 Figure 3A.1. Graphical representation of the CGPS observations. ... 105 Figure 3A.2. The common power spectrum for all CGPS stations filtered with the

window length of 11 days. ... 106 Figure 3A.3. Comparison of different noise models according to the Maximum

Likelihood Estimation values. ... 107 Figure 4.1. The EPC main window shows the estimated Euler pole parameters for the

North American tectonic plate, based on the sample input data file. The upper- and lower-left tables show the imported and the calculated velocities based on parameters of the Euler pole, respectively. The map canvas on the upper-right hand showing a map of tectonic plates

superimposed on the world map gives the user an overview of the place of stations and velocity vectors. The statistical information on lower-right side of the window provides information about the quality of the least-squares adjustment in the inverse Euler pole problem. The regression canvas in the lower-right corner shows the scatter plot of the observed (input) versus the [estimated] (output) velocities separately for the north

and the east components. ... 126 Figure 5.1. Instrumental earthquakes with M ≥ 3 recorded from 1945 until mid-2014

and historical earthquakes estimated since 1663 in eastern Canada (data source: Earthquake Canada and the Advanced National Seismic System of the United States). The clusters of seismic activities are delineated as

well as the seismic zones along the Saint Lawrence River valley ... 135 Figure 5.2. Spatial distribution of the CGPS stations used in this study. Green solid

triangles show the final selection. Other stations are excluded from the estimation process because they are affected by different phenomena explained in the text and therefore do not present the real tectonic rotation of the study region ... 137

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Figure 5.3. (A) North and (B) east residual velocities for the final 19 stations used for the estimation of the absolute Euler pole of rotation for eastern Canada. In general, east residuals are smaller than north residuals despite their larger uncertainties. This explains the better accuracy in longitude of the

estimated rotation pole shown in Table 5.2. ... 141 Figure 5.4. Intraplate horizontal velocities calculated from Euler poles for the North

American plate ITRF 2008 (NOAM08) and from eastern Canada ITRF 2008 (EC08) models illustrated by red and blue arrows,

respectively. Although consistent to the first degree, the EC08 intraplate horizontal velocities are generally smaller over the Saint Lawrence River valley (see the inset). This shows the EC08 model can model the

horizontal velocity field of this region better than the NOAM08 model. ... 144 Figure 5.5. (A) North and (B) east postfit residual velocities for all stations except

MINW, HULL, GAS2, GODR, and MCHN. Stations are sorted according to their longitudes. In general, the postfit residual velocities calculated from eastern Canada ITRF 2008 (EC08) model are smaller especially for stations located at the Saint Lawrence River valley. ... 145 Figure 5.6. (A) Overview of the vertical velocity field obtained from CGPS

observations. Stations GODR and LOZ1 have very different vertical velocities with larger sigma values compared to the nearby stations and therefore are excluded. (B) Horizontal velocity field predicted by the ICE-5G model. Bold arrows show predicted velocities by this model at the CGPS stations. (C–D) Misfits between CGPS-derived vertical velocities and predicted velocities from ICE-5G and ICE-6G models, respectively. Misfits in (C) are larger than in (D) and are spatially

systematic. ... 148 Figure 6.1. A typical (A) strain ellipse and (B) strain hyperbola and their strain

crosses. Axes are directed along the eigenvectors of the strain tensor. ... 166 Figure 6.2. Concept of the collocation method in a one dimensional longitudinal case.

The trend and the signal in data are shown by Ax and s in (6.19), respectively. The noise n is the difference between the signal and the

observation points. ... 171 Figure 6.3. Relationship among covariance functions. (A) Holds under assumption of

zero-means and the fact that the signal s and the noise n are stationarily uncorrelated. The gray area represents the covariance function of the noise. (B) Holds in practice when the measuring errors are uncorrelated, and therefore C d n

 

0 when d 0 and C dl

 

C ds

 

for all d 0 (Mikhail and Ackermann, 1976). d is the distance between any two

points whose covariance is considered. ... 173 Figure 6.4. The main window of GeoStrain. ... 177 Figure 6.5. Comparison of the observed and interpolated velocities with different

noise levels: (A) without noise, (B) ±0.5 mm/yr noise, and (C) ±1 mm/yr noise. (D) Correlation coefficients of results with respect to the noise

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Figure 6.6. Comparison of the theoretical and estimated strain rate tensors in

10μstrain/yr (A and B), rotation rate tensors in °/102_{Myr (C and D), and}

maximum shear strains in 10nstrain/yr (E and F). ... 181 Figure 7.1. Seismicity of eastern Canada including shallow instrumental earthquakes

with depth of less than 30 km between 1945 and mid-2014 with M ≥ 3 and historical earthquakes since 1663 (data source: Earthquake Canada

and the US Advanced National Seismic System). ... 192 Figure 7.2. Variance-covariances of the vertical velocity field and the best-fitted

empirical covariance function (ECF). Covariances with negative values were not used to estimate the parameters of the ECF, and therefore not

shown in this figure. ... 200 Figure 7.3. (A) CGPS-derived vertical velocities and the model. (B) Differences

between CGPS vertical velocities and ICE-6G (VM5a) model. ... 201 Figure 7.4. Misfits between CGPS vertical velocities and radial velocities of

