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THE DEFORMING BED BENEATH A SURGE-TYPE GLACIER: MEASUREMENT OF MECHANICAL AND ELECTRICAL PROPERTIES by ERIK WESTON BLAKE B.A.Sc., The University of Toronto, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Geophysics and Astronomy We accept this thesis as conforming to the required standard Signature(s) removed to protect privacy THE UNIVERSITY OF BRITISH COLUMBIA March 1992 ® Erik Weston Blake, 1992 In 57 2.4.2 Leaf spring tilt sensors 34 2.5 Potential sources of error 38 2.5.1 Sensor scale effects 38 2.5.2 The ice—bed interface 39 2.5.3 Sensor attitude 41 2.5.4 Sediment intrusion into the borehole 42 2.5.5 Connecting wires 44 Chapter 3. BED DEFORMATION: DATA ANALYSIS 46 3.1 Introduction 46 3.2 Experiment design 47 3.2.1 Ancillary information 48 3.2.1.1 Internal deformation 49 3.2.1.2 Basal sliding 53 3.3 The 1988 experiment 53 3.3.1 Correlation with effective pressure 3.3.2 Effective viscosity 61 3.4 The 1989 experiment 66 3.4.1 1989 tilt results 70 3.4.2 1989 strain rates 70 3.4.3 Subglacial pressure 73 3.4.4 Effective viscosity 74 3.4.5 Net strain and mean strain rate 75 3.5 Negative strain rates 76 3.5.1 Fluid models 77 3.5.1.1 Sheet flow 77 3.5.1.2 Extrusion 78 3.5.2 Roller bearing models 82 iv 100 103 104 107 108 112 113 115 118 119 3.5.3 The shadow box computer . 84 3.6 Discussion 85 3.6.1 Boulton and Hindmarsh flow models 86 3.6.2 Shear stress and normal stress 87 3.6.3 Effective viscosity 89 Chapter 4. ELECTRICAL PHENOMENA THEORY 91 4.1 Introduction 91 4.2 The rock—electrolyte interface 91 4.2.1 Gouy—Chapman model 92 4.2.2 Stern model 94 4.3 Conduction mechanisms 96 4.4 Electrical resistivity 97 4.4.2 Measuring electrical resistivity . 99 4.4.2.1 Potential fields 99 4.4.2.2 Interpretation 4.4.2.3 Current switching 4.4.2.4 Transient effects 4.5 Natural Potentials 4.5.1 Irreversible thermodynamics 4.6 Electrokinetic phenomena 4.6.1 Observing streaming potentials . 4.6.2 A theoretical development 4.6.3 Hydrodynamics and boundary layers 4.6.4 Zeta potentials 4.6.5 The reverse current 4.6.5.1 The charge accumulation model 4.6.5.2 The charge conservation model V 4.6.6 Calculating the streaming potential 120 4.7 Electrical phenomena relevant to this study 121 Chapter 5. ELECTRICAL PHENOMENA — METHOD 123 5.1 Introduction 123 5.2 The 1987 apparatus 123 5.2.1 Electrode configurations 124 5.2.2 Electrode design 124 5.2.3 Voltage measurement 125 5.2.4 Current source and current measuring 126 5.2.5 Additional control 128 5.2.6 Technical specifications 129 5.3 The 1988 apparatus 129 5.3.1 EPROM programs 129 5.3.2 The current multiplexer 130 5.3.3 The potential multiplexer 131 5.3.4 Electrode design 133 5.4 The 1989 apparatus 135 Chapter 6. ELECTRICAL PHENOMENA DATA ANALYSIS 136 6.1 Introduction 136 6.2 Predicted forcing/response relationships 137 6.2.1 Diurnal phenomena 138 6.2.2 Episodic phenomena 139 6.3 Assumptions 139 6.4 The 1987 experiments 141 6.4.1 Forefield operational test 141 6.4.2 Experimental design 142 6.4.3 Diurnal cycling of d.c. resistivity 144 vi 6.4.4 Geometrical corrections 145 6.4.5 Polarity reversals 145 6.4.6 Streaming potentials 147 6.4.7 Recapping the 1987 field season 148 6.5 Dedicated electrode arrays 149 6.6 The 1988 Experiments 149 6.6.1 Experimental design 150 6.6.2 Telluric noise 154 6.6.3 Potential error 155 6.6.4 Potential gradients 157 6.6.5 Hole connections 158 6.6.6 Overwintering events 162 6.7 1989 Experimental design 164 6.7.1 Fall shutdown 166 6.8 Manipulation experiments 168 6.9 Conclusions 173 6.9.1 Apparent resistivity 173 6.9.2 Streaming potentials 174 Chapter 7. CONCLUSIONS 176 7.1 General comments 176 7.1.1 Shear stress and normal stress 176 7.2 Electrical phenomena 178 7.2.1 Streaming potentials 178 7.2.2 Electrical resistivity . 179 7.3 Basal deformation 179 7.3.1 Rheology 179 7.3.2 Effective viscosity 180 vii 211 215 217 REFERENCES.. 182 Appendix A. INCLINOMETER DESIGN AND DATA PROCESSING 197 A.1 Introduction 197 A.2 Historical overview 198 A.2.1 Basic dip and azimuth measurements 198 A.3 Electronic incinometry 200 A.3.1 Measuring tilt 200 A.3.2 Measuring azimuth 200 A .3.2.1 External azimuth control 201 A.3.2.2 Internal azimuth control 202 A.4 The UBC inclinometer 203 A.5 Coordinate systems 205 A.6 Data analysis • . 207 A.6.1 Calibration • • . 208 A.6.2 Transformations A.6.2.1 Normalization 212 A.6.2.2 Eulerian Angles . 