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Digital impulse radar for glaciology : instrumentation, modelling, and field studies Jones, Francis Hugh Melvill 1987

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D I G I T A L I M P U L S E R A D A R F O R G L A C I O L O G Y : I N S T R U M E N T A T I O N , M O D E L L I N G , A N D F I E L D S T U D I E S by F R A N C I S H U G H M E L V I L L J O N E S B.Eng.(Electr ical) , M c G i l l University, 1981 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department of Geophysics and Astronomy We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A November 1987 © F r a n c i s H . M . Jones, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of 6? er 0 PHYZfCS &r /\STft.c?AJ0rty The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date TUtOc XO lf%7 A B S T R A C T Several aspects of impulse radar echo sounding of small glaciers are investigated. First , the ranges of values expected for conductivity and relative dielectric permitt ivity of glacier ice, glacier bed materials and mixtures of ice and rock are established. These parameters, and the fundamentals of electromagnetic wave propagation, are employed in a modelling scheme that examines the reflection of pulses from planar reflectors within the glacier. The glacier bed can be modelled as solid rock or unconsolidated debris and as either frozen or wet. A layer of mixed ice and rock between the glacier ice and bed can also be included. Signal enhancement, especially using multi-channel principal component analysis, is discussed. Discussion of practical application of the technique begins with the description of a portable microprocessor-controlled instrument capable of recording digitized echograms. Then results from experiments on Trapridge Glacier, Yukon Territory are presented. Surveys up to half a kilometer long with soundings at ] to 20 rn intervals were conducted. Bed topography is presented and locally anomalous sections are examined. Smaller-scale parameters such as the attenuation constant of ice and reflector properties are also extracted from the data. Subglacial and englacial temporal variations were studied by automatically recording echoes at one location every 20 minutes over a three-day period. Such experiments are to be used in the future in conjunction with other, concurrent, geophysical and hydrological investigations. T A B L E O F C O N T E N T S A B S T R A C T : i i L I S T O F T A B L E S v L I S T O F F I G U R E S v i A C K N O W L E D G E M E N T S v i i i C H A P T E R I I N T R O D U C T I O N 1 C H A P T E R II E L E C T R O M A G N E T I C P U L S E P R O P A G A T I O N IN G L A C I E R S . 4 2.1 Introduction • 4 .2.2 Electr ical Parameters of Glacier Materials 4 2.2.1 Glacier Ice 5 2.2.2 M i x e d Ice and Rock .6 2.2.3 Glacier Bed 7 2.3 Propagation 10 2.4 Reflections 13 C H A P T E R III D I G I T A L M O D E L L I N G A N D D A T A E N H A N C E M E N T 17 3.1 Introduction 17 3.2 Fi l ter Model l ing 20 3.2.1 Sampling 20 3.2.2 Forward Model l ing 22 3.2.3 Glacier Bed Filters 23 3.2.4 Fi l ter ing Results 26 3.3 Da ta Enhancement; 28 3.3.1. Alignment and Mean Stack 29 3.3.2 Pr inc ipa l Component Decomposition 31 3.4 Conclusions 36 C H A P T E R . IV I N S T R U M E N T A T I O N 38 4.1 Introduction 38 4.2 Transmitter 39 4.3 Antennas 43 4.4 Receiver 48 4.5 Computer , Cont ro l , and Data Handling 51 - iv -4.6 F i n a l Comments 55 C H A P T E R V F I E L D W O R K A N D D A T A C H A R A C T E R I S T I C S 56 5.1 Prel iminary F ie ld Trials 56 5.2 F ie ld Operations on Trapridge Glacier 57 5.3 Characteristics of Echo Signals 59 5.3.1 Signal Features Caused by the Instrument 59 5.3.2 Quanti tat ive Interpretation of Individual Traces 61 C H A P T E R V I A N A L Y S I S O F F I E L D D A T A 65 6.1 Introduction : 65 6.2 Centreline 67 6.3 Profiles Coincident W i t h D r i l l Holes 71 6.4 Profile W i t h Closely Spaced Soundings 78 6.4.1 Englacial Reflector: Location and Reflectivity 78 6.4.2 Est imat ion of Attenuation Constant 80 6.4.3 Basal Reflection Coefficient 83 6.4.4 Mul t ip les and Secondary Bo t tom Echoes 85 6.5 Three-Day Da ta Set 86 C H A P T E R V I I S U M M A R Y 94 R E F E R E N C E S 96 A P P E N D I C E S 100 - v -L I S T O F T A B L E S 2.1 Electr ical Parameters -• 10 2.2 Reflection Coefficients • • 14 3.1 Reflection Model l ing Input Parameters 23 4.1 System Instructions 53 L I S T O F F I G U R E S Frontispiece: Operations on He lm Glacier, Gar iba ld i Provincial Park. ix 2.1 At tenuat ion constant 12 3.1 Fi l ter models of the echo sounding process 18 3.2 Wavelets and spectra •••• 21 3.3 Glacier bed filters 24 3.4 Results of filtering experiments 27 3.5 Da ta and mean stack of decomposition example 30 3.6 Pr inc ipa l component reconstruction examples 33 3.7 Eigenvectors of decomposition example 35 4.1 Instrument configuration 39 4.2 System block diagram 40 4.3 Silicon-controlled rectifiers 41 4.4 Impulse generator waveforms 44 4.5 Simplified transmitter diagram 44 4.6 Antenna diagram 47 4.7 Receiver block diagram 49 4.8 Simplified software flowchart 52 5.1 One example from early transmitter trials 56 5.2 Equipment deployment for 1986 field work 58 5.3 Single trace examples 60 - vii -6.1 M a p of 1986 field work 66 6.2 Centreline profile 68 6.3 Centreline cross-section of Trapridge Glacier 70 6.4 Profile 2 72 6.5 Profile 3 73 6.6 Profile 4 74 6.7 Mode l l ing of water-filled crevasses 76 6.8 Close-spacing profile 79 6.9 Ampl i tude plots of close-spaced profile 81 6.10 Complete raw data from three-day study 87 6.11 Al igned data from three-day study 89 6.12 Ampl i tude plots of three-day study 90 6.13 Misfi t reconstruction of data from three-day study 92 - viii -A C K N O W L E D G E M E N T S The successful completion of this project would not have been possible without the guid-ance and encouragement of my supervisor, Dr . G . K . C . Clarke, and the enthusiastic support and advice from Dr . B . B . Narod. M y thanks also to M . J . Yedlin for provid-ing insight into diffraction processes. Valuable field assistance from Guy Cross, Patr ic ia B i r c h , and Andrew Lawrence was much appreciated, and Er ik Blake provided the sur-veying information. I also thank Patr ic ia Bi rch for proofreading final drafts of this thesis. Thanks are due to the superintendents and staff of Kluane National Park, Jasper Na-t ional Park and Gar ibald i Provincial Park for permission to work in their parks. This work has been supported by grants from the Natural Sciences and Engineering Research Counci l of Canada and Northern Scientific Training Grants from the Department of Indian and Northern Affairs. F R O N T I S P I E C E : Operat ing the U B C portable digital impulse radar echo-sounding equipment on Helm Glacier, Garibaldi Provincial Park, May, 1986. - 1 -C H A P T E R I I N T R O D U C T I O N Radio echo sounding has been established for many years as a useful technique for study-ing polar ice sheets (Bogorodsky and others, 1986), but application of similar methods to the investigation of small mountain glaciers has had mixed success. Various problems have contributed to this lack of consistency. The attenuation of electromagnetic energy at frequencies commonly used (over 30 M H z ) was often too high to permit usable bot-tom echoes to be recorded. Also , resolution higher than that obtained in polar work is often required, navigation needs are more stringent, and logistical difficulties of working in mountain environments often preclude the use of large amounts of highly technical equipment. Smith and Evans (1972) examined absorption and scattering of electromagnetic en-ergy by ice and water inclusions, and Watts and England (1976) extended the theory to show that frequencies below 5 M H z would likely be required if reliable results were to be expected on temperate glaciers. They suggested the use of very short pulses to avoid the loss of resolution that would otherwise occur at such low frequencies. The resulting echograms would appear similar to seismic records, in which the travel times of echoes could, be measured at. specific points on the wavelet, rather than having to wait for several cycles of energy to arrive before recording a usable signal. Impulse radar of this type was first used for ground probing (Cook, 1974) and in permafrost studies (Annan and Davis, 1976). Interest is stil l strong in these areas, and instruments working at frequencies in the U H F and V H F ranges are being used in civi l engineering applications (Ulriksen, 1982) and in permafrost (Arcone and Delaney, 1984) - 2 -and sea ice studies (Fagan, 1987). Glaciological applications were first proposed by Cook (1960), and had become commonplace by the late 1970s (Sverrisson and others, 1980; Watts and Wright, 1981). A t present, the method is most often used to make spot measurements of glacier depth. Appl ica t ion of modern digital techniques has been slow, perhaps because of the size and power requirements of high-speed digit izing oscilloscopes and other equipment. Though some groups are carrying out sophisticated experiments (Jacobel and Raymond, 1984; Walford and others, 1986), there is certainly room for improvement in this area of glaciology. The project discussed in this thesis was begun in 1980 by B . B . Narod and G . K . C . Clarke, who designed a portable, microprocessor-controlled, digitizing instrument. The goal was to build a lightweight, self-contained instrument that stored echograms in digital form, and that would be capable of automatically gathering records at pre-set intervals for the purpose of studying changes in glacier dynamics over a period of time. The instrument was completed as part of this project, although the design now lags behind state-of-the-art technology by a few years. Potential improvements wil l become apparent in the course of this report. Digi tal recordings are useful in facilitating the application of seismic data processing techniques. One such method, digital forward modelling, was used to assess how much detail concerning glacier bed properties might be revealed in field data. These theoretical experiments prompted the use of multi-channel principal component analysis to aid in separating gross echo features from more subtle characteristics. Fie ld testing of the instrument went through a series of phases culminating in the acquisition of a variety of data sets from Trapridge Glacier, Yukon Territory. Results can be analyzed most successfully if a reference signal from some known reflector can be simultaneously recorded. Signals that have propagated as surface waves along the ice/air interface do not make useful references because this type of propagation is complicated - 3 -and poorly understood. In this study, the use of echoes from a crevasse in the vicini ty of the instrument, as well as the use of multiple reflections, allowed estimates to be made of the glacier bed's reflectivity. A similar analysis showed that apparent temporal variations in basal reflectivity over a three-day period were in fact not due to changes at the glacier bed. In this thesis, I consider these aspects of impulse radar echo sounding as follows. Elec-tr ical properties and the propagation of electromagnetic pulses in glaciers are first dis-cussed theoretically. These results are then applied in digital modelling exeriments that investigate how reflection from realistic glacier beds affects short electromagnetic pulses. Some digital processing techniques for emphasizing different aspects of the echograms are also presented. Then the instrument is described in some detail to explain how the records are generated. Field methods are then discussed, followed by the analysis of data obtained in July, 1986. Final ly , I summarize the project and present some ideas for improvements and future experiments that were suggested in the course of the study. - 4 -C H A P T E R II E L E C T R O M A G N E T I C P U L S E P R O P A G A T I O N I N G L A C I E R S 2.1 I N T R O D U C T I O N M a n y basic texts on electromagnetic waves discuss propagation in dielectric media (e.g. Jordan and Ba lma in , 1968) and there is now extensive coverage of monochromatic radio echo sounding theory in the glaciological literature (e.g. Bogorodsky and others, 1986; Robin and others, 1969). When discussing wideband signals, much of this theory must be applied cautiously, because scattering, attenuation and reflection can be frequency dependent. Some attention has been paid to these issues in the engineering, glaciol-ogy and permafrost literature but, in general, interpretation of impulse radar work has been qualitative. (Exceptions include Jacobel and Raymond (1984); Walford and others (1986); Arcone and Delaney (1982); Morey and Kovacs (1985).) Subsequent chapters of this thesis wi l l attempt to be more rigorous in the consideration of current work on Trapridge Glacier and this chapter wi l l discuss the prerequisite theory. 2.2 E L E C T R I C A L P A R A M E T E R S O F G L A C I E R M A T E R I A L S Before introducing the equations describing electromagnetic pulse propagation in glaciers, the electrical properties of relevant materials must be considered. A l l these materials are non-magnetic, so the magnetic permeability fi will be taken as that of free space; i.e. n = /.i0. Electrical conductivity wi l l be shown to range over several orders of magnitude and to depend on the material , on the free or bound water content, and on the temperature. Relative dielectric permitt ivity, the other important property, varies - 5 -from 1 (in air) to 81 (in free water). These properties w i l l be considered for the glacier bed, the glacier ice itself, and for mixtures of ice and rock. 2.2.1 Glacier Ice In general the relative dielectric permitt ivi ty (e r) and conductivity (o) of ice depend mainly on frequency, density, temperature, and concentration of impurities in the ice. (See review papers by Evans (1965), Smith and Evans (1972), Glen and Paren (1975).) In practice the frequency dependence can be ignored since the spectrum of energy used in radio echo sounding is well removed from the relaxation spectra of ice (around 100 kHz) and water (around 500 M H z ) as well as the infrared absorption spectrum of ice (over a gigahertz). Density variations wi l l also be ignored because all work on Trapridge Glacier was carried out below the firn line; hence only solid ice was encountered. In the accumulation zone or other areas where significant depths of firn occur, this aspect would have to be considered (see for example Robin and others (1969)). Concerning the dependence of e r on temperature, Paren (1970) notes that as long as the amount of free water in the ice is small , variations in c r at temperatures between —10° C and 0° C are very small . According to Clarke and others (1984), temperatures in Trapridge Glacier are wi th in this range so variations in er due solely to temperature are also negligible. In the articles cited above, experimental and calculated values for e r of ice vary between 3.17 and 3.2, so e r = 3.18 wi l l be used, which implies a propagation velocity of v — 1 6 8 . 2 m s - 1 . Conduct iv i ty (o) depends on the concentration of impurities and on temperature. T w o relations are given by Smith and Evans (1972) for a as a function of temperature, one for "pure''' ice (that made from nearly distilled water) and one for ice containing an amount of solids at or beyond equilibrium solubility for solids in ice grains. Smith (1971) mentions that field measurements on temperate glaciers closely match the pure ice formula; he ascribes this to the flushing out of impurities. From Smith and Evans - 6 -(1972), this relation for conductivity of pure ice is: a = 4.6 x 1 0 _ 5 e x p where the activation energy E = 5.5 x 10 4 J m o l - 1 , the gas constant R = 8.314 J / ( m o l ° K ) and T 0 = 273°K. Equat ion 2.1 can also be used for solubility l imit ice at temperatures less than —10° C', but then E — 2.5 x 10 4 J m o l - 1 . Between —10° C and 0° C , excess impurities contribute to conductivity increasing it up to 6 x 1 0 _ 5 S m _ 1 at 0° C . 