ICE 5G/6G GIA models. ... 203 Figure 7.5. (A) Estimated CGPS intraplate horizontal velocities. Velocities in

zones A, B, and C are corresponding to Dome of Hudson over Ontario, Dome of New Quebec over Quebec, and Dome of Foxe to the northeast of Hudson Bay, respectively. (B) CGPS interpolated and ICE-6G

intraplate horizontal velocities. ... 204 Figure 7.6. (A) Principal axes of strain rates and (B) rotational rates of eastern

Canada. ... 207 Figure 7.7. (A) Dilatation rates and (B) maximum shear strain rates of eastern

Canada. Epicenters of earthquakes with depth of less than 30 km are also plotted (data has the same source as in Figure 7.1). ... 209 Figure 7.8. (A) Principal axes, and (B) maximum shear strain rates for the Saint

Lawrence River valley. ... 211 Figure 7.9. World stress map for the Saint Lawrence River valley. ... 213

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List of abbreviations

The following is the list of the most important abbreviations used in this dissertation. Gen-eral and common abbreviations such as m (stands for meter) or geographical directions are not mentioned here.

AIUB Astronomical Institute of the University of Bern ARP Antenna Reference Point

ASCII American Standard Code for Information Interchange

BIFROST Baseline Inferences for Fennoscandian Rebound Observations, Sea-level, and Tectonics

BPE BERNESE Processing Engine

BSD Berkeley Software Distribution

BSW BERNESE GNSS software

CACS Canadian Active Control System CASMI Create A Stress Map Interactively CATS Create and Analyze Time Series

CBN Canadian Base Network

CCS Cartesian Coordinate System

CentOS Community ENTerprise Operating System CGPS Continuously operating GPS

CL Covariance Length

CME Common-Mode Error

CORS Continuously Operating Reference Station (of the United States) CRG Center for Research in Geomatics

CSV Comma-Separated Values

CSZ Charlevoix Seismic Zone

EC Eastern Canada

ECEF Earth-Centered Earth-Fixed ECF Empirical Covariance Function

EGPS Episodic GPS

EPC Euler Pole Calculator

FFGG Faculty of Forestry, Geography, and Geomatics FFT Fast Fourier Transformation

FK Flicker (noise)

GIA Glacial Isostatic Adjustment

GIMP GNU Image Manipulation Program

GIS Geographic/Geospatial Information System GITSA GPS Interactive Time Series Analysis

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GNSS Global Navigation Satellite Systems

GNU GNU's not UNIX

GPL General Public License GPS Global Positioning System GSC Geological Survey of Canada

GSD Geodetic Survey Division (of Canada) GUI Graphical User Interface

GYBP Giga Years Before Present HPC High Performance Computing

Hz Hertz

IGS International GNSS Service

INGV Istituto Nazionale di Geofisica e Vulcanologia

(National Institute of Geophysics and Volcanology of Italy) ITRF International Terrestrial Reference Frame

IQR Interquartile Range JPL Jet Propulsion Laboratory JVM Java Virtual Machine

KML Keyhole Markup Language

kYBP kilo Years Before Present

LG Local Geodetic

LGM Last Glacial Maximum

LGPL Lesser General Public License LIS Laurentide Ice Sheet

LSC Least-Squares Collocation

LSZ Lower Saint Lawrence River valley Seismic Zone MATLAB Matrix Laboratory

MERNQ Ministère de l'Énergie et des Ressources Naturelles du Québec (Ministry of Energy and Natural Resources of Quebec)

MLE Maximum Likelihood Estimation MYBP Million Years Before Present

NaN Not a Number

NASA National Aeronautics and Space Administration (of the United States) NGS National Geodetic Survey (of the United States)

NNR No-Net-Rotation

NOAM North America

NRCan Natural Resources Canada

NS Number of Stations

NSERC Natural Sciences and Engineering Research Council (of Canada)

OS Operating System

PBO Plate Boundary Observatory PCV Phase Center Variation

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PEM PlatE-Motion

PGR Post-Glacial Rebound

PL Power-Law

PSD Power Spectral Density

PSInSAR Persistent Scatterer Interferometric Synthetic Aperture Radar QIF Quasi-Ionosphere-Free

RAM Random Access Memory

RW Random-Walk (noise)

SLRV Saint Lawrence River valley

SOPAC Scripps Orbit and Permanent Array Center TRF Terrestrial Reference Frame

UNAVCO University NAVSTAR Consortium

VM Viscosity Model

VMF Vienna Mapping Function

WF White plus Flicker (noise)

WFR White plus Flicker plus Random-walk (noise)

WH White (noise)

WQSZ Western Quebec Seismic Zone WR White plus Random-walk (noise)

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Dedication

In dedication to my family

with love

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Acknowledgements

Many individuals helped me during my study at Laval University and my stay in Quebec City that I would like to state my truthful thanks to them. My first appreciation goes to my first research advisor, Dr. Marc Cocard, for his advice, encouragement, commitment, im-mense knowledge, and unsparing support. He taught me how to be an independent re-searcher by letting me to make my own decisions at pivotal points along the way. I would also like to convey my gratitude to my second research advisor, Dr. Rock Santerre, for his continuous encouragement and generous support. He was always ready to assist me, and to answer my emails and questions promptly. I would like to thank both of them for their sig-nificant support, criticism, and enthusiasm in our biweekly meetings especially during the last year of my research.