213 A.6.2.3 Eulerian Transformation A.6.2.4 Universal application of transformations A.6.3 Inverse problem • . 217 A.7 Interpolation Scheme 220 A.8 Sensitivity 223 A.9 Discussion 227 Appendix B. SUBGLACIAL WATER AND SEDIMENT SAMPLERS 229 B.1 Niskin sampler 229 B.2 Subglacial vacuum sampler 230 B.3 Considerations 234 yin Appendix C. SUBGLACIAL DRAG SPOOL 235 C.1 Introduction 235 C.2 The “Slide-O-Meter” or “drag spool” 235 ix LIST OF FIGURES 1.1. Location of Trapridge Glacier . 10 1.2. Topographic map of Trapridge Glacier 12 2.1. The borehole percussion hammer . • 20 2.2. Bed casts 23 2.3. Results from rubber rod experiment 24 2.4. Electrolytic tilt sensors • 27 2.5. Data from electrolytic tilt cells 32 2.6. Leaf spring tilt sensor 35 2.7. Data from leaf spring tilt sensors . 37 2.8. Drag spool data 43 3.1. Location of Trapridge Glacier 48 3.2. Velocity proffle through Trapridge Glacier 49 3.3. Internal deformation proffle 52 3.4. Location map for 1988 experiment . 54 3.5. Data from 1988 experiment 56 3.6. Comparison with Boulton and Hindmarsh data 65 3.7. Location map of 1989 experiment . 67 3.8. Data from 1989 experiment 69 3.9. Strain rate data from the 1989 experiment 71 3.10. Pressure data from the 1989 experiment 74 3.11. The vertical displacement record . 81 3.12. Roller bearing model 83 3.13. The shadow box 85 4.1. The rock—electrolyte interface 93 4.2. Detail of the Stern model interface . 95 x 106 120 125 127 135 142 143 146 147 148 150 151 152 153 156 157 159 160 167 170 4.3. Pseudo-depth calculation . 104 4.4. The d.c. resistivity current waveform 105 4.5. Induced polarization 4.6. Streaming potential equivalent circuit 5.1. The 1987 d.c. resistivity apparatus configurations 5.2. High voltage current limiter 5.3. A Cu—CuSO4 porous pot electrode 6.1. Forefield pseudo-section 6.2. Resistivity record P1, 1987 6.3. Resistivity record P2, 1987 6.4. Polarity reversing electrode pattern 6.5. Natural potential record from 1987 experiment 6.6. Relative locations of electrode arrays 6.7. Electrode array template 6.8. The 88DC01 electrode array 6.9. The 88DC02 electrode array 6.10. Effect of telluric noise on measurements . 6.11. Electrode noise 6.12. Natural potential fluctuation 6.13. Borehole forcing response 6.14. Diurnal cycling 162 6.15. Overwintering apparent resistivity record . 163 6.16. Overwintering natural potential record . 164 6.17. The 89DC01 electrode array 165 6.18. Fall shutdown electrical phenomena 6.19. Map of 88DCO1B electrode array 6.20. Subglacial phenomena during manipulation 172 xi A.1. Block diagram of UBC inclinometer 204 A.2. The inclinometer coordinates systems 206 A.3. The inclinometer orientation vectors 208 A.4. Eulerian angles transformations 214 A.5. The circular arc interpolation method . 220 A.6. Detail of circular arc interpolation method . 221 A.7. Interpolation of coplanar vectors 222 A.8. Monte Carlo analysis of inclinometer sensitivity 226 B.1. Niskin sampler 231 B.2. Subglacial Hoover 233 C.1. The drag spool 237 XII LIST OF TABLES 1.1. Geometrical characteristics of Trapricige Glacier 13 1.2. Characteristics of Trapridge Glacier study site 13 4.1. Established phenomenological relations . 111 5.1. Control line function, 1987 apparatus 128 5.2. Control line function, 1988 current multiplexer . 131 5.3. EPROM programs, 1988 current multiplexer 132 5.4. EPROM programs, 1988 potential multiplexer 133 5.5. Control line function, 1988 potential multiplexer 133 xlii LIST OF SYMBOLS Symbol Meaning a glacier surface slope /3 glacier basal slope e charge on an electron E electric field e dielectric constant strain rate mean strain rate dynamic viscosity J electrical current density J generalized flow density g gravitational acceleration C d.c. resistivity geometrical factor 7 sediment yield stress h layer or glacier thickness H pore geometrical factor I electrical current k reflection coefficient kB Boltzmann’s constant K1 thermal conductivity K2 hydraulic conductivity phenomenological coefficients 1u ion chemical potential n number density of ions fl surface normal vector P water pressure potential 4 interface potential o interface potential at surface total electric potential q fluid flow density xiv Symbol Meaning p scalar electrical resistivity Pap apparent resitivity pi density of ice pv volumetric charge density pv.