2.2.2 Mixed Ice and Rock T w o methods for predicting relative dielectric permitt ivity of mixtures (c r ) are listed by Glen and Paren (1975). Both methods assume that one material (with permitt ivi ty £2) is uniformly dispersed in a matrix which has permitt ivity t j . They use a so-called shape factor A, which describes the general form of the inclusions, and some third permitt ivi ty representing that of the material very near to and surrounding the inclusions. One formula is known as Bottcher's mixing equation: (•r ~ Cl V2{^2 - <M) 3 c r " e> + 2 r r in which is the volume fraction of material 2 . The other equation is Looyenga's equation: < y 3 = v 2 4 / 3 + ( i - v 2 ) e ; / 3 . ( 2 . 3 ) In both, the particles of material 2 are assumed to be spheres so that the factor A = 1/3. (These derivations do not make use of the "Forrnzahl" concept, i.e. the use of a single parameter to describe how one medium is dispersed in another, because this would require ( V - T - 1 ) S m -1 (2.1) ( 2 . 2 ) - 7 -that the geometry of the electric field be independent of the relative proportions of the two media. See Evans (1965) for a further discussion of this point.) Both equations given above have apparently agreed well wi th experiments even for high concentrations of included material . Also, comparisons of the two equations in the present case differed by less than 0.4% for 0.1 < V2 < 0.9. Looyenga's equation is the simplest, so it wi l l be used in the modelling experiments discussed in chapter 3. Conduct ivi ty of mixtures is more difficult to estimate because it depends mainly on how well interconnected the higher conductivity components are, rather than on relative volume concentrations. It is safe to say though, that the bulk conductivity of the rock/ice mixture wi l l be less than that of ice alone since rock conductivities are several orders of magnitude less than that of ice. 2.2.3 Glacier Bed Various types of glacier bed should be considered in the modelling since each wil l have different electrical parameters. Dielectric permitt ivi ty of a dry, solid rock glacier bed would be between 7 and 11; the values for solid limestone (Ulriksen, 1982) and solid basalt (St. Amant and Strangway, 1970). Corresponding conductivities would be on the order of 1 0 _ 8 S m _ 1 . However, it is more likely that a hard glacier bed would be somewhat fractured and wet. This would raise er by very little but a would be raised by several orders of magnitude (Ulriksen, 1982). For soft beds of unconsolidated debris, both frozen and unfrozen cases must be con-sidered. Most measurements made in frozen ground indicate that a < H P ^ S m - 1 and that 4 < cr < 7 (e.g. Olhoeft, 1978; Wong and others, 1977). Ice-rich gravel is quoted by Arcone and Delaney (1981) as having cr -• 5.1, which agrees with the value equation 2.3 gives for a limestone gravel with about 40% porosity. This formula wil l therefore be used in the frozen bed model, although we should perhaps bias the values of cr upwards. This is because, as noted by Davis (1975), an increased content of very fine material - 8 -such as clay will tend to raise e r . The properties of the minerals themselves are partly responsible but a very small increase in unfrozen water will have the same effect. Ander-son and others (1978, p.80) show that free water content can be more than 0.3 grams of H 2 0 per gram of material at between — 3° C and 0° C , if the soil is rich in clays or very fine-grained material . This wi l l affect o even more drastically since water is much more conductive than ice. For frozen beds, equation 2.3 wil l again be used to find e r , this time using water as the mat r ix in which rock spheres are distributed. In this case, the following consid-erations imply that the values wi l l only be estimates. Davis and others (1976) present experimental results giving a curve of er versus water content that is steeper than that of the mix ing formula. They also suggest, as do Hoekstra and Delaney (1974), that the relation between t r and water content is fairly independent of soil type. However, it should be noted that, unlike subglacial debris, the warm-climate surface soils used by these authors are probably rich in clay and organic material. The effect on er of clay con-cent was mentioned above, and Arcone and Delaney (1982) note that increased organic matter tends to increase tr. The difficulties of assessing a in mixtures were noted above but more literature is available on conductivity of wet ground than that of frozen ground. Based on the review article by Kel ler (1967). bulk conductivity of subglacial debris was found using the Archie formula, for weakly cemented detrital rocks in which porosity is between 25% and 45%. This formula is appropriate because t i l l samples from areas that were once over-ridden by Trapridge Glacier are thought to have porosities of 20% to 40%. The relation is 1 0.88 , , 7 . , — < r 1 3 ? , (2-4) - 9 -in which OT is bulk conductivity, is the conductivity of interstitial water and <f> is porosity. In order to find the bed conductivity, ow is obviously required but it is difficult to obtain the true value of in situ water. Samples taken directly from the bed cannot be used because of contamination by dri l l ing water, subglacial runoff is likely to be mixed wi th surface melt in the summer months, and in both cases, simply exposing a sample to air and measuring equipment can cause chemical changes which wil l alter the resistivity. Reasonable estimates can be made, however, by referring to other work and by consid-ering the local environment. A n eleven-month study by Collins (1981) of water draining from the snout of Gornergletscher, Switzerland, revealed a maximum conductivity of 1 2 0 / x S c m - 1 in the winter when surface melt was at a minimum. Spot measurements made in July 1986 around Trapridge Glacier revealed conductivities of 20 to 8 0 / i S c m _ 1 for surface melt and up to 6 5 0 / z S c m - 1 for ground water (C. Smart, pers. comm., 1986). Local geology also suggests that carbonate rocks constitute a large proportion of Trapridge Glacier 's bed so that the solute concentration of subglacial water is likely to be high. In addit ion, Keller (1967) notes that in situ conductivity of interstitial water is increased by ionization of clay minerals and by surface conductance such that pore water conductivities are rarely less than 1 0 0 / / S c m - 1 in sandstone or 1000/.iS c m - 1 in siltstone. These do not necessarily apply in our case since the glacier bed is likely to be a poorly sorted mixture of the various clasts produced by subglacial geologic processes (Drewry, 1986: ch. 3-5), but similar effects on ow might be expected. A l l of these considerations suggest that a likely range of values would be 1 0 2 / / S c m _ l < aw < l O ' / i S c m - 1 . To summarize, 1 have introduced the basic physical parameters that wi l l appear in the equations describing electromagnetic pulse propagation and reflection within glaciers, and discussed the physical features affecting them. Their values may be expected to be wi thin the ranges listed in table 2.1. Although the uncertainties are quite large for some - 10 -Table 2.1: Electrical parameters materia/ parameter mm. max. comments* i ce 3.17 3.2 a Oi ( S m - 1 ) 6 x 1 ( T 1 2 x 1 0 - 1 a, b m i x e d 3.18 11.0 c l a y e r o m ( S m - 1 ) io- 8 6 x 1 0 " 5 d g l a c i e r ft 7.0 81 c b e d (wet ) ot ( S m - 1 ) I O - 3 I O - 1 e , f * Comments: Parameters depend mainly upon (a) temperature; (b) concen-tration of impurities; (c) concentration of solids in matrix; (d) connectivity (or permeability); (e) conductivity of interstitial water (aw); (f) porosity. parameters, one of the purposes of the modelling discussed later wil l be to determine how significantly these parameters affect the shape of echoes. 2.3 P R O P A G A T I O N Having defined the "primary" constants (c, o, /n) of the media in which pulses wi l l be propagating, we can find expressions for the electric field strength E(r, t) by solving the general electromagnetic wave equation. This is done in many texts on electromagnetic wave theory (for example Jordan and Balmain (1968, section 5.05)) with the result £ ( r , t ) - £ - e " 7 V w l (2.5) r where: r is the distance from the source; u is angular frequency; 7 = \/(ju>(j.)(a -f jwe) = a + j/3 is the propagation constant; £ = \/gpWtrl'/^n is a source term found using fundamental antenna relations discussed by Jordan and Balmain (1968: section 11.11); (jv is the antenna's power gain (a measure of efficiency and directionality); Wt is the total input power; and 77 = yjjoJf.il(a + jtoe) is the intrinsic impedance of the medium in which the antenna lies. - 11 -A l l the primary constants are some combination of those applicable in ice and air; recall that the antennas are resting at the interface of these two effectively infinite dielectric semiconductors. Equat ion 2.5 shows that the electric field strength is inversely proportional to distance from the source, is further reduced according to the attenuation constant a , and may be phase shifted according to the phase constant /?. Simplification of a and /? is possible if the ratio (cr/W) <C 1 (valid in good dielectrics) or if (a/ut) » 1 (valid in good conductors). For example, at 1 M H z typical ice has Since this is not conclusively much less than 1, figure 2.1 was constructed to demonstrate that propagation of signals between 100 kHz and 25 M H z is practically non-dispersive. Figure 2.1a shows the magnitude of a for both warm and cold ice. As a comparison, figure 2.1b shows that propagation in t i l l wi l l be highly attenuative as well as highly dispersive. Arcone (1981) discusses a similar problem by modelling the propagation of pulses centered around 85 M H z through a medium similar to frozen ground, but this wi l l be unnecessary in our case. A complete treatment of electromagnetic wave propagation in ice must also include scattering processes, especially when temperate glaciers are being considered. Smith and Evans (1972) consider scatterers as small (with respect to wavelength) dielectric spheres that re-radiate incident energy by becoming electric dipoles (Rayleigh scattering). Their formulae show that the power lost from the forward wave per unit length of path through the medium is cr 3.0 x 10~5 (2TT x 10 6 x 8.854 x 1 0 ~ 1 2 x 3.18) 0.17 . (2.6) - 12 -A. A t t e n u a t i o n C o n s t a n t f o r Ice 0 . 0 0 5 0 0 . 0 0 4 5 0 . 0 0 4 0 o-. 0 . 0 0 5 5 U 0 . 0 0 3 0 0 . 0 0 2 5 0 . 0 0 2 0 0 . 0 tT = 5 . 0 X l C T 5 m h o m " 1 , £ = 3 . i t a — 2 . 0 - 1 0 5 - - . r i c rm . f - j . l E 1 . 0 0 E + 0 7 2 . 0 0 E + 0 7 F r e q u e n c y ( H e r t z ) B. A t t e n u a t i o n C o n s t a n t f o r Wet Ti l ! g 4 0 0 3 5 - / 0 3 0 t - I 'w 2 5 1 2 0 1 a = i . 0 ' ' ' 0 ~ •• m h o m " ' , c = l 8 • 3 -/ 1 5 / i _ /' / i i I i i ; ; . 0 0 E J - 0 7 2 . 0 0 E + 0 7 F r e q u e n c y ( H s ' " l z ) Figure 2.1. Attenuation constant a, determined from the propagation constant 7 of equation 2.5. Conductivi ty and permitt ivity used in each case are noted inside the graphs, and the media in which propagation is occurring are noted as titles to the graphs. A) a. for both warm and cold ice. Warm ice has o = 5 x 10~ 5 S m ~ 1 ; cold ice has o = 2 x 10'"'5 S m"" 1 . B) In wet t i l l , attenuation is much more pronounced and dispersion occurs at all frequencies. T i l l porosity was 30%. - Vi -where m is the number of scatterers per unit volume, b is the radius of spherical scatterers, £1 and t'2 are relative permittivities of the scatterers and medium, and X is the wavelength in the medium. This proves to be negligible for frequencies less than 500 M H z if scatterers are reasonable configurations of air- or water-filled bubbles in ice or firn. Masking of target echoes by scattered energy is considerably more significant. Watts and England (1976) use a similar but more general theory to that presented by Smith and Evans (1972) to suggest that water-filled voids smaller than 1 m in diameter wi l l not obscure target echoes as long as sounding frequencies are below 5 M H z . It wi l l be seen in data presented later that results from Trapridge Glacier are vir tually unaffected in this way, probably because most of the glacier is colder than the pressure melting point (Clarke and others, 1984). For the sake of completeness, however, it is worth noting that masking effectiveness can be described by a signal-to-noise ratio when the power ( P p ) from the target is the signal and power scattered from an equivalent range (Ps) is noise. Equation 11 from Watts and England (1976) gives this ratio as _ P = m (2.T) Ps 2mlK,gi,sG in which: R is the reflection coefficient of the target; g^/G is the ratio of squared antenna gain to antenna directionality; rn is the number of scatterers per unit volume; / is the pulse length in ice; and Kgi,s is the product of scattering cross-section and backscatter gain (which allows non-spherical scatterers to be considered). 2.4 R E F L E C T I O N S So far, only propagation in infinite media has been considered. If a change in primary characteristics is encountered, some energy wi l l be transmitted through this boundary and some wi l l be reflected back. For normal incidence on a plane, smooth boundary - 14 -(a specular reflector) the ratio of returned to incident energy is given by the amplitude reflection coefficient V2 + Vi (2.8) where the incident energy is travelling in a medium wi th impedance n\ and medium 2 is the other side of the boundary. Similarly the transmission coefficient T is r = . (2.9) Clearly a boundary with greater impedance contrast wi l l reflect more energy back and transmit less into the second medium. Also, if the impedances are frequency-dependent, the echoing process wi l l be dispersive. Table 2.2 summarizes representative values of p for different reflectors. Note that throughout this thesis, complex reflectivities are expressed in phasor notation: p = Re(p) + j lm(p) is given as p = \p\L t a n - 1 (lm(/))/Re(/>)). Table 2.2: Reflection coefficients i j Oj (S m 1 ) Pij \Pii\ (dB) air ice 5 x 1 0 " 5 3.18 0.28Z180 -11.1 ice air 0.0 1 0.28 Z0 -11.1 ice water 0.01 81 0.67Z179 -3.5 ice limestone 10" 8 7 0.19Z176 -14.5 ice t i l l 4> = 15" 8.5 x 1 0 _ 4 11.8 0.32/: 177 -9.9 ice t i l l 4> = 15+ 5.1 x 10~ 3 11.8 0.44 Z 164 -7.1 ice t i l l 4> = 30' 2.2 X 1 0 ~ 3 18.3 0.42 L.176 -7.5 ice t i l l <f> = 30* 1.3 x 1 0 - 2 18.3 0.59 L167 -4.6 Pij, calculated using equation 2.8, is given as magnitude and phase angle of the reflection coefficient for electromagnetic waves travelling in material " i " and incident on a smooth boundary with material " j " . Note that a phase angle of 180° implies an effectively negative reflection coefficient, ey of mixtures was found using equation 2.3. a} was found using equation 2.4. using ou, = 0.01 S m " 1 t using aw — 0 . 