Besides my research advisors, I specially thank my thesis jury, Dr. Mir Abolfazl Mostafavi from Laval University, Dr. Joe Henton from Natural Resources Canada, and Dr. Georgia Fotopoulos from Queen’s University for serving as my committee members, and for letting my defense be an enjoyable moment, as well as their insightful comments and suggestions that improved further the quality of my thesis.

I gratefully thank Dr. Alfred Leick (the Editor-In-Chief of the GPS Solutions journal), Mr. Steve Hilla (the US National Geodetic Survey), Dr. Mike Craymer (Geodetic Survey of Canada), Dr. Donald Argus (Jet Propulsion Laboratory, California Institute of Technology), Dr. Jeff Freymueller (University of Alaska Fairbanks), Dr. Matt King (University of Tas-mania) and the anonymous reviewers of my papers for their brilliant comments and sound advices that considerably improved the quality of my dissertation and my developed soft-ware applications.

I thank the whole Geomatics Department of Laval University for their administrative sup-port. Specially, I would like to name Mrs. Stéphanie Bourgon for translating abstracts of chapters 2–7 as well as the main abstract of the dissertation into French. She also trans-ferred me the GPS data of the Ministry of Energy and Natural Resources of Quebec. Fur-thermore, I gratefully thank Dr. Mir Abolfazl Mostafavi for providing access to the Regard Computer cluster for processing the huge GPS data set of this research.

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I appreciate all the help and support I received from my Iranian colleagues and friends in Quebec City. Among them, I can name: the Alvandi family, the Hosseini family, the Ho-seinizadeh family, the Mashreghi family, the Mostafavi family, the Rahimi family, the Rezvani family, the Soroushian family, and many others. I appreciate their presence and support, particularly in difficult times, and wish them all good luck.

I extend my deepest gratitude to my father and mother who went through a lot while I was absent. They have given me tremendous support and deserve so much more than a simple “thank you”. I owe them a lot and will be grateful to them all my life. I apologize them sin-cerely because of my long absence and therefore not being able to help them at their old age. This work would not have been possible without the vital financial support and en-couragement of my dear father who paved me the road to success. Words cannot express how grateful I am to my father for all of the sacrifices that he made on my behalf.

Last but not least, I thank my spouse, Bahareh, and my children, Parmida and Pouya, for being tolerant angels and bringing happiness and enjoyment to my life. Although I always did my best to fulfill their desires, wishes, and needs, I apologize them for the shortcomings and not being the husband/father they deserve during my PhD period.

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Foreword

This dissertation is the brief description of methods used for yet the comprehensive discus-sion of the results obtained from studying the tectonic deformation of eastern Canada using continuous GPS observations and geodetic methods. I spent almost three years and half to complete this research at Center for Research in Geomatics (CRG) of Laval University. The main purpose of this research is to quantify the contemporary crustal deformation in eastern Canada. There are two major contributions that can be considered as a novel component for this research:

 Assessing uncertainties within the data through models. Since the level of accuracy or resolution required by geophysical phenomena is quite high, it is often difficult to work within the error envelope. However, a start point is to acknowledge and ad-dress this issue with known tools. The next step would be to incorporate this infor-mation and update models and projections.

 An empirical approach for modelling the velocity and strain rate fields of eastern Canada using GPS position time series. This can provide important constraints to seismic hazards models by defining the spatial distribution and magnitude of the fu-ture large earthquakes.

The main outcomes of the work consist in a present-day (a) three-dimensional (intraplate) velocity field and (b) vertical velocity model for the entire study region, and (c) a horizontal strain rate field for the Saint Lawrence River valley, among others. Furthermore, I devel-oped three software applications for analysis of position time series, direct and inverse Eu-ler pole problem, and strain rate calculation based on the least-square collocation method. The achievements of this study are organized in six chapters according to the objectives. Of this number, four chapters have been already published in, and two chapters are submitted to peer-reviewed journals. One of the published papers, about GPS time series analysis, was not included in this thesis in order to increase the consistency among chapters. The list of publications can be found in Appendix 3, and the permissions to include them in this dissertation are provided in Appendix 4. All these papers have been written by the author of

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this thesis under the supervision of Dr. Marc Cocard and Dr. Rock Santerre from Laval University, Canada, and the collaboration of Dr. Tsehaie Woldai, from University of Twen-te, the Netherlands (only for the omitted paper as mentioned earlier).

In order to integrate the papers in this dissertation, it was sometimes necessary to add some texts in order to adapt them with the format of the dissertation mandated by Faculty of Graduate and Postdoctoral Studies of Laval University. Therefore, along with adjusting section numbers to the new format, I used square brackets to enclose new words added oth-er than the original published text in ordoth-er to clarify the situation. Some figures woth-ere repro-duced to get benefit of more space allowed for a standard dissertation compared to a journal paper. I also unified the terminology and the writing style among chapters by replacing some terms (e.g., “site” with “station” or “paper” with “chapter”), abbreviations (e.g., “USA” with “US”), and punctuation. Furthermore, keywords of each chapter were sorted alphabetically and abbreviations were excluded. Since each paper has almost the same structure of a complete thesis (i.e., abstract, introduction, methodology, etc.), repetition was inevitable. However, I put forth my best effort to reduce redundancy among chapters. In this way, I avoided to repeat the description of general methods, e.g., GPS data processing, which helped to keep the dissertation more concise.

The intensive numerical calculations of this research including GPS data processing and noise analysis were performed on the cluster computer of the Regard Laboratory of CRG. The cluster computer comprises 13 computing nodes, including eight 64-bit XEON CPUs with the core speed of 2.33 GHz and 8 GB Random Access Memory (RAM) per computing node, and operates by the CentOS release 6.5. Such a processing capability provided a High Performance Computing (HPC) facility for this research.

The dissertation comes with supplementary materials, including all the outputs of the GPS data processing software (e.g., SINEX solution files), position time series in different coor-dinate systems (e.g., ECEF and LG) or processing level (e.g., raw and outlier-cleaned), jump epoch files, residual time series, power spectra, maximum likelihood estimations, shape files, and all other intermediate results as well as MTLAB or BASH scripts for data analysis and visualization. They are published in the form of a DVD accompanying this dissertation. Some other results, computer codes, or personal experiences in geodetic data

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processing and analysis will be published on my personal weblog available at http://geonics.blogspot.ca. Lastly, I hope that readers of this dissertation find it a useful work and inform me about their constructive comments.

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Chapter

1

.

Introduction

1.1. Introduction

Eastern Canada is subject to two important geophysical processes: the glacial isostatic ad-justment (GIA), and intraplate tectonic activities. After the overall rotation of the North American plate, the GIA is the most major geophysical process causing vertical uplift over this region and subsidence across northern United States (Figure 1.1). It is estimated that the last glacial maximum (LGM) has occurred about 20 kYBP (Richmond and Fullerton, 1986), during that many areas in North America and Scandinavia peninsula were covered by ice sheets of up to four kilometers depth extended over thousands of kilometers. During the Wisconsin ice age (late Pleistocene), the ice sheets advanced over the Saint Lawrence River valley (SLRV) and extended to the east into the Maritime Provinces and to the south into New England. As a consequence of the ice weight, the lithosphere was depressed and the resulting viscoelastic flow in the mantle caused peripheral bulges (Mitrovica et al., 2001). The ice sheets began melting and getting thinner since 10 kYBP. This caused the lithosphere rebounds upward to the regional isostatic equilibrium and the peripheral bulges migrate inward to the center of uplift as it was gradually dissipated. This process is called GIA.

The GIA has a clear evidence in the form of a three dimensional movement on the earth’s surface accompanied by change in gravity measurements in consequence of crustal uplift and mantle flow (Wahr et al., 1995). The GIA is continuous and the regions of highest up-lift rates are generally consistent with areas of the thickest ice accumulation during the last period of continental glaciation (Dyke, 2004; Peltier, 1994). The uplift rate reaches 13 mm/yr or more around Hudson Bay and decreases further away (Figure 1.1). The rate of uplift is much larger than inland sedimentation rate (0.3 mm/yr) far from coasts (Árnadóttir

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micity (Adams and Basham, 1991). Large earthquakes within the stable plate boundaries are evidence of accumulating significant amounts of elastic strain along geologic structures far from plate boundary faults (Calais et al., 2006).

Figure 1.2. Historical and instrumental earthquakes in or near Canada between 1627 and 2012 (source: http://www.earthquakescanada.nrcan.gc.ca/historic-historique/caneqmap-eng.php, accessed: June 18, 2015).

Even though earthquakes can occur everywhere in eastern Canada, the earthquake cata-logue of seismicity (Figure 1.3) clearly shows five distinct clusters of seismic activity in (a) Baffin Bay to the eastern north of the continental margin, (b) a band from northwest of Hudson Bay to north of Quebec, (c) along the SLRV and Ottawa valley, (d) the northern Appalachians region including most of New Brunswick and extending into New England down to Boston, and (e) the Laurentian Slope comprising southeastern coast of Canada and including the Grand Banks of Newfoundland (Adams and Basham, 1991, 1989a, 1989b; EqCan, 2015; Mazzotti and Adams, 2005; NRCan, 2013).