0 6 S m " 1 - 15 -A more realistic reflector consists of a relatively thin layer of a third material sepa-rating two half spaces. This allows more accurate modelling of glacier beds which may include a thin film of water or a basal layer of mixed ice and debris. Drewry (1986: ch. 7) discusses various mechanisms that can create such a layer (called a glacier sole by Post and LaChapel le (1971)), and Maxwel l (1986) considers in detail the observed basal layer under Trapridge Glacier. ( A n analogous situation in optics would be the reflec-tion of light from thinly coated surfaces.) A n expression for the appropriate reflection coefficient can be found by considering al l the multiple reflections within the thin layer and summing their contributions to the output signal as an infinite series. The resulting frequency-dependent amplitude reflection coefficient is R[u) = Pim + 7 T i T ^ which contains the following parameters: reflection coefficients of two boundaries pjm and Pmi'-, transmission coefficients at the first boundary r t r n and Tmi\ propagation constant of the middle layer ^y m ; and the thickness of the layer x. In these, subscripts i , m , and t denote ice, middle layer, and t i l l or bedrock respectively. Reflections from this boundary are even more dispersive than the simple case of equation 2.8; frequency responses of these reflectors are considered in detail in the chapter on modelling. In this thesis, these results wi l l not be generalized to include non-specular and rough reflectors although there are several ways to proceed. Many conventional radar systems record rectified envelopes of returning signals so phase information is lost. Nevertheless spatial and temporal fading of such records can be used to estimate statistical properties of small-scale reflector roughness, as well as whether the roughness is blocky, undulating, or smooth wi th patchy variations in permittivity. Berry (1975) and Oswald (1975) discuss these methods which are based on Kirchhoff diffraction theory; they also discuss how to (2.10) - 16 -use the same data to infer large-scale bed topography. A second approach uses an instrument capable of recording the phase of conventional radar echoes. This type of data is used by Walford and Harper (1981) who apply Berry's diffraction theory, as well as concepts akin to downward continuation of wave fields, to the interpretation of detailed glacier bed shape. In order to improve the resolution of their interpretations, they also consider a form of aperture synthesis. A l l these methods were developed for use wi th quasi-monochromatic radar data so would need to be modified for application to wide-band impulse radar data. The similarity of impulse radar to seismic sounding suggests that the vast body of seismological literature could be tapped with a view to resolving some of these differences. Walford and Harper (1981) mention that they were considering the application of their work to impulse radar data, and a P h D . dissertation on that work is currently in preparation by M . Kennett under Walford's supervision. - 17 -C H A P T E R III D I G I T A L M O D E L L I N G A N D D A T A E N H A N C E M E N T 3.1 I N T R O D U C T I O N In many respects, radio frequency echo sounding can be conveniently compared to seis-mology, the main difference of course being that pulses of electromagnetic energy are used instead of acoustic energy. As in seismology, propagation and reflection of pulses can be analyzed by considering these processes as a sequence of filtering operations (fig-ure 3.1a). Since these operations are linear, they can be conceptually rearranged to isolate any process of particular interest. In this study glacier bed properties are being investigated, so the system is rearranged as per figure 3.1b which can be described in the frequency domain by the equation The assumption is that all the processes that have been lumped together to create the input wavelet Eo(co) are well defined and that a solvable expression for the reflection coefficient R{w) can be found which involves the interesting bed characteristics. The general reflector model considered in this work consists of a relatively thin layer of some material separating two half spaces, ice and glacier bed. Chapter 2 presented a discussion of this reflector and the materials involved; the equation is reproduced here for convenience: (3.1) TimP miJ mi** -2nr„. i R{u) = Pim + -2-7,,, i (3.2) - PimPmte 18 Voltage Transmit ~-- Ice Reflector Ice ^ Receive Recorder Pulse Antenna —^ Antenna A) Voltage 2 Antennae^ Ice twice, & Recorder. R(w) E(w) Pulse Reflector Output Data B) Figure 3.1. (A) Electromagnetic echo sounding modelled as a sequence of fil-tering operations. Six filters are required to describe the processes of pulse gen-eration, propagation, reflection and reception. (B) The system rearranged to isolate the reflection process. EQ(UJ) and E(u) are the input and output wavelets and R(u) is the reflection filter's impulse response. The parameters are: reflection coefficients of two boundaries, pim and Pmt'i transmission coefficients at first boundary, T j m and rm,-; propagation constant of middle layer 7 m ; and thickness of the layer x. The subscripts i, m , and t denote ice, middle layer and t i l l or bedrock respectively. It should be noted again that equation 3.2 is a simplified model which assumes that plane waves are impinging at normal incidence on a plane, specular reflector and that the media in which propagation "occurs are homogeneous dielectric semiconductors. A l l the components in this equation are frequency-dependent, so reflection from a boundary of this type is, in effect, a dispersive process. Therefore echoes of wideband impulse radar signals might be expected to show changes in character that can be in-terpreted in terms of the properties of the two-boundary reflector. On the basis of this expectation, one plan for analysis would be to estimate bed characteristics from field data by using a forward modelling scheme. The relations from chapter 2 would be used in equation 3.2 to find R(OJ) and equation 3.1 would then be solved repeatedly using var-ious values for the parameters (ensuring of course that the values chosen make physical sense). The calculated data E(u>) obtained in these trials could then be compared to the - 10 -true data, the parameters readjusted, and further trials carried out until a reasonable match was obtained. The difficulty encountered with this scheme is the common geophysical problem of wavelet estimation. In order to solve equation 3.1, the input wavelet EQ(OJ) must be determined. This involves determining the transfer functions of all those operations in figure 3.1a that have been lumped together as one in figure 3.1b. Of these, propagation through ice can be approximated as a non-dispersive, attenuating process (shown in chapter 2) and the recording apparatus can be considered transparent for our purposes. The actions of the antennas on the other hand must be carefully considered if the wavelet is to be determined analytically. A short digression is required here to explain this point. Chapter 4 shows how the echo sounding impulse is generated by impressing a high voltage step function onto a damped dipole antenna. The behavior and impulse response of such an antenna in free space is discussed by Kanda (1980) for both receiving and transmitt ing modes of operation. In our case however, there are several complications. We have not yet determined the current as a function of position on the antenna arms, the antennas are not in free space but at the interface of two infinite dielectrics (air and ice), and we would have to consider both near and far field components in the radiating equations. Incorporating Kanda's transfer equations in this analysis is therefore far from simple. As a result, rather than beginning by solving this problem, the first job is to determine whether real reflectors wi l l have any significant effect on electromagnetic pulses such as those used in impulse radar. Some kind of estimated wavelet is therefore required. It is noted in chapter 4 that, because of propagation effects, the signal Eo(u>) wi l l have at best three lobes. A con-venient waveform of this type is the so-called Ricker wavelet; a zero phase wavelet used extensively by seismologists which is given by equations 3.3 and 3.4 from Sherriff and - 20 Geldart (1982): e0(t) = (1 - 27r2^nt2)exp\-w2u'tnt2 (3.3) r 2 / 2 exp[ -w /u)n (j>{u) = 0 . (3.4) Further justification for using a Ricker wavelet in the modelling can be seen in figure 3.2. A real echo is shown to have a magnitude spectrum that is very similar to that of a Ricker wavelet, and the echo itself looks like a phase rotated Ricker wavelet. If we assume that phase rotation is caused by complex propagation processes; then a Ricker wavelet is a reasonable input signal to start wi th . As a result of these considerations, the modelling experiments discussed in this chap-ter involved solving equation 3.1, with equation 3.2 as the filter impulse response R(OJ) and a Ricker wavelet as the input £ o ( w ) . Various versions of R(w) were tried and the resulting output wavelets were compared to the original Ricker wavelet. In this way, parameters affecting echo shape were determined and estimates were made of the range of values revealed by real data. 3.2 F I L T E R M O D E L L I N G 8.2.1 Sampling Before carrying out the modelling procedure itself, the sampling parameters must be set to ensure that field data, modelled data and filters are compatible. The one fixed param-eter is the sampling rate of field data. This was measured to be very close to the design specification of At = 10 /xs/1024 samples = 9.766 ns/sample. Next , the number of points considered adequate to yield useful results without compromising either numerical accu-racy or computational efficiency was chosen to be n = 128 points. Fi l ters are constructed in the frequency domain and are made compatible with these data sets by setting the frequency sampling interval at A / = fN/l28, where fN is the Nyquist frequency, the A) MEAN STACK OVER 10 R E C O R D S AMPLITUDE S P E C T R U M OF MEAN STACK 0 .0 2 . 0 E - 0 7 + . 0 E - 0 7 6 . 0 E - 0 7 0 .0 2 .0E + 0 7 ,. 4 .0E + 07 TIME ( S E C O N D S ) F R E Q U E N C Y (HERTZ) B) :NP.JT WAVELET AMPL ITUDE S P E C T R U M .0E + 0 7 Figure 3.2 (A) A n average wavelet and its spectrum. This is the mean stack over records 24 to 33 from the close-spaced survey (chapter 6). The 64 point data window consists of samples 120 to 184. (B) A Ricker wavelet and its spectrum. Note that u m (used in equations 3.3 and 3.4) is the frequency wi th maximum amplitude. - 22 -highest frequency reproducible with the given sampling rate. Therefore Af = 400.2 kHz and filters were calculated at 128 positive frequencies from 0 to 51.23 M H z . The Ricker wavelet EQ(OJ) (or e0(t) in the time domain) was calculated with the same sampling inter-val ( A / or At) using equations 3.3 or 3.4. It was made to resemble field data as closely as possible by setting the parameter u» m close to the approximate peak frequency of real data. It wi l l be shown later that reasonable reflectors can be expected to emphasize low frequencies so, since figure 3.2a depicts an echo, the estimate of E0(u) has used a max imum frequency of / m = wm/2n = 7.7 M H z which is slightly higher than that of the average signal in figure 3.2a. 3.2.2 Forward Modelling Glacier bed properties wi l l now be examined using forward modelling. In order to facil-itate what is basically a trial and error process, a two-step procedure is employed. The first program calculates the reflection coefficient R(w). It uses the 10 basic parameters listed in table 3.1 to generate a set of R(u>)s over which any one of the parameters may be varied. The second program then passes an input wavelet Eo{ui) through each one of these filters and plots the output wavelets so that the effects of varying one parameter at a time can be easily examined. F i rs t consider the program for calculating R(UJ). Details wi l l not be dwelt upon but it is worth pointing out some of the important features. The sampling constants (Af, At, and n) are set first and passed to the second program to ensure consistent processing. Options such as whether the glacier bed is to be wet or frozen are chosen interactively and a list is kept of the init ial input parameters (table 3.1) as well as those subsequently calculated. The relations of chapter 2 are used to calculate the final R(UJ), which consists of complex amplitudes at 128 frequencies from 0 to 51.23 M H z . The last few points of this spectrum are tapered to ensure a smooth transition to zero amplitude at the edge of the spectrum. This minimizes oscillations when inverse transforming to - 23 -Table 3.1. Input parameters to the program which constructs R(u). Conductivity of glacier ice Oi Permitt ivi ty of glacier ice U Conductivi ty of mixed layer O m Volume fraction of rock in mixed layer Vrockm Permit t ivi ty of rock in mixed layer <l>m Thickness of mixed layer X Bulk conductivity of frozen layer ot Conductivi ty of interstitial water ow Volume fraction of rock in t i l l Vrockt Permitt ivi ty of rock in t i l l (•t the time domain, and is done by mult iplying the last eight points wi th a cosine bell function as per Kanasewich (1981, section 9.3). If more than one version of R{u>) is to be produced, their spectra are listed sequentially so that the second program can use them in successive runs. The filtering itself is carried out by the second program. Unless otherwise requested, the input to the filter EQ('JJ) wi l l be a Ricker wavelet constructed with the sampling parameters specified by the first program. The filtering can be carried out either by mult ipl icat ion in the frequency domain or by convolution in the time domain; use of both helps validate the results. If a set of R(u>)s is available, the corresponding final output wavelets (and/or spectra) are plotted to facilitate comparisons between them. 3.2.3 Glacier Bed Filters Results from various filtering experiments wi l l now be presented, starting wi th examples of reflection coefficients generated by program 1. Figure 3.3a shows the magnitude spec-t rum of R(OJ) for a model consisting simply of glacier ice resting on a wet t i l l bed with 30% porosity. The increased amplitudes at lower frequencies occur because the intrinsic impedance of t i l l approaches 0 at w = 0. Also shown is the t ime domain representation - 24 -(A) R(L>) & r(t) F O R I C E / T I L L I N T E R F A C E ; P A R A M E T E R S L I S T E D B E L O W . o.o 2.0E + O7 4 0E + 0 7 F R E Q U E N C Y (HERTZ) 1: - O . i - 0 . 2 - 0 . 3 - 0 . 4 0 .0 . 0 0 E - 0 7 8 . 0 0 E - 0 7 1 2 0 E - O 6 TIME (SECONDS.) (B) R{u) & r[t) F O R 3 m T H I C K L A Y E R ; P A R A M E T E R S L I S T E D B E L O W . 0 . 1 0 0 0 2 .0E + 0 7 4 .0E + 0 7 0 .0 4 . 0 0 E - 0 7 8 . 0 0 E - 0 7 1 . 2 0 E - 0 6 F R E Q U E N C Y (HERTZ) TIME ( S E C O N D S ) PARAMETERS OF REFLECTOR CONDUCTIVITY OF GLACIER ICE; PERMITTIVITY OF GLACIER ICE; CONDUCTIVITY OF MIXED LAYER: VOLUME FRACTION OF ROCK IN MIXED LAYER" PERMITTIVITY OF ROCK IN MIXED LAYER; THICKNESS OF MIXED LAYER; BULK CONDUCTIVITY OF FROZEN T I L L ; CONDUCTIVITY OF INTERSTITIAL TILL WATER VOLUME FRACTION OF ROCK IN T I L L ; PERMITTIVITY OF ROCK IN T I L L : PERMITTIVITY OF BASAL MIXED LAYER IS EPSM-4.A717 (CALCULATED FROM VROCM.EPSI AND EPSRCM) PERMITTIVITY OF GLACIER BED (WET) IS EPST-18 339 (CALCULATED FROM MIXTURE FORMULA) CONDUCTIVITY OF WET GLACIER BED IS SIGMA-. 10918E-01 (CALCULATED USING SIGMAW & VROCT IN THE ARCHIE FORMULA FOR POORLY CONSOLIDATED SEDIMENTS) SIGMAI> 0.29999996E-04 EPSI - 3.I80CO03 SIGMAM. 0.9OO0OOO1E-O4 VROCM" 0.39999998 EPSRCM- 7.COO000O THIC" 3.0000000 SIGMAT- 0.10000003E-05 SIGMAW- 0.50000001E-01 VROCT* 0.69999999 EPSRCT- 7.0COO0O0 Figure 3.3 Spectra and time domain filter responses of two models. Signals used with these filters are bandlimited below 2 0 M H z ; see figure 3.2. The last eight points of the spectra are tapered to zero. Important characteristics used or calculated by the program are listed in the table. (A) Glacier ice resting directly on a wet t i l l bed. (B) Same but including a 3 m thick layer of mixed ice and rock between the ice and bed. of the filter. It is an approximate delta function at time zero; the approximation would become closer to a true Dirac delta if the filter was less frequency-dependent. Small oscillations are a result of imperfectly approximating the spectrum near the Nyquist fre-quency. They are insignificant in our case because signals are bandlimited to less than 2 0 M H z (see figure 3.2). The parameter most responsible for frequency dependence is the conductivity of interstitial water ow. Higher values of ow result in larger -R(w) at the lower frequencies, although the asymptote at high frequencies is unaffected. Note that this asymptote is 0.412 but that the last eight points are tapered to zero. The asymptote can be verified by solving an approximate formula for the reflection coefficient for the case in which the ratio a/ux. <C 1 (Jordan and Balmain , 1968). In this case, the intrinsic impedance rj approaches y/fi/e so that where et = 18.34 and et = 3.18 from the list of figure 3.3a. Inserting a layer 3 m thick consisting of 40% rock and 60% ice results in the filter spectrum shown in figure 3.3b. Features of note include the increased amplitudes at lower frequencies (similar to figure 3.3a) and the oscillating nature at higher frequencies. Th i s occurs as a result of interference wi th in the layer which results in min imum echo amplitudes occurring at frequencies for which the layer thickness x is an odd multiple of a quarter wavelength (that is the wavelength wi th in the layer). In this example, i = 3 m and velocity in the layer is v = c/y/e^ = 300/\/4~.472 =-141.9 m / / s - 1 , so there should be min ima in the spectrum at fn = (2n - l)v/4x or at / = 11.83 M H z , 3 5 . 4 8 M H z , This is confirmed in the figure. These phenomena affect a significant portion of the wavelet spectrum (see figure 3.2), emphasizing the importance of ut i l iz ing exact, complex = 0.412 - 26 -relations throughout the modelling process. Also noticeable in the second example is the decaying amplitude at higher frequencies, due to conductive losses in the middle layer. F ina l ly , note how the time domain response implies that there wil l be two main echo features, a small echo from the top interface (the ice/mix boundary) and the main echo from the lower boundary across which there is a greater impedance contrast. The effect on an incident pulse wil l be seen in figure 3.3. 3.2.4 Filtering Results The final modelling experiments can now be discussed, in which reflection coefficients such as those above are used as the impulse responses of filters and the Ricker wavelet of figure 3.4a is used as the input. Figure 3.4b shows a set of output wavelets calculated using the simple model of glacier ice resting on a porous t i l l bed. A different porosity was used when generating each wavelet. As expected, greater porosity results in stronger reflections since the presence of more interstitial water raises the intrinsic impedance of the glacier bed. Further experiments showed that, in a bed with 30% porosity, variations of water conductivity in the range 1 0 - 4 S m ~ 1 < ow < 1 0 - 1 S m - 1 yielded minor changes of echo amplitude, with minor phase shifts becoming apparent for ow > 1 0 - 2 S m - 1 . For figure 3.4c, a layer consisting of 40% rock and 60% ice was inserted between the glacier ice and a bed with 30% porosity. Over the first six trials, the thickness (1) of this layer was varied from 0 to 5 m , and for the last, x = 5 m and the bed was assumed frozen instead of wet. The impedance contrast from middle layer to bed is therefore reduced, resulting in a smaller echo. It should be made clear at this point that the time axis represents delay time in seconds after receipt of the echo from the first boundary, i.e. the ice/middle layer boundary. So, for the 5 m thick layer (with velocity of propagation v = 141.9m / i s - 1 as mentioned previously), the first and therefore strongest return from the lower boundary appears after a two-way travel time of t = 2x/v — 7.05 x 1 0 - 8 s . •11 -A ) I N P U T W A V E L E T - 5 . 0 0 E - 0 7 0 .0 5 . 0 0 E - 0 7 D E L A Y T I M E A F T E R FIRST R E T U R N ( S E C . ) G ) R E T L M S O F F W E T T I L L ( N O L A Y E R ) 0 . 0 - 0 . 5 - ' . 0 - 1.5 - 2 . 0 *> E ~~ i. • - 3 . 0 - 3 . 5 'j % V P T = 1 0 0 % V R T = 9 5 %VRT = 9 0 5VRT = 8 0 WRT = 7 0 ,VRT = 50 ~ V P T = 5 0 • 6 . 0 0 C - 0 7 0 .0 6 . 0 0 E - 0 7 DELAY TIME AFTER FIRST R E T U R N ( S E C . ) C) L A Y E R r H I C K N E S S = X ; % V R T = 70 % V R M = 4 Q X = 3rn =5m F R O Z E N BED - 5 . 0 0 E - 0 7 0 .0 6 . 0 0 E - 0 7 D E L A Y T I M E AFTER FIRST R E T U R N ( S E C . ) 0 .0 - 0 . 5 - 1 . 0 - 1 . 5 - 2 . 0 - 2 . 5 - 3 . 0 - 3 . 5 D) LAYER T H I C K N E S S = 3 . 0 m , %VRT=70 - " V ; V R M = O % V R M = 1 2 % V R M = 2 4 % V R M = 3 6 % V R M = 4 g % V R M = 6 0 %VRM = 6 0 F R O Z E N BED - 6 . 0 0 E - 0 7 0 .0 6 . 0 0 E - 0 7 DELAY TIME AFTER FIRST R E T U R N ( S E C . ) Figure 3.4 Results of filtering experiments. (A) The wavelet eo(t) that is incident on the reflector, i.e. the filter input. (B) Seven trials wi th a model of ice on a wet t i l l bed. A l l parameters are kept constant except for the percent volume of rock in the t i l l bed. The uppermost record represents an echo from a bed with 100% rock by volume. The other models have, glacier beds consisting of varying amounts of uniformly dispersed rock spheres in a water matr ix . (C) Now the model includes a thin layer between ice and bed. Layer thickness x is varied in six steps as per the figure title. The last record assumed a frozen bed. Percent volume of rock in the layer ( % V R M ) is 40% and in the bed ( % V R T ) is 70%. (D) Same as C but thickness is constant at 3 .0m and percent volume of rock in the layer is varied from 0% to 60%. - 28 -The final frame of figure 3.4 shows results from a model with x - 3 m and a glacier bed porosity of 30%. Percent volume of rock in the middle layer was varied from 0 to 60%. This figure suggests that it would be difficult to accurately determine thin layer characteristics such as rock content from radar data such as ours. Vis ible effects to the wavelet occur only for layer thicknesses greater than about 3 m and for rock concentrations greater than about 35%. Such layers are not uncommon however (Drewry, 1986; Maxwel l , 1986) so these results suggest that subglacial layers must be considered when interpreting data. One more glacier bed studied consisted of a layer of wet t i l l between ice and solid bedrock. Results confirmed the suspicion that the t i l l /bedrock interface would be nearly invisible because the ice / t i l l interface reflects most of the incoming energy and the t i l l layer itself is highly attenuating. Final ly , it is interesting to examine whether a thin layer of water at the glacier bed (or a Weertrnan film (Drewry, 1986)) wi l l be visible to the radar. Table 2.2 gives a summary of reflection coefficients for single boundary reflectors. Consider the result of using these in equation 3.2. If the thickness of the water film is x < A mm, then e~ J " ' z « 1 and equation 3.2 becomes R « plw + 0.25/ — 58.2° = 0 . 4 0 / 1 6 4 ° . This is similar to the coefficient for wet t i l l and not far from that of solid rock (see table 2.2). The implication is that these various reflectors would be difficult to distinguish given the type of data we have, a difficulty elaborated upon in chapter 6. 3.3 D A T A E N H A N C E M E N T These experiments demonstrate that variations of reflector parameters of glaciological interest wi l l cause only small changes in echo character. Examinat ion of field data sug-gests that such subtleties are likely to be masked by other contributions making up the complete signal. These wi l l include the wavelet itself, large-scale reflector characteristics - 29 -(such as the bulk properties of ice), and random noise. Clearly what is needed is some method of discriminating between the various components of the final complete echo. S.S.J Alignment and Mean Stack i f large-scale reflector properties are of interest, the simplest way to eliminate small-scale features is to find an average across the section or, in seismological terminology, to generate a mean stack. For best results this requires the removal of any so-called residual statics, which are minor shifts in echo return time not due to changes in reflector depth. T i m i n g anomalies do exist in data gathered wi th the U B C instrument and are caused by hardware instabilities that have not yet been corrected. A n automatic aligning program has therefore been used across sections when true depth information is no longer of interest but bed properties, i.e. echo shape, are. To align each trace, time shifted or "lagged" versions of the trace are cross-correlated with a reference trace, and the lag which yields the highest correlation value is used to shift the trace in question. The window over which correlations are calculated and the number of time shifts tried for each trace are both chosen interactively to help minimize computational expense. To state the procedure more formally, lagged or time shifted versions of the trace to be aligned, xn(t), are cross-correlated wi th the reference trace, £] (£) , using equation 3.5 (see for example Kanasewich, 1981: ch. 6). in which t\ and t2 are end points of the correlation window and L is the lag applied to trace 2. Trace 2 is then shifted by an amount Lm which produces the largest value of XL(t). This method of aligning traces is not very robust but works well if there is a strong common signal such as that of figure 3.5. (3.5) 30 1200 1600 2000 ~h B) Figure 3.5. (A) Section consisting of al-ternate traces from the close-spacing survey discussed in chapter 6. Only the echo is pre-sented (a time window of 90 samples) and they have been aligned with the program dis-cussed in the text. (B) The mean stack across the records of A . A ) Now with the section of aligned traces, an average trace can be calculated using equation 3.6, 1 N i=i where x(t) is the average trace and N is the number of traces. As an example, figure 3.5a shows an aligned portion of data. Equat ion 3.6 was applied with TV = 30 traces and time going from 1.14 fis to 2.03/xs (i.e. 90 samples were used) to produce the trace of figure 3.5b. This average record could be used in comparison wi th modelling experiments (using a correct input wavelet Eo(w)) to estimate bulk properties that apply across the entire section. Bu t we are st i l l unable to interpret features that appear to vary across the - 3] -section. In this example the trail ing (right hand) edges may reveal spatial variations in subglacial properties, and in other cases, englacial features or temporal changes of glacial or subglacial properties may be of interest. To facilitate the interpretation of such subtle echo features, the multichannel Karhunen-Loeve transform ( K L T ) has been employed, the rudiments of which wi l l now be discussed. 3.3.2 Principal Component Decomposition The goal is to differentiate between signal components that are coherent from trace to trace, and components that are more variable. The multichannel Karhunen-Loeve transform ( K L T ) does this by converting a set of n real data signals X{(t) i - I , . . . , n into an alternate set xpi(t) i = 1 , . . . , n . The conversion is optimal in the sense that the resulting ipi(t) are orthogonal and are arranged in order of decreasing energy content, and the greatest possible amount of coherent information is packed into the smallest possible number of vectors tl>i(t). The transform can be written as n V-V(0 X , a'Jx'(0> i = i , . . . , n 1= ] and its inverse, or the reconstruction of the data using the 0,(2), as n Xi{t) =• £ bijipjit), i = 1 , . . . , n (3.8) y=i which are from Jones (1985: ch. 2). Both transformation matrices A (with elements a, ; ) and B (with elements 6,-y) can be shown to be the eigenvector matrix R derived from the covariance matrix of the input data. The derivation of this result is carried out by first defining a truncated reconstruction of the data Xi(t) using less than all the ipi(t). The square of the difference, or truncation error, between X{(t) and £ i ( t ) is then minimized (3.7) - 32 -by setting the partial derivatives of this difference with respect to a^ y and bi-j to zero. A pair of equations is obtained in which the covariance matrix of the data T = XXT appears along with A , A T , B, and BT. Manipula t ion of these equations shows how A = B —- R if the truncation error is to be minimized. So the K L T is carried out by first forming the covariance matrix F and then decomposing it into its eigenvector matrix R and the corresponding diagonal eigenvalue matr ix A. In other words, T = RAR1. Then the multichannel K L T is writ ten as the pair of equations * = R T X (3.9) X = . (3.10) The columns of R are the eigenvectors of T, the rows of X represent discretized versions of the data traces and the rows of are known as the principal component vectors of the transformation. The interactive program I have written to perform the K L T on subsets of real data (up to 100 traces with up to 100 points each) includes the following functions: (i) parameters such as the number of traces, position and length of the time window along the trace and output format can be selected; (ii) a mean stack can be calculated (as in figure 3.5b); (iii) eigenvectors and eigenvalues of the correlation matr ix can be either listed or plotted graphically; (iv) any number of principal components (p.c.'s) can be calculated and plotted if required; (v) any subset of these p.c.'s can be used to reconstruct the data. M a k i n g each step interactive ensures economic use of computer time by, for example, l imi t ing the number of principal components generated to only those required. Figure - 33 -1 1' I 1 ' 1' 1 1 1 1 J B C Figure 3.6. Data from figure 3.5a after reconstruction wi th only a few of the principal components derived with the Karhunen-Loeve transform. (A) Recon-struction wi th only the first principal component. (B) Reconstruction with the first and second principal components. (C) Part ial misfit reconstruction with the second and third principal components. 