The cause of earthquakes in eastern Canada is not well-understood. In general, it is hypoth-esized that the seismic activity in intraplate zones is related to the regional stress fields, and earthquakes concentrate in regions with the crustal weakness. Rondot (1968) suggests a volcanic origin for the Charlevoix semi-circular structure due to its location on the margin

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and specific objectives of this work are introduced in Sections 1.6 that is followed by the general methodology in Section 1.7. Finally, the main contributions and the structure of the whole dissertation are outlined in Section 1.8.

1.2. Study area

Canada east of Cordillera, extending north from the US border to the Arctic Ocean, com-prises about two-third of the stable craton of the North American plate. Although most of this large area appears to be substantially aseismic, it contains several zones of significant seismicity and a few other regions with lower-level of seismicity. Located in eastern Que-bec, the SLRV is still prone of substantial intraplate seismicity and earthquake hazards (Figure 1.3), even though it is seismically less active compared to the plate boundary to the west. This area has a large range of intraplate earthquake patterns, from zones with large earthquakes (M = 6–7) to zones with very little background seismicity (Adams and Basham, 1991).

Along the SLRV and the Ottawa valley, earthquakes are mainly concentrated in three dis-tinct clusters of activity: the western Quebec seismic zone (WQSZ) along the Ottawa River from Montreal to Temiscaming as well as Laurentians and eastern Ontario, the Charlevoix seismic zone (CSZ) located about 100 km downstream from Quebec City, and the Lower Saint Lawrence seismic zone (LSZ) located in the same direction to the CSZ in the estuary of the SLRV about 400 km far from Quebec City (Adams and Basham, 1991; NRCan, 2013).

The CSZ is the locus of the strongest earthquakes with five M ≥ 6 events in the past 350 years (NRCan, 2013). Because most of the earthquakes in this area occur under the SLRV, between Charlevoix area on the north shore and Kamouraska area on the south shore, this region is also referred to as the Charlevoix-Kamouraska seismic zone. Occurrence of more than 200 earthquakes per year makes the CZS the zone of highest seismic hazard in eastern Canada.

The LSZ experiences lower seismic activity compared to the CSZ in terms of the number and the magnitude of earthquakes. Only two events are known to have exceeded the magni-tude of 5.0 during the past 70 years. While the LSZ has had five earthquakes of magnimagni-tude

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4.0 or larger between 1977 and 1997, the CSZ has had eight events during the same period. About 60 events happen in the LSZ annually, most of them under the SLRV within a trian-gular zone defined by the towns of Baie-Comeau, Sept-Iles, and Matane. This area is also named “Lower Saint Lawrence-Quebec North Shore” seismic zone, as the most earth-quakes occur under the SLRV between the regions of the Quebec north shore and the Low-er Saint Lawrence. In contrast to the CSZ and the LSZ, the area between Quebec City and Montreal does not show high seismic activity.

The WQSZ constitutes a vast territory that encloses the Ottawa valley from Montreal to Temiscaming, as well as the Laurentians and the eastern Ontario. Earthquakes are apparent-ly concentrated in two sub-zones within this area: one along the Ottawa River and the other along the more active Ottawa–Maniwaki axis. The WQSZ was shocked by four M ≥ 5.0 earthquakes during the past 300 years (NRCan, 2013).

The seismo-tectonic setting of the SLRV makes it an interesting area for testing the rela-tionship between crustal strain, paleotectonic structures, and earthquake locations and mag-nitudes in an intraplate environment. In particular, the LSZ provides a good opportunity to study the present day crustal strain rates in regions of high, medium, and low past earth-quake activity (Mazzotti et al., 2005).

1.2.1. Geological settings

The SLRV is located within an intraplate tectonic setting since about 200 MYBP but has been the locus of several major tectonic events in the last approximately 1 GYBP. The ear-liest tectonic phase is the Grenville Oregon (Figure 1.4) from about 1100 MYBP to about 900 MYBP, which is associated with the accretion of allochthonous terranes to the south-east margin of the Laurentia (North America) craton. In the late Proterozoic (700– 600 MYBP), the region was affected by the rifting and opening of the Iapetus (proto-Atlantic) Ocean (e.g., Kumarapeli, 1985). This major episode of extension corresponds to the formation of large-scale systems of normal faults along the rifted margin and associated aulacogens across most of eastern North America. Major structures of the Iapetan system include the Saint Lawrence, Ottawa, and Saguenay grabens in Canada and the Reelfoot Rift, Rough Creek grabens, and southern Oklahoma aulacogen in the center of the United

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States (Wheeler, 1995). The closing of the Iapetus Ocean corresponds to different devel-opment phases of the Appalachian Oregon during the mid to late Paleozoic, possibly as late as Permian (about 250 MYBP) (Faure et al., 1996; Williams, 1979). The Appalachian nappes were thrust over the North America craton as far west as the SLRV. During the Ju-rassic rifting and opening of the North Atlantic ocean, the reactivation of Iapetan normal faults marks the last phase of significant tectonic activity in the Saint Lawrence area (Lemieux et al., 2003).