3.5 was generated with this program and figure 3.6 illustrates the use of the K L T on the same data set. Some insight can be gained into how the K L T works by comparing figure 3.6 to the original data and corresponding mean stack. When only the first p.c. (calculated using equation 3.9) is used in equation 3.10, the resulting reconstructed traces wi l l only contain information that is coherent across all traces. Such a reconstruction is not generally very useful but is given in figure 3.6a to illustrate that, as expected, each new trace is very - u similar to the mean stack of figure 3.5b. Less coherent information is retained in the lower order principal components. A reconstruction which uses both the first and second principal components (figure 3.6b) includes some of the trail ing edge features that are visible but confused in the raw data of figure 3.5a. Variations from trace to trace can be further emphasized by reconstructing traces without the most coherent information. For example, figure 3.6c was generated by using only p.c.'s two and three. Such misfit reconstructions also serve to emphasize particularly anomalous or noisy records such as traces 12 and 14. The eigenvectors and eigenvalues of the correlation matrix can also be of use. Insert-ing the relation X X T = RAR1 into equation 3.10 shows that A = tytyT. In other words, A is the covariance matrix of vj/, so the eigenvalue A t may be viewed as a measure of the energy content of the corresponding principal component tpi(t). The sum E = Ylj represents 100% of the energy in the data so the amount of energy represented by each individual p.c. can be found from e3 — X}/E. These can be used to determine how many components would be needed if a reconstruction containing a certain percentage of total energy is required, to emphasize either coherent energy or incoherent energy. A further application of the eigenvalues involves using their ratios to make quantita-tive assessments of coherency or similarity. For example, the so-called modified eigenvalue ratio, E V R , discussed by Jones (1985) E V R = T = 1 \ (3.11) wi l l be large for a record set with similar signals (since most of the energy wi l l be packed into the first few p.c.'s) and wi l l be smaller for a set of dissimilar signals. Such a similarity - 35 -i g e n v e c t o r 1 0 5 10 15 20 TRACE N U M B E R T 0.5 WEIGHTING: - Q 5 25 30 Figure 3.7. The first five eigenvectors found using equation 3.9 on a slightly smoothed version of the data in figure 3.5a. "Weighting' 1 represents the weight of a particular trace's contribution to the p.c. corresponding to the eigenvector number. If a cluster of traces have similar weights for a particular p.c. then those traces have similar components at energy levels represented by corresponding eigenvalues. measure could be used in various forms of cluster analysis to compare features exhibited by separate sets of records. The eigenvectors of F , noted above to be the rows of the matrix R, can also be of use. If rij is the element in the ith row and j t h column of R, it can be considered as a measure of the contribution of the iih trace to the j i h principal component. In other words, it indicates how much of the ith trace is projected onto the j i h principal component. A measure of the similarity between two traces can be found by calculating the square of the difference between projections of the two traces onto a given set of pr incipal components. - 36 -Alternatively, the eigenvectors could be plotted to graphically depict the weight of each trace's contribution to a given p.c. Figure 3.7 is a plot of the first five rows of W constructed from a slightly smoothed version of the data in figure 3.5a. The smoothing reduced the worst of the random noise by low pass filtering with a cutoff around 35 M H z . (The software described by Prager (1983) was used to perform this task.) The first eigenvector shows that most traces contribute similarly to the first p . c ; this is because the traces have a strong common signal. The second eigenvector shows that traces 1 through 10 are similar and traces 20 through 30 are similar. Lower order vectors show more random contributions from each trace, reflecting the randomness of lower energy components of the signals. The method of K L T can be further refined to involve the use of complex data so that phase changes are incorporated into all applications. In this way greater compression is possible, frequency domain data can be dealt with directly, and even residual statics can, wi thin limits, be accommodated. Jones (1985) shows how, for Ricker wavelets, time shifts of up to ts < 0Aujm (refer to equation 3.4) can be accommodated for using phase shifts. The current work has not used the more expensive complex K L T because the data have large t iming anomalies (see chapter 5) and have required alignment. Such an unreliable t iming reference makes small-scale phase information difficult to extract and interpret. 3.4 C O N C L U S I O N S This chapter has been concerned mainly wi th placing limits on how much can be inter-preted from impulse radar echoes from a glacier bed. Two analytical approaches have been considered; the first was based on modelling electromagnetic pulse propagation and reflection as a filtering process and the second was aimed at enhancing field data. Mode l l ing experiments using Ricker wavelets showed that some glaciological properties - :j,7 -should be easily determinable, such as whether there is a fro/en or wet bed, while other properties, such as whether basal layers exist, wi l l be harder to define accurately using radar data alone. Enhancement using p.c. decomposition was shown to have good po-tential for emphasizing data characteristics that would otherwise be obscured by strong common components or noise. The remaining chapters of this thesis wil l examine field data in the light of these con-siderations and the methods wil l be applied with a view to making practical glaciological interpretations. - 38 -C H A P T E R I V I N S T R U M E N T A T I O N 4.1 I N T R O D U C T I O N The original requirments for the U B C portable impulse radar were that it be capable of generating very short duration signals centred at a frequency of a few megahertz, and that it be able to record echoes with a depth precision of 1 in and a maximum penetration depth of a few hundred metres. It was desirable to obtain records which could be processed in the lab, or even in the field, using signal enhancement techniques similar to those of seismology. Problems of practical field operations were also addressed. Small size, light weight (and hence low power requirements), and automatic operations are all important if the difficulties of working on temperate glaciers are to be minimized. These considerations resulted in the instrument illustrated in figure 4.1. It consists of a transmitter and an antenna which together emit a pulse of about 20 M H z bandwidth wi th a peak at about 8 M H z , and a digi t izing receiver which records the electric field strength at its antenna for 10//s after emission of the pulse. From a system point of view (figure 4.2), the instrument is organized around a microprocessor which, in response to commands from the operator, wi l l initialize the acquisition of records and handle the operations of identifying, storing, retrieving and displaying them. The following more detailed discussion considers each of the four major components separately: the transmitter; the antennas; the receiver and digitizing circuitry; and the microprocessor, software, and peripheral functions. Final ly , 1 wi l l comment on the instrument's physical configuration as it relates to actual field operations. Figure 4.1. Field configuration of the U B C impulse radar instrument. Trans-mitter ( T X ) is triggered by the receiver ( R C V R ) via the optical cable. Energy path 1 is known as the surface or direct arrival; energy path 2 is the glacier bed echo. 4.2 T R A N S M I T T E R Most impulse radar systems discussed in the literature (e.g. Watts and England, 1976; Sverrisson and others, 1980; Morey, 1974; Sellman and others, 1984) generate the re-quired impulse of electromagnetic energy by delivering a single-phase voltage pulse to the terminals of an antenna designed to radiate over a broad band of frequencies. The voltage pulse is usually generated by using a solid state switch to connect as nearly in-stantaneously as possible a charged capacitor directly to the antenna. Watts and Wright (1981) describe a pulse generator of this type that uses for the high speed switch a set of bipolar transistors operating in the avalanche mode. Such a design has many advantages. It is simple, inexpensive, has a voltage rise time of a few nanoseconds, can develop a few kilowatts wi th a single transistor and can run either at a fixed rate as a relaxation oscilla-tor or as a triggerable pulse generator. A conceptually similar system can be built using a C P U 5 n r = M E M O R Y K E Y -P A D l / P P O R T S X m t r R C V R & T I M E -B A S E T T A P E O / P P O R T S L E D s R S -2 3 2 C S C O P E D R I V E Figure 4.2. System block diagram. Components are discussed in the text. - 41 -silicon-controlled rectifier (SCR) as the switch (Sverrisson and others, 1980). Rise times are somewhat slower but S C R s are more efficient than avalanche transistors, eliminating the need for heat dissipation and reducing the total power requirements. This is the type of transmitter designed for the U B C impulse radar instrument. GATE ANODE G A) A CATHODE C B) G A NT—-N c C ) LC2 [C02 r A >'c 0 7 J 6 f?2 D) C Figure 4.3 Conceptual operation of S C R switches. See text for details. (A) S C R symbol. (B) S C R construction. (C) S C R function. (D) S C R func-tional diagram. lco is leakage current. If Ic and represent collector and base currents, then hje is forward gain such that Ic — Ico -r hje(Ico + It,). It is crit ical to the generation of useful pulses that the voltage step be as fast as possible, so a discussion of S C R switches is in order. Referring to figure 4.3, an S C R can be viewed as a pair of transistors in series so that the anode current I A wi l l depend on the individual current gains, hje\ and hfe2, and collector-emitter leakage currents, Icoi and Ic„2, according to equation 4.1 (Gutzwiller , 1967): (1 + hfel){l + hfe2){ICol +-ho2) 1 - hfelhfe2 (4.1) Th i s equation results from algebraic manipulation of the following three equations, re-42 -lat ing currents 1A, l c o i and IC02' I A = hi + ^61, Jcl = h.o\ + hfe\{hol + hi), hi = Ic2 = h.o2 + hje2{ho2 + hi)-A n S C R is in the forward blocking or off mode when the anode is at a positive voltage wi th respect to the cathode and the so called loop gain G — hfe\hfe2 <C 1. As G approaches 1, I A increases, the second transistor applies a positive feedback current to the base of the first, and they both drive each other into saturation. This is the on condit ion in which the anode and cathode are virtually short-circuited. This avalanching or switching on can best be initiated by increasing the leakage currents because hje is directly proportional to emitter current. Current leakage between anode and cathode is dependent on anode-to-cathode voltage drop, the rate of change of this voltage (due to device capacitance), and temperature (due to carrier mobility in semi-conductors). But the most straightforward method of init iating avalanching is to inject a small charge into one of the two internal layers; hence the provision of a "gate" terminal on the internal P (conventional SCRs) or N layer (complementary S C R s ) . Once in the on mode, the S C R wi l l revert to its off state either if J A drops below the device's so called "holding current" (regardless of gate current), or if I A drops below the "latching" current after the gate current has been removed. These characteristics are specified by the manufacturer. The radar transmitter consists of two S C R s arranged in a push-pull configuration. When they are simultaneously triggered by a current pulse at their gates, they discharge a pair of capacitors into the antenna such that one arm of the dipole receives a large positive pulse and the other arm receives a large negative pulse. The resultant 1200 V pulse at the antenna terminals has an exponential edge which reaches a rate of change - A?, -of 10.2 V n s _ 1 over its latter half (figure 4.4). Before switching, the S C R s are holding off approximately 800 V on each anode and after triggering, the anode voltage drops rapidly to a point where I A falls below the latching current. Then the S C R s revert to the off condition and the capacitors can recharge in time for the next trigger signal. Figure 4.5 is a simplified schematic diagram to which the following practical notes refer (see the appendices for the complete schematic). Capacitor C\ was chosen to be 0.01 /xF and Rc l imits the charging rate to suit the small D C - t o - D C converter used as a high voltage supply (Venus Scientific, Inc. model C 8 T ; converts 12 V D C at 190 ma to 800 V D C ) . Resistors, Rp, are required to reference the circuit to ground and to provide a slow discharge path for the current which was dumped into the antenna arms. These are discussed in section 4.3. The trigger generator converts the optical trigger signal into a current pulse suitable for forcing the S C R s into an avalanching condition. A pulse transformer wi th dual secondary windings ensures simultaneous t iming of the two triggers and resistors RQI and R q o a r e selected so that trigger currents are appropriate for the individual characteristics of each S C R . In this way avalanche breakdown of both S C R s can be tuned to occur at exactly the same time as long as ambient conditions are identical, a condition ensured by fixing the two devices close to each other on the same heat sink. Dur ing field trials it was found that overall t iming is temperature-dependent such that lower ambient temperatures result in greater delays between arrival of the trigger signal and emission of the pulse. This is because a greater charge (i.e. a longer current pulse) is required to initiate avalanching when the semiconductor junctions are at a lower temperature. 4.3 A N T E N N A S The next step is to consider how the pulse that is applied to the antenna (illustrated in the oscilloscope photographs of figure 4.4) is radiated as a short electromagnetic wavelet. -44-B ) Figure 4.4. Oscilloscope photographs of pulse generator waveforms. (A) Shows the complete voltage pulse at the antenna terminals. The small , negative, square pulse is the trigger command arriving from the receiving unit. Scale: 150 V per vertical division for the spike, 1.5 V per vertical division for trigger pulse, 20 [is per horizontal division for both. Note that both traces start at the second division. (B) Same as A in all respects except that the time axis is 0.1 [is per division. This emphasizes the approximately 0.8 /zs delay between arrival of the trigger signal and the actual switching of the SCRs . Colder ambient temperatures increase this delay. S C R switching results in an exponential rise in voltage across the antenna terminals. This can be considered as a good step function because the trai l ing edge visible in photo A is very long relative to the rise time exhibited by photo B . 12V H.V PSU SUPW :IBER OPTICS IN. Figure 4.5. Simplified circuit diagram of the transmitter referred to in the dis-cussion of transmitter operation. A very broad bandwidth antenna (one with good transient performance) is required to damp out natural resonances. A dipole antenna with this characteristic is shown by Wu and K i n g (1965) and by Rose and Vickers (1974) to consist of dipole arms for which internal resistance increases towards the outside ends. The effect is to reduce the current towards zero as the pulse travels outward along the dipole arms, thus reducing reflections at the ends of the arms and preventing the current distribution on the antenna from being a standing wave. The internal resistance profile that optimizes the impulse response (regardless of efficiency) can be found using relations derived by Wu and K i n g (1965) (with corrections by Shen and K i n g (1965)). They show that at a position i from the centre of the dipole, the internal impedance Z(x) for which a pure outward travelling wave exists on an antenna arm of length h is given by / { X ) = 2-^h—x) = k--X • ( 4 - 2 ) The term £ is the intrinsic impedance of the medium and tp is the ratio vector potential on the antenna surface 0 current along the antenna at the point where the current is a maximum. If ip is considered as vir tual ly constant wi th respect to x, and the antenna radius a is small , ie. a <C h, then the magnitude of ip is given by 2 ( s i n h - 1 - - C(2ka,2kh) ) + j 2S(2ka,2kh) + TV(1 - e~'2kh) kh (4.3) (Wu and K i n g , 1965 (equation 29), and Shen and K i n g , 1965) where, for the antenna used on Trapridge Glacier: h = 5 .0m is the length of each dipole arm; a = 0 .5mm is - 46 -the radius of the antenna wire; k = u/v is the wave number; hk = n/2 since this is a half-wave dipole; h/a = 1 x 10 4 ; and 2ka — 7r X 10 4 . Also , C 1 — cos t t dt if b < x . S(b,x) « / 2 sin t dt if 6 -C x . t These so-called Cosine and Sine integrals are handled as per Abramowi tz and Stegun (1972) and ijj is found to be = 116.5 — j'2.43| = 16.68. Concerning the intrinsic impedance f = y V / e , the method of Sverrisson and others (1980) is followed, whereby the permitt ivi ty of the medium in which the antenna operates is found by using 281.1 and equation 4.2 yields Z(x) — 748.8/(/i - x) . For this optimally damped antenna, Shen and K i n g (1965) show that the efficiency is only around 8% or 9%. Therefore Ro must be reduced and a compromise found between sufficient damping and adequate radiated energy for sounding. In general, Ro wi l l not be the same for different antenna lengths, nor wil l a single R0 be opt imum for a given antenna on different glaciers. Only rough estimates can be made unless optimization is carried out in the field where ice depth, temperature, scattering properties, and instrumentation wi l l all contribute to system performance. The length h determines the centre frequency of the pulse emitted and is also chosen as a compromise between resolution and power loss due to scattering. In the present case, the resistive loading was approximated by inserting fixed resistors ].78e 0 Magnetic permeability is that of nonmagnetic materials (/i — /x0), so f = yMo/ l -78eo - 47 -h=5m 0.5m 1.0m 0.5 m —vW vVV <AAr- WV—I Vv\ vVv »AA— 69 12C 200 820 Figure 4.6 Diagram of antennas used on Trapridge Glacier. Resistances are in ohms and the two sides are symmetrical. of values found using equation 4.2 with RQ = 300 H , and the resulting antenna used on Trapridge Glacier is shown in figure 4.6. The actual wavelet emitted when the antenna in figure 4.6 is excited by the input of figure 4.4 is difficult to estimate analytically because the current distribution on an antenna resting on the air/ice interface is not accurately known. However, the situation can be considered qualitatively. Our damped antenna is modelled as a resistor in series wi th a capacitor (Wu and K i n g , 1965). Therefore a step voltage applied to the driving point wil l result in a "one-lobed" current pulse; that is, current wi l l be in one direction and wil l first rise and then fall. Now, it is fundamental to the theory of electromagnetic radiation (Jordan and Balrnain, 1968, p.319) that the vector potential in the far field of an antenna is proportional to the first time derivative of the current in the antenna. B y the reciprocity theorem of antennas (Jordan and Balrnain, 1968, p.345), the voltage on a receiving antenna is related in a similar way to the far field vector potential, so the waveform recorded by the receiver wi l l look like the second time derivative of the original current pulse. Therefore, if the pulse generator can impress a step voltage onto the antenna, the best possible echo wi l l be a three-lobed waveform. The frequency emitted depends on the antenna length. Since it behaves approxi-mately as a half wave dipole, it is tuned close to a frequency wi th wavelength A « 2h\ that is to a frequency fc « v/2h where v = c/y/e\ce. Consequently, wavelet spectra are expected to have a peak around fc = c/(y/3.18 x 2h) = 8.4 M H z . Considering that this is a damped, not a true dipole antenna, that effective antenna lengths have not been calculated, that they rest on an interface of dielectrics, and that echoing and propagation are dispersive, the spectra of wavelets received agree reasonably well wi th this estimate (figure 3.2). Ra p id discharge of the current in the antenna would produce negative currents result-ing in secondary emissions that would degrade the waveform. This is why the resistors RD in figure 4.5 are large, resulting in the long trail ing edge of the pulse seen in figure 4.4, and hence causing negligible reverse antenna currents. (Recall that current in a capacitor (i.e. in the antenna) is proportional to dV/dt.) 4.4 R E C E I V E R The receiver's task is to amplify the signal on the receiving antenna and to digitize it at an effective rate of 100MHz without the high cost, large power requirements and low resolution of most real-time "{13511" digitizers. The solution is to use the sampling time base method, and the circuit (see figure 4.7 for a block diagram) is a modification of one described by Narod and Clarke (1983). This method uses a high-speed sample-and-hold (S/H) device to grab one sample of the signal and hold it for digit izing. The subsequent sample is obtained by repeating the echo and moving the S / H 10ns further along the signal. In order to gather a complete record, this process is repeated 1024 times until 10/is of data has been collected. Precise t iming is obtained by comparing an accurate linear voltage ramp to a reference voltage. If the reference voltage is changed, the time at which both signals are identical w i l l change by an amount proportional to the ramp height, ramp duration and change in reference voltage. In the U B C radar, successive sample positions are obtained by lowering the reference by 10 m V . The ramp voltage runs from 10.00 V to 0.00 V over a period of 10 fis so, for each new sample, the time at which the two voltages are equal is moved forward by ( l O m V / l O V ) x 10/xs = 10 ns. The transmitter is triggered simultaneously C L O C K & C N T R L F A S T R A M P S L O W R A M P A T T E N . T R I G P U L S E C O M P A R A T O R f i b r e o p t i c s SA M P LE| & H O L D T R A N S M I T T E R Figure 4.7. Receiver block diagram. Components are discussed" in the text. - 50 -with the start of the ramp, so echoes returning within 10(.is wi l l be recorded; in other words, the maximum depth observable wil l be d — (v x 10/xs)/2 840m. This complex procedure is required because our low power, 12-bit analogue-to-digital converter ( A D C ) takes 35 /ts to perform the conversion and the resulting number must then be properly stored. In fact, the rate at which samples can be gathered is further l imited by the max imum pulse repetition rate of the transmitter. This is 250 Hz because capacitors C] of figure 4.5 take 1ms to recharge. Therefore, since the 1024 samples each require one complete pulse, gathering one record takes 4.1 seconds. Details of the electronics wi l l not be presented but some notes concerning the blocks in figure 4.7 are worthwhile. Clocking and control are based on a 1 M H z crystal clock, wi th divider circuits generating the required t iming pulses. The transmitter is triggered synchronously with the fast ramp which is generated by an operational amplifier config-ured as a precision integrator! The slow ramp is the variable reference voltage referred to above. It is generated by clocking a 10-bit binary counter once for each sample and converting the count into an accurate voltage level wi th a digital-to-analogue converter. The comparator is a precision circuit which produces a 50 ns pulse when one input volt-age passes from greater than to less than the other. The S / H device starts tracking the input signal on the rising edge of this pulse and the trail ing edge signals the S / H to hold the input level for conversion into a digital number by the A D C . The input stage is a five-transistor wide band amplifier preceded by a variable at-tenuator. Traditionally, the input impedance of a receiver is designed to match that of the receiving antenna (which in our case is identical to the transmitter antenna). This maximizes the transfer of power from antenna to receiver and prevents the antenna from reradiating a portion of the signal. To date, however, most impulse radar work on glaciers has been carried out by simply plugging the receiving antenna into the high impedance input of an oscilloscope and photographing the trace triggered by the surface arrival. - 51 -Such mismatching can work for two reasons. First , the antenna itself is designed not to ring by including the damping resistors. Second, the low signal-to-noise ratio expected for severely mismatched systems is not important since local ambient radio frequency noise in mountain environments is usually very low. Given these considerations, it be-comes desirable to have a receiver with a high input impedance because then the voltage on the antenna can be seen with a minimum of that signal being dropped across the input impedance. The U B C radar's receiver was not optimized in the prototype, but since the records obtained on Trapridge Glacier were entirely adequate, the system has not yet been improved. 4.5 C O M P U T E R , C O N T R O L A N D D A T A H A N D L I N G It has already been mentioned in the introduction that the instrument is under the control of a microprocessor. The computer is built with components of the G O S M A C 1800 microcomputer system, manufactured by R C A ( R C A , 1977) and consists of a CDP1802 central processing unit, 4 kbytes of read-only memory (containing the program), 1.25 kbytes of random-access memory (used as a data buffer), and input /output ports for communication with peripheral hardware. As figure 4.2 illustrates, these peripherals include: (i) a keypad with which the user enters commands and identifies records, (ii) an L E D display to inform the user of the current system status, (iii) a digital cassette tape recorder for permanent data storage, (iv) an RS-232C interface for transferring data to other devices, (v) a digital-to-analogue converter for displaying a record on an oscilloscope, and (vi) the sampling time base receiver discussed previously. The entire system is under software control and operates as follows (see the flow chart of figure 4.8). After init ializing the registers, pointers and control lines (at power up or by pressing "reset"), the system rests idle until an instruction is keyed in on the hexpad. The sequence of keys is stored until the "enter" button is recognized, at (^START ^ INITIALIZE SYSTEM RESET ^ Figure 4.8 Simplified software flow chart. See the text for an explanation. Table 4.1 System instructions F i l l data buffer wi th byte ' X X ' AOXX Load forward write command Al Cassette rewind A2 Write byte ' X X ' onto cassette A3XX Load forward read (finds file gaps) A4 Reverse one file A5 Backspace and load forward to file gap A6 Read one byte off cassette onto L E D ' s A8 List tape byte by byte on L E D ' s A9 Auto-acquisition every ' X X ' minutes AFXX List current header buffer on L E D ' s DC List first ' X X ' bytes of data on L E D ' s BDXX List current format block on L E D ' s BF Initialize data cassette CI Gather a record and display on oscilloscope CD Dump header and data onto RS-232C DB Dump entire cassette onto RS-232C DC Display data buffer contents on oscilloscope DD Dump next file onto RS-232C DF Write L E O T mark (use with caution) Fl Advance tape ' X X ' files and read data FAXX Reverse tape ' X X ' files and read data FBXX Display current file header FC Open new file and store current data FD Find file ' X X ' and read it FFXX List of instructions currently available for controlling the radar. New instructions require additional software. which point the sequence is decoded and the requested task init iated. These can be classified as data collection, display, record identification, storage and retrieval tasks, or as diagnostic functions; a complete list of instructions is given in table 4.1. Suitable status messages or requests for information are displayed on the 8-digit display and when a task is completed, the system either returns to its idle state or displays appropriate error messages. Records are gathered by the sampling time base asynchronously wi th respect to the computer. After the ini t ial start command, transfers of data from the A D C to the buffer memory (one sample at a time) include two-way hand-shaking communication between the C P U and receiver. After a complete record has been collected, it can be - 54 -visually displayed by outputt ing pairs of numbers representing amplitude and sample number to the oscilloscope's Y and X channels respectively. This is done wi th two digital-to-analogue converters by the oscilloscope driver which outputs the complete record 25 times per second. This means that a small , low-cost, low-power oscilloscope can be used for inspecting results in the field; the Tektronix model 211 was used on Trapridge Glacier. Da ta are stored permanently on cassette tapes as files of 1024 samples, each sample having 8-bit resolution. The system wi l l also request identification information from the operator and attach this to each record as a header containing the time, date, location, gain, and record number. A maximum of 50 such records can be stored on standard digi tal data cassettes. The digital recorder/player and its control card are a commercial unit supplied by Memodyne Corporat ion (the model 333 "minicorder"). Da ta are recovered by reading the records off" the cassette either individually by file number or sequentially to dump a complete tape. It can be released to another computing system through the on-board RS-232C serial interface. For the present, data is reformat-ted to make it compatible wi th the plotting and processing package that was designed for dealing with data produced by the U B C U H F radar system (Narod and Clarke, 1983). This package (Prager, 1983) performs such operations as plott ing, smoothing, D C bias removal, signal differentiation, and time-dependent amplitude variation either on indi-vidual traces or on suites of traces. Addi t iona l subroutines were added specifically for impulse radar data. For example, instrument bias can be subtracted and traces can be shifted or truncated. Various other processing programs have also been wri t ten, includ-ing the alignment, spectral analysis, principal component decomposition and amplitude processing routines discussed elsewhere in this thesis. - 55 -4.6 F I N A L C O M M E N T S In order to facilitate field operations, the instrument is configured as two separate units; the first is the transmitter and the second contains all the remaining components. The transmitter trigger signal is sent from the receiver v i a an optical cable which electrically isolates the two units while maintaining reliable, uncomplicated operation. Identical antennas are used for transmitting and receiving so that they are interchangeble in the field. Dipole arms are 5 m long and are constructed as 1 m lengths of 18 A W G wire with loading resistors at their midpoints. These are installed in sections of plastic pipe so that the antennas are rugged, collapsible, and can have loading resistors or length varied conveniently in the field. Each unit requires a power supply capable of maintaining a min imum of 12 V . Twelve " D " size dry cells in series (18 V) are adequate to run the transmitter but the higher currents demanded by the cassette deck and high-speed circui try in the receiver have been found to drain such a source too quickly. This is in spite of using C M O S technology for the digital circuits, as well as using software to power down the sampler when it is not being used. Lantern batteries or gel cells are more appropriate and automobile batteries were used when time-varying targets were being studied over long periods of time. These experiments use a software routine which wi l l record echoes at regular intervals selectable in one-minute steps from 1 to 255 minutes. The entire system was configured to fit in a backpack for small-scale studies (see frontispiece) and was fitted into a rugged, waterproof case for more extended field work on Trapridge Glacier . These and other specifications of the impulse radar instrument are summarized in appendix 1. - 56 -C H A P T E R V F I E