The SLRV is characterized by large eastward dipping normal faults with up to a few kilo-meters of motion documented in the Precambrian basement (Kumarapeli, 1985; Tremblay et al., 2003). The normal fault system is capped by westward verging thrust faults and nappes of the Appalachian Oregon. This Paleozoic cover is only a few kilometers thick in most of the Saint Lawrence region. A meteorite impact (about 350 MYBP) in the southern part of the Charlevoix seismic region contributed additional complexity by creating an ap-proximately 60 km diameter system of concentric faults and fractures (Lemieux et al., 2003).

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1.2.2. Seismicity

Most of seismicity within intraplate regions is associated with inactive rifted margins, failed rifts, and extensional basins (Johnston, 1989). This pattern is found in southeastern Canada where the Iapetan rift system is the locus of most of the medium and large earth-quakes (Adams and Basham, 1991). The seismicity in this region corresponds to about 4 events with M ≥ 4 and 30 events with M ≥ 3 per year and about three M ≥ 5 earthquake per 10 years (NRCan, 2013). Most of these background earthquakes are concentrated in the CSZ and the LSZ, but the CSZ has experienced predominantly more powerful events. The region has also experienced large and destructive earthquakes in the past. In 1982, a series of earthquakes occurred in the northern Appalachians seismic zone with M = 5.7 for the largest event (Figure 1.3). The large earthquake (M = 7.2) of 1929 near the Grand Banks in the Laurentian Slope seismic zone produced a large tsunami. At least 4 earthquakes with M ≥ 5 have been recorded in the WQSZ in 1732 (M = 5.8), 1935 (M = 6.2), 1944 (M = 5.6), and 1990 (M = 5). The CSZ is the locus of the strongest earthquakes among other seismic zones. This zone has been subject to at least five large (M ≥ 6) events in the past 350 years in 1663 (M = 7), 1791 (M = 6), 1860 (M = 6), 1870 (M = 6.5), and 1925 (M = 6.2). Among them, only the event of 1925 was recorded by seismographs and the previous events have approximate magnitudes evaluated using felt areas and the damage. Since 1977, the CSZ is monitored using a local network of seven seismographs concentrated on the active zone. From 1978 to 1997, the network detected about 2200 local earthquakes, among them 54 events with M ≥ 3.0 and 8 events with M ≥ 4.0. On average, an earthquake occurs in the CSZ every day and a half. The LSZ has the lowest rate of seismic activity and only two earthquakes of M ≥ 5 have been occurred in 1944 (M = 5.1) and 1999 (M = 5.1) in this area. Between 1977 and 1997, the LSZ has had five earthquakes of M ≥ 4.0, whereas the CSZ has had eight events during the same period. The LSZ is also closely monitored by a net-work of five local stations of seismographs. About 60 events are recorded in the LSZ annu-ally. On average, an earthquake occurs in the LSZ every five days (NRCan, 2013). In contrast to the CSZ and the LSZ, significant seismic activity is almost absent in the upriver, between, and downriver areas from these two zones.

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Large earthquakes in eastern Canada have had casualties. The M = 6.5 earthquake of 1870 had two casualties in the Les Éboulements area (Lamontagne, 2008). 27 people were com-pletely sank on the south coast of Newfoundland due to the consequent tsunami of the M = 7.2 Grand Banks earthquake of 1929 (Adams and Basham, 1989a).

1.3. Previous works

Since the early 1970s, the SLRV has been under ongoing monitoring of the earthquake hazard by a number of institutions. Among them, the Earth Physics Branch now a part of Geological Survey of Canada (GSC) concentrated on the CSZ, and the Geodetic Survey Division (GSD) of the Natural Resources Canada (NRCan) started an extensive program to study the geodynamics of eastern Canada.

The CSZ is a well-known area along the SLRV due to occurrence of many large historical earthquakes during the last four centuries (Section 1.2.2). However, details of the small scale earthquakes and geographical extent of the area were incomplete, mainly because of the large errors in determination of the epicenters (Buchbinder et al., 1988). The first field experiment was conducted in 1968 in order to define the extent and rate of the micro-seismicity (Milne et al., 1970), albeit with very few instruments and essentially inconclu-sive results. A larger experiment undertaken in 1970 (Leblanc et al., 1973) located the CSZ boundary to the southwest and an even larger survey in 1974 (Leblanc and Buchbinder, 1977) found the boundary to the northeast. The earthquake potential of the CSZ led the GSC to conduct two seismic field surveys in 1970 and 1974. These two surveys clearly delineated the CSZ to be an active zone about 30 km by 85 km, extended along the SLRV and enclosing the towns of Baie-Saint-Paul, La Malbaie, and La Pocatière (NRCan, 2013). In 1974, the Earth Physics Branch began an extensive geophysical monitoring program in the CSZ. Many parameters including micro-seismicity, seismic travel times, electrical im-pedance, vertical movement, horizontal movement, tilt, gravity change, and strain through water well level changes were studied with the goal of developing the capability of predict-ing earthquakes in the area. Although no clear precursor was detected in the months before the largest seismic event of 1974 with M = 5.0 that occurred during the observation period,

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the multi-parameter experiment provided new insights into the structure and the mechanics of this active region (Buchbinder et al., 1988).