L D W O R K A N D D A T A C H A R A C T E R I S T I C S 5.1 P R E L I M I N A R Y F I E L D T R I A L S In this chapter, experiences gained in early trails wi l l be briefly discussed, current field methods wi l l be explained, and basic characteristics of signals obtained on Trapridge Glacier in July 1986 wi l l be considered. In July 1984 the first transmitter test was conducted on Trapridge Glacier by trig-gering the t r a « s m i t t e r continuously and recording echoes on the screen of a high speed oscilloscope connected directly to the receiving antenna. A set of soundings down the centreline of the glacier was obtained and results were encouraging enough to continue the development of the digitizing receiver (see figure 5.1.). Figure 5.1 One sounding from the transmitter tests of Ju ly 1984. The array was similar to that used in more recent work except that no digitizing receiver was used. Horizontal scale is 0.1 /zs per division and vertical scale is 50 m V per division. - 57 The entire system was taken to Trapridge Glacier in July 1985, but poorly designed receiver electronics prevented any useful results from being obtained. These problems were corrected in time to take the system to Athabasca Glacier in the Canadian Rockies in November 1985. Unseasonably cold temperatures (between —25° and — 40° C) prevented this prototype system from providing any data, but useful experience in cold temperature field operations was gained. The trip also prompted a laboratory assessment of the behavior of S C R s at low temperatures. The extended switch-on delay times discussed in section 4.2 were discovered by running the transmitter in a box cooled with dry ice. These and other temperature-dependent effects wi l l be noted later when the three-day continuous survey is discussed. In May 1986, the complete system was taken to Helm Glacier in Gar iba ld i Provincial Park near Vancouver for final system verification, and to assess the feasibility of using the equipment on very lightweight expeditions. Although the data obtained from this very warm, shallow glacier (less than 4 0 m deep according to Park personnel) were of marginal use, experience wi th the equipment resulted in further minor modifications (such as reconstruction of the antennas) which greatly simplified subsequent field operations. It was also found that two operators can handle enough gear to carry out three or four days of echo sounding without extra logistical support. The frontispiece illustrates how the system was deployed for this work. 5.2 F I E L D O P E R A T I O N S O N T R A P R I D G E G L A C I E R Owing to the extensive amount of work planned for the 1986 field season, a more rugged and convenient configuration of the equipment was required than that used on Helm Glacier . Figure 5.2 illustrates how the transmitter, antennas and receiving unit (including receiver, monitoring oscilloscope and miscellaneous operating gear) were deployed so that the system was easily operated by one person on safe terrain. - 58 -Figure 5.2 Equipment configuration as used on Trapridge Glacier, Ju ly 1986. (A) Transmitter installed in a small tool box; power supply consisting of twelve " D " size dry cells is included. Also note the modular construction of the an-tenna as described in section 4.2. (B) Receiver, monitoring oscilloscope, power supplies for both (dry cells for the oscilloscope and dry cells or external higher ca-pacity batteries for the receiving unit) and miscellaneous equipment. The optical cable is visible in the upper left. The padded metal case is on a small sled. - 59 -In all cases, the sounding array was the same; antennas were placed 20 to 25 m apart and were perpendicular to the survey line. Other antenna polarizations were found to be inadequate. When placed in line with each other, inductive coupling between the antennas resulted in unacceptably large surface wave signals, and when placed perpen-dicular to each other the echo amplitude became very small . Further experiments with antenna configuration showed that shortened or folded dipoles did allow visible echoes to be recorded but never at amplitudes approaching those obtained with the original setup. 5.3 C H A R A C T E R I S T I C S O F E C H O S I G N A L S 5.3.1 Signal Features Caused by the Instrument Those features of the signal due specifically to the instrument wi l l now be considered, wi th reference to figure 5.3. The calibration record provides a crystal-controlled t iming reference (] M H z ) and helps confirm that the system is recording correctly throughout its dynamic range. Also shown are two records made at the same location at different gain settings. The surface wave signal is prominent near the beginning of these traces, followed by the echo at about 1.4 //s. These signals are superimposed on a low-frequency negative bias which is probably caused by inductive coupling between the two antennas. If the receiver input impedance was much higher, the receiving antenna would be unable to support a current flow, thus reducing this effect substantially; see for example the trace of figure 5.1 made wi th the high input impedance of an oscilloscope loading the antenna. This effect is not otherwise associated with equipment because a recording made without the transmitter firing (i.e. wi th the optical cable disconnected) shows only small effects over the first microsecond of the record, most probably owing to interference within the receiving electronics. This can be removed from data traces by subtraction. Figure 5.3c helps explain the problem of t iming uncertainty prevalent throughout most of the records. Previous researchers have used the surface wave signal to trigger - 60 -C) Figure 5.3 Examples of raw data recorded on Trapridge Glacier, 1986. C o m -plete, 1024 sample records are shown in (A) and (B) , wi th the first and last samples having been forced to plus and minus full scale respectively. (A) Crystal-controlled calibration record of 1.0 M H z . (B) Two soundings at the same location; the first was recorded wi th a gain of 40 and the second wi th a gain of 150. (C) Various records at low gain taken within hours of each other on the centreline profile. Note that only the first 3 /xs of these traces are displayed. - 61 -the receiver (e.g. Walford and others, 1986; Jezek and Thomson, 1982; Watts and Wright, 1981) but with only variable success. The U B C radar was designed to begin recording before the transmitter fires in order to ensure that the complete surface wave is recorded, thus providing reliable t iming reference points. However, most traces are recorded with a gain sufficient to preserve the details of the echo but which severely clips the surface wave signal. Figure 5.3c shows several recordings made at low gain and demonstrates how variable the surface wave signal can be from one location to another. Therefore the exact time of onset is often uncertain by as much as 150 ns, resulting in potentially large depth uncertainties. This variability also emphasizes the problem of wavelet estimation alluded to in chapter 3. 5.3.2 Quantitative Interpretation of Individual Traces When analyzing echo characteristics, either absolute quantities of the signals can be con-sidered, or relative variations within a signal or set of signals can be examined. The first method must take into account the relations describing propagation of electromagnetic \yaves from a transmitting antenna, through the medium of propagation, to a receiving system. If all the invariant parameters in these relations are known, it is possible to relate Wr, the useful power delivered to the receiving antenna's load (and presumably the measured quantity), to Wt, the total power fed to the transmit t ing antenna. Firs t the receiver is assumed to be recording signals that have travelled a distance r > A , the wavelength in the medium. Also , both antennas are assumed to have identical antenna power gain gp: a parameter which characterizes the antenna's efficiency and direction-ality as a function of frequency. The power density P of the electromagnetic field at a distance r from the transmitter is given by P — gpWt/4nr2, and the received power is given by Wr = PA, where A = gp\2/4n is the effective antenna aperture. For propaga-t ion in a lossless medium, combining gives Wr = Wt(gpX/4nr)2. If there is attenuation and/or dispersion during propagation, and received energy has been reflected from a boundary with reflection coefficient R, then P is reduced by a factor of (Re i r ) 2 . Thus the received and input powers are related by \ g v R t - i r 4nr (5.1) Consider now what is known about the parameters of equation 5.1. Constants associ-ated wi th the media of propagation were discussed in chapter 2. They are the attenuation constant 7 , the range r, which is deduced from the two-way travel time, and R, the re-flection coefficient. R is presumably the least well known quantity, but can be estimated if the glacier bed properties are known. The instrument properties are not so easily obtained. Chapter 4 discusses how difficult it is to describe the behavior of the antennas quantitatively, but gp is likely to be small since efficiency of such antennas is low (Shen and K i n g , 1965). Many other types of radar can find their respective gp by recording echoes from known reflectors (for example, airborne systems can record echoes from wa-ter; e.g. Narod and Clarke (1983)), but this is impractical for the ground-deployed U B C system wi th its 2 0 m centre-frequency wavelength. Wt is also hard to estimate for this wide band system. The total power available at the antenna terminals as well as the antenna's dr iving point impedance must be measured on the ice if correct values are to be obtained; this has not been done as yet. The ratio Wr/Wt could be replaced by the squared ratio of input and received voltages if the driving and receiving impedances were identical; this is not so and again, to circumvent this problem, the antenna driving point impedance is required. Rather than pursuing analysis of absolute quantities, more reliable results may be obtained by considering ratios of signal components in such a way that factors common to both parts, such as antenna properties, can be cancelled. Jezek and Thompson (1982) attempt to estimate signal attenuation from the ratio of echo amplitude to surface wave - 03 -amplitude. This measure of total attenuation At is attributed to absorption Ai, geometric losses Ay, scattering losses As, and reflection R. If all these terms are expressed in decibels, then At = Ah + Ag + As + R. (5.2) For Trapridge Glacier the attenuation constant can be calculated using the relations following equation 2.5. Using an average temperature of —3° C . , a — 0.004 at a fre-quency of 8.0 M H z . Then , if the glacier depth is assumed to be 75 m (two-way travel path re = 150m), Ab = ( 2 0 l o g 1 0 e ~ a r ' ) / r e = - 0 . 0 3 5 d B m - 1 . This is in excellent agreement with estimates compiled from various sources and presented in Jezek and Thompson (1982: F i g . 4). Scattering losses As wil l be considered negligible for this cold glacier at frequencies below 1 0 M H z (after considering Smith and Evans (1972), Watts and England (1976), and the temperature profiles from Clarke and others (1984)), and the reflection coefficient R can be estimated from equation 2.8 if necessary. Geometric spreading causes a reduction in echo strength proportional to l / r e (equation 2.5) and a reduction in surface signal strength presumed (from Annan, 1973) to be proportional to \jr\ where ra is the antenna separation. Then, following Jezek and Thomson (1982), propagation and antenna parameters are assumed the same for both surface and echo signals, and total geometrical losses that contribute to At are Ag = 20 l o g 1 0 ( r „ / r e ) d B . Using these values from Trapridge Glacier , and considering the reflection coefficient to be R — 2 0 l o g ] 0 0 . 4 6 « —7dB (suitable if the glacier is resting directly on a wet t i l l bed with 30% porosity; see chapter 3), equation 5.2 becomes At ~ —5 + 17 — 0 — 7 = 5 d B . Therefore the ratio of echo amplitude to surface signal amplitude is 1 0 5 / 2 0 = 1.8, i.e. the glacier acts as an amplifier. The most probable reason for this absurd result is the invalidity of assumptions made wi th respect to Ag. Firs t , the transmit and receive an-tennas, although themselves identical, do not have identical driving point conditions. - 64 -Second, it is not likely that their parameters are the same for both surface and internally emitted energy. Perhaps most importantly, they are not in each other's far field; their separation distance is similar to one wavelength of the centre frequency. Even without these difficulties, the value of Ag is highly sensitive to the separation distance. B y way of example, for ra = 24 m, the resulting geometric loss is Ag = 14.7dB and for ra — 25m, the resulting geometric loss is Ag = 17.4 d B . Final ly , the variations in surface signals demonstrated in figure 5.3c suggest that there are too many uncertainties in this part of the records to allow surface wave signals to be of much use. As a result of all these considerations, the surface wave signal wi l l not be used in the analysis of our data. Only echoes originating from within the glacier at distances of over two wavelengths wil l be considered, so that ratios can be taken which wil l reliably eliminate characteristics caused by the surface and equipment. There are a few miscellaneous concerns that can be conveniently dealt with at this point. A l l theoretical and practical work has assumed that the energy arrives at a reflector at normal incidence. This is not strictly true since the antennas are spaced about 25 m apart. However, application of the appropriate equations for oblique reflection of electromagnetic energy (Jordan and Balmain , 1968) shows that for depths greater than 60 m , errors in the reflection coefficients are never wrong by more than 2%. One more concern might be that a correction to account for the antenna spacing should be included in depth calculations. Without a reliable time reference, however, this correction becomes meaningless. - fi5 -C H A P T E R V I A N A L Y S I S O F F I E L D D A T A 6.1 I N T R O D U C T I O N In this chapter, results of echo sounding work carried out on Trapridge Glacier in July 1986 wi l l be presented and, to some extent, interpreted. Exhaustive analysis is inappro-priate because the 1986 field program was designed to assess how suitable the system is for addressing various glaciological problems, rather than to consider any such problems in detail . Referring to the map of figure 6.1 for orientation, the surveys carried out are as follows. The centreline of the glacier was first profiled in order to use the instrument as a simple depth sounding tool in as many different situations as Trapridge could con-veniently offer'. The next three profiles followed lines of dri l l holes, and were meant to provide additional depth measurements as well as potentially complementary informa-tion on other features of the dri l l ing program. Then a 60 m profile with soundings spaced 1 m apart was collected. The purpose was to provide a densely spaced set of data for bed property analysis and to try delineating where on the glacier bed a hole drilled the previous year had connected with a cavity. Finally, a set of records was gathered at one location at 20-minute intervals for 3 continuous days. Here, the object was to correlate temporal variations in the signals with concurrent measurements of basal pressure made by a sensor placed at the glacier bed directly below the radar. Correlat ion with other hydrological data collected at a site downstream of the glacier terminus was also planned. Before considering these data sets individually, some general comments are in order. In most cases, only the first 5 its of data are presented, and bad traces (most often - c>(; -Figure 6.1 Radar profiles on the lower portion of Trapridge Glacier, Yukon Territory. Inset shows the study area. Coordinates are given as the last four digits of the respective Universal Transverse Mercator ( U T M ) coordinates, and contours are 10 m. Profile lines 1, 2, 3, 4, and 5 are labeled; small numbers locate specific dr i l l holes. A l l points were surveyed by theodolite and laser ranger. The three-day continuous survey was carried out at hole number 28, the junct ion of profiles 1, 4 and 5. Note that glacier topography is now more rugged than this 1980 map indicates. - 67 -caused by tape writing or reading errors) are replaced by straight lines or blanks. Also, some editing was required to remove calibration traces and low gain records, and to otherwise rearrange the traces into logical sequences or profiles. The uncertainty in t iming referred to in chapter 5 has been minimized as follows. For sections not requiring depth information (for example, if bed features were being studied over short distances), traces were aligned using the program discussed in section 3.3.1. Otherwise, traces were aligned individually with respect to visible features of the surface wave signal. In most cases there is also good control information from dril l ing data. These difficulties wi l l be elaborated upon when each profile is considered separately. 