Mazzotti et al. (2005) have studied the amplitude, pattern, and origin of the crustal defor-mation in the upper SLRV using observations of 16 GPS stations from the Canadian base network (CBN) surveyed three or four times between 1994/1996 and 2003 with an average of ~3.5 days for each survey. The GPS stations have shown coherent south-eastward mo-tion of 0.6±0.2 mm/yr relative to the North American plate, and uplift rate of 2.6±0.4 mm/yr. The average value of the horizontal strain rates are mostly ESE-WNW shortening at −(1.7±1.0)×10−9_{/yr. They have also measured a coherent pattern of the GIA}

with the uplift rate of 4–5 mm/yr in the northwest decreasing progressively to less than 1 mm/yr in the southeast of their study area. Based on these measurements, they have con-cluded that the shortening rate across the CSZ is about twice as big as the regional average and that the motion is consistent with the lithospheric GIA.

In another study published by Lamothe et al. (2010), the first-order precise levelling data has been used along with GPS measurements in order to quantify the local horizontal and vertical deformations in the CSZ. The study is based on the analysis of repeated levelling lines of the Canadian first-order vertical network measured between 1909 and 1991 in the CSZ, as well as the first-order GPS network along the SLRV surveyed in two campaigns of 1991 and 2005. The results from the precise levelling analysis showed that the pattern of relative uplift is increased toward northwest, perpendicular to the direction of the SLRV. The GPS observations showed a coherent horizontal velocity field toward the east and the southeast, and a coherent vertical velocity field compatible with the previous GPS cam-paigns and GIA models was observed.

George et al. (2011) have quantified the GIA in eastern Canada using less than 5.3 years observations of 39 CGPS stations from 2001 to 2006. Tiampo et al. (2012) constrained the pattern and magnitude of the regional crustal deformation using a subset of 43 CGPS sta-tions with the same time span as used in the former research.

According to predictions of the GIA models (e.g., ICE-3G VM1), the hinge line between crustal uplift and subsidence is located to the south of the SLRV (Tushingham and Peltier,

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1991). This prediction is validated by a number of researchers. The uplift pattern in the SLRV found by Mazzotti et al. (2005) is consistent with the model, to the first order. A similar location of the hinge line was found by Sella et al. (2007) based on the analysis of motions of 360 GPS stations (continuous and episodic) in Canada and the United States. According to the latter study, the hinge line is also consistent with data from water level gauges in the Great Lakes, showing uplift and subsidence along the northern and the south-ern shores, respectively.

1.4. Motivation for this research

The seismic background stated in Section 1.2 shows the probability of occurring earth-quakes all along the SLRV and Ottawa valley. Whether damaging or not, recurrence of such earthquakes is an important issue for the seismic hazard especially in the urban centers of Quebec City, Montreal, Ottawa, Gatineau, and Cornwall, among others. To our best knowledge, this area was never studied before with CGPS observations and there is neither a study about noise behavior of CGPS stations in eastern Canada nor about physical stabil-ity of their monuments. This is of special importance because, (a) the intraplate tectonic signal, which is the main cause of deformation, has a very low rate in this region, and (b) many CGPS stations in this region have not been principally intended for geodynamic studies. In other words, despite its importance, no dedicated GPS network has yet been es-tablished in this area with the primary goal of monitoring intraplate tectonic activities such as in Southern California and Southern Nevada (Langbein, 2008; Tiampo et al., 2004; Wdowinski et al., 1997; Zhang et al., 1997), Fennoscandia (Bergstrand et al., 2007; Johansson et al., 2002), and Central Europe (Kenyeres and Bruyninx, 2009). Nevertheless, there are several CGPS stations managed by different federal or provincial agencies that can potentially be used for geodesy and geodynamic studies. The non-geodetic monument of some stations motivated to perform a noise analysis in order to test their physical stabil-ity and therefore deciding whether to include or exclude them from further deformation studies such as strain analysis.

1.5. Research problems

Despite all the valuable geodetic researches that were already done to quantify the tectonic deformation of eastern Canada, the following issues are not yet fully addressed.

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1.5.1. Campaign data

Although Mazzotti et al. (2005) have shown that campaign GPS measurements over 6– 9 years can provide useful information on the recurrence period and maximum magnitude of large earthquakes, there are still major limitations associated with campaign GPS meas-urements such as: (a) lack of resolution of short-term (annual/semi-annual) deformation episodes, and (b) less accurate estimates of long-term velocities (Henton et al., 2006). Fur-thermore, the discrete character of episodic GPS data prevents the direct estimation of the amplitude of different noise components (Chapters 2 and 3).

1.5.2. GIA horizontal motions

High precision GPS-derived horizontal velocities can provide an important additional con-straint to the GIA models that generally predict a pattern of horizontal divergence away from centers of uplift (James and Lambert, 1993; Peltier, 2002, 1998). Near the margin of the formerly glaciated region, horizontal motions may exhibit more complex patterns relat-ed to the details of forebulge collapse. Further away from the deglaciatrelat-ed region, the direc-tion of horizontal flow can be either toward or away from the loads, depending on the assumed early glacial history and mantle viscosity profile (Mazzotti et al., 2005). Although the vertical motions are generally consistent with predictions of GIA models, the horizontal data illustrate the need and opportunity to improve the models via more accurate descrip-tions of the ice load and laterally variable mantle viscosity (Sella et al., 2007) (Chapter 2).

1.5.3. Assumption about the noise model

The CGPS position time series usually show complex non-linear behavior, and the associ-ated noise is more complicassoci-ated than simple white noise. Analysis of the CGPS time series by Mao et al. (1999) and Williams et al. (2004) has indicated that the uncertainty associated with frequency-dependent noise is mostly analogous to a combination of white and flicker noise. The complication is often related to geophysical phenomena such as offsets due to earthquakes, post-seismic transient behavior, and more noise-like phenomena such as cy-clic water table changes. It can also be originated from offsets due to change in the receiver, antenna, or antenna radomes (Herring, 2003). Other candidates to explain non-linearity in the position time series may be side effects caused by the succession of GPS satellite block

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types (Ge et al., 2005), contributions from higher order ionospheric terms (Kedar et al., 2003), and physical instability of GPS stations (Chapter 3).

1.5.4. Resolution of the geodetic methods

While relative velocities across tectonically active regions are typically of the order of 5– 50 mm/yr, which can be easily resolved with annual GPS campaign data over a period of three to five years, relative velocities across intraplate regions are typically few millimeters per year. Previous studies of crustal deformation in intraplate seismic regions, such as New Madrid in center of the United States, have shown that the current strain level in regions of past large earthquakes is at or below the resolution of geodetic methods (Hamburger et al., 2002; Newman et al., 1999). At the same level of importance of the amplitude and patterns of crustal strain rates, a robust estimation of the uncertainties on geodetic measurements is a major issue for seismo-tectonic studies in intraplate environments (Chapter 2).

1.5.5. Other considerations

Further to the listed problems, there are still some more limitations in geodetic models and methods, among them, sensitivity of the GIA models to their parameters, possible limita-tions in the velocity solulimita-tions, and practical difficulties to apply new improvements.

The location of the hinge line as well as the amplitudes and spatial gradient of the predicted vertical rates are sensitive to parameters of the GIA model. Different viscosity structures for the same ice model show substantial differences in the predicted uplift rate (Peltier, 1998), and different deglaciation models for the same viscosity structure also show differ-ences of the same type (Peltier, 2002).

The choice of the earth tide model may influence derived station velocities as shown by Watson et al. (2006). Furthermore, a specific study on aliased tidal signatures in the GPS time series are presented in Penna and Stewart (2003), and the propagation of unmodeled systematic errors into the GPS position time series is investigated in Stewart et al. (2005) (Chapter 3).

New advances have been made in the recent years to improve precision of the results. For example, new tropospheric mapping functions (e.g., Tesmer et al., 2007), or absolute

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cali-bration values for GPS satellites and receivers antenna phase center variations (PCVs) are now available. Some of the possible improvements at the conceptual level may be, howev-er, difficult to be implemented in practice. As an example, including corrections for atmos-pheric loading at the observation level will improve the analysis (Tregoning and van Dam, 2005) but it is hard to apply due to, for example, manipulating the internal software of the GPS receiver or measuring real-time atmospheric parameters. As another example, the PCV determined by absolute antenna calibration may be valid for an isolated antenna, but may change due to electro-magnetic coupling and scattering effects when the antenna is attached to its monument (Granström and Johansson, 2006). Therefore, special attention should be directed to the mix of perturbations originating in the succession of GPS satellite blocks, antenna PCV models (relative or absolute), limitations in tropospheric mapping functions, and sites at high latitudes where satellites are no more visible up to zenith eleva-tion. This complicated budget of systematic errors with its non-stationary character is likely to result in systematic changes of estimated vertical position over time.

1.6. Research objectives

1.6.1. General objective

The main objective of this research is “to determine highly-accurate three-dimensional crustal movement and strain rate fields in eastern Canada using CGPS observations”.

1.6.2. Specific objectives

The specific objectives are also defined to support the overall objective of the research, as follows:

1. Deriving a three dimensional velocity field of the study region.

It is desirable to achieve a present-day three-dimensional velocity field using rela-tively long-term CGPS observations that is as independent as possible of any non-tectonic process occurring at a single station and various types of noise. This objec-tive is fulfilled in Chapter 2.