6.2 C E N T R E L I N E P R O F I L E The centreline (figure 6.2) is a 500 m profile with soundings spaced at 2 0 m intervals. It is bounded by an icefall at the western end (although three records were taken within the icefall; another advantage of small, lightweight equipment) and by the now heavily crevassed bulge at the eastern end. (See Clarke and others (1984) for a discussion of this feature, which is characteristic of surge-type glaciers.) Detailed interpretations from this type of survey are impractical because, as we shall see in section 6.4, the fine structure visible at such shallow depths varies greatly wi thin the 20 m sounding spacing. Therefore, this and the next three sections wi l l simply be presented with accompanying figures and major features wil l be noted. For the centreline profile, traces were aligned with respect to the first falling edge of the surface arrival. Al though in general this has been successful, some traces are poorly aligned, notably the fourth from the eastern end. A change in depth of 10 m within 20 m horizontal distance would likely have some form of surface expression on such a shallow glacier; however, none was evident at that location. Use of depths from the dri l l ing program has helped constrain the zero time position on the vertical axis. Note that two records have some superimposed spikey noise. This is likely caused by tape reading or wri t ing errors, most of which are corrected by a parity checking 0.0 1.0 -o O £ 2.0-Q. <D Q 3.0-I c e f a I I rO.O AA A A C r e v a s s e l o c a t i o i B u l g e c r e v a s s e s H ' ' 1 " — H " h 1 1 1 1 1 - -+-—I 1 1 - 1 1 -1 0 0 2 0 0 3 0 0 4 0 0 1 5 0 0 - u s t i n g D i s t a n c e ( m ) 1.0 2.0 3.0 4.0 Figure 6.2 Profile 1, the glacier centreline (see the map of figure 6.1). Traces are unprocessed except for truncation of the latter half, alignment of the air wave signal and plotting. Depth scale was derived using v = 168.2 m/as" 1 for the velocity of e m ' waves in ice. Small x ' s indicate depths from the dril l ing program; triangles on top of the section locate profiles that cross this line; arrow heads under the section are locations of crevasses known to exist at the surface. scheme upon reading of the tape. Major errors may not be recoverable, resulting in apparent amplitude spikes, but in most of these cases, the entire trace has been affected and has therefore been left out. Observable surface features may help explain other apparently noisy intervals of traces. The first three traces were recorded in the lower portion of an icefall where internal structure is likely to be quite complex. Also, surface crevasses may represent vertical ice/air interfaces capable of generating echoes. The crevasse noted in the figure at 100 m was roughly l m across at the surface and was of considerable depth. Other crevasses noted were less than 0.5 m across. The trailing edges of echoes are of particular interest since they represent effects either at the glacier bed, or at greater distances in directions other than vertically down. Tt is unclear whether the secondary lobe seen on most traces is a result of the wavelet emitted by the transmitter, or whether it represents a real feature at ' the glacier bed. A combination of both causes is likely because the lobe is present to varying degrees in vir tually all traces gathered at Trapridge. Model l ing results from chapter 3 (figure 3.6) suggest that a basal layer of debris-rich ice would have to be roughly 5 m thick to produce a secondary reflection 100 ns after the primary echo. It would also have to contain at least 40% rock by volume for the trail ing echo to be as big as those observed. These values are possible but tend to be near the extremes of those observed under stagnant ice below Trapridge Glacier's current terminus (Maxwell , 1986). Some trailing-edge effects may simply represent energy that has arrived indirectly at the reflector, possibly as a result of multiple echoing within complex structures of the glacier. Records from the icefall may be demonstrating these effects. The trail ing edges of the records from near the terminus are more intriguing. The echoes themselves have stronger amplitudes, and the appearance of multiple echoes at twice the travel time of bot tom echoes suggests that here, the bed is a stronger reflector J I I I I 1 1 1 L 0 600 800 536000 200 East ing D is tance - UTM Coo rd i na tes (i.e. m ) Figure 6.3 Cross-section of Trapridge glacier derived from the centreline profile. Note that vertical exaggeration is 2:1. Plott ing this as a true east-west line is not strictly correct but is a good approximation in this case; see figure 6.1 for profile orientation. Surface locations (dots) were surveyed in July 1986 and permanent surface markers are noted (some wi th labels) by small lines. Positions of radar soundings are marked with small arrow heads. Bed topography was obtained by plotting circular arcs of echo range taken from figure 6.2 below each sounding site. The envelope of arcs was plotted as bed topography and agrees well with that derived from dril l ing information by Clarke and others (1984). The 1981 positions of two permanent centreline markers (stakes 12C and 2C) are also noted in the figure. - 71 -than higher up the glacier. This is at odds with the temperature data from Clarke and others (1984) which show that downstream from the bulge the glacier is frozen to its bed. However, that paper considers data that were gathered in 1983 and the glacier has evolved substantially since then. Also , the true elevation profile of figure 6.3 suggests that there is a topographic levelling at this location. It is conceivable that there is a tendency for water to collect at this location, resulting in stronger reflections of electromagnetic energy. Focussing of echo energy by large-scale topographic features may contribute to these bottom echo characteristics. Harrison (1970) discusses how two closely spaced returns are possible if topography is such that energy will return to the source location from two sides of a concavity. Applicat ion of migration algorithms designed for solving the analogous problem in seismology would help determine whether such effects are occurring, but the current data do not warrant the application of such complicated procedures. Unfortunately, no other work was done in this region during the 1986 field season, partly because it has become more crevassed in recent years. These crevasses may indeed be the cause of the complexity of the echoes, but if this is true, it is curious that there is not more detail between the surface and the bottom echo. 6.3 P R O F I L E S C O I N C I D E N T W I T H D R I L L H O L E S Sounding lines 2, 3 and 4 (figures 6.4, 6.5, 6.6) can be conveniently discussed together. For all of them, aligning in the same way as the centreline profile was less successful, as is evident from the numerous traces which have echoes at depths apparently discontinuous relative to their neighbours. The reason for this inconsistency is uncertain, although it should be pointed out that all the records except the first 17 of the long section (figure 6.4) are much noisier than sections taken at earlier dates (the centreline and close-spaced profile). This noise is not altogether random, indicating that the instrument itself may cr CD CD CD 3 o 3 CL. I - -<<• S CD o ^ o 3> CD O a CD rs O 3 3 CD n CD w CD P to cr " -i 3^  CD ^ o 3 £ ^ 1 3 O 3^  CD w 3 cr o -( E. 5" OP ro on C/i <r+ ft) 3 CD p cr 3 " I <: CD CD 1/1 CD CD *~ 00 t-i 3 CD ^ 3 o • 3 - 2! pj o 3 £ CD >-( C- 37 2. OP = 3 3" CD I" °> S to Dep th ( m - M O O ) b b rO b o b o-• o 5 ZL o Q _ 73 tn O o CD O-r-o o b b ro O O b 2 Woy Trave l T i m e (/xs) Figure 6.5 for notes. Profile 3, parallel to and north of the centreline. See figure 6.4 Figure 6.6 6.4 for notes. Profile 4, the shorter, eastern transverse survey line. See figure be at, fault. Whatever the cause, it appears to be intermittent since the three-day data set (discussed in section 6.5) is neither as noisy nor as poorly aligned. Glacier features along these lines should be noted next. The southern end of both transverse lines is bounded by a series of large crevasses, associated with a topographic rise. Also there is known to be a medial moraine running perpendicular to these two profiles, located roughly between 100 and 130m of the long profile and between 37 and 70 m of the shorter profile. Note the anomalous dril l ing depths in profile 2 around 120m, which probably indicate the presence of morainal material in the path of the dr i l l . It should also be noted that the dri l l ing equipment consisting of propane bottles, pumps, hoses, equipment cases etc. was at the intersection of the centreline and profile 2. Finally, surface conditions were extremely wet over the first 100 m of the long profile, but virtually dry and clear of snow for the rest of these three profiles. Before looking at the most striking features of these profiles, it is worth noting that the trai l ing edges of most echoes do not exhibit secondary pulses as prominently as the centreline records. Also, at the points where profile lines cross each other, the echoes are similar in character, so it is probably safe to say that whatever causes the secondary lobes on the centreline is generally less evident across the width of the glacier under the dri l l ing lines. There are notable exeptions, however. In all three profiles, secondary echoes appear in the vicinities of anomalous recordings. One is around the zone of buried morainal material , and another is located roughly 80 m further north. No mechanism for causing such dramatic effects on radar signals has been found, but there are a few ideas worth considering. Chapter 2 discussed how a thin layer of contrasting intrinsic impedance wi l l prefer-entially reflect frequencies for which the layer thickness is an odd multiple of a quarter wavelength. The fact that ringing echoes are possible from such a layer has been dis-cussed by Smith and Evans (1972), and figure 6.7 models the effect using the scheme - 70 explained in chapter 3. This is for a water layer bounded on both sides by ice, for exam-ple a water-filled crevasse. Such an effect could not occur at the glacier bed, however. It was noted in chapter 3 that thin "Weertman films" are not detectable wi th these radar techniques, and a thick basal water layer wi l l not ring for the same reasons: attenuation in water is too great and the reflectivity of a water/glacier bed interface is too small. The observed anomalous records are therefore unlikely to be caused by water layers, especially those records that start ringing near the surface. WATER FILLED C R E V A S S E S ; T H I C K N E S S = X _ 4 _ 0 1 1 1 1 1 1 1 1 1  - 6 . 0 0 E - 0 7 0 . 0 6 . 0 0 E - 0 7 D E L A Y TIME A E T E R EIRST R E T U R N ( S E C . ) Figure 6.7 Model l ing as per the methods of chapter 3 using the same input wavelet as figure 3.6. Ice parameters: Oi = 3 X 10~ 5 S m _ I , t.t — 3.18. Water parameters: ow = 0.01 S m _ 1 (appropriate for subglacial water but not for surface melt) , cw = 81. Jacobel and Raymond (1984) suggest that ringing records observed on Variegated Glacier , Alaska, are caused by voids within the glacier. This explanation is less likely on Trapridge because it is cold throughout at this location. Furthermore, the theoretical work of Watts and England (1976) shows that the scattering efficiency of spheres is very small for radii less than 0.1A. If the frequency is around 8 M H z , spheres at least 4 m in - 77 -diameter would be required, and lower frequencies would require sti l l larger scattering targets. Such large water-filled voids are unlikely to exist wi thin a cold glacier. Some of the records that have noisy rather than ringing characteristics are probably affected by morainal material; this is likely for traces between 110 and 140m of profile 2 and for traces between 30 and 70m of profile 4. These sti l l have unexplained pulses following the bottom echo which are similar to a feature on the short, close-spacing survey presented next. Another possibility is that wiring on top of or within the glacier may be causing some effects. However, there is no consistency when comparing records that have been made near known emplacements of long wires. Crevasses may explain minor noise-like features on some records near the extremities of the profiles, but there are none near the northern ends of the surveys. Final ly , it is intriguing to note that the confused records at the north end of profile 2 (also evident on profile 3 at the point where these two lines cross) are in the same location as those dri l l holes that first revealed hydraulic connections to the glacier bed. No connections were found in any earlier holes, while most holes drilled after the first connections did in fact connect. Therefore the feature near the center of profile 2 had no associated connection, and there were connections over parts of profiles 3 and 4 that show no extraordinary characteristics. In addition, it is hard to see how features associated with the glacier bed could cause ringing or noisy signals at shorter delay times than those of the bot tom echo. The most important conclusion to be drawn from these three surveys is that more extensive coverage is required if anomalous echoes are to be better understood. Sound-ings must be taken at very dense spacing, two-dimensional coverage is required, and soundings with various antenna orientations should be made to distinguish features that may respond to different polarizations of incident electromagnetic waves. - 78 -6.4 P R O F I L E W I T H C L O S E L Y S P A C E D S O U N D I N G S The profile made with soundings taken at 1 m intervals (figure 6.8) provides a number of possibilities for interesting glaciological interpretations. Two features become prominent after alignment with respect to the bottom echo (valid since depths along this line, determined from dril l ing data, were all 71.5 ± 0.5 m). The first feature, at the southern end, is a secondary pulse following the bottom echo. The second is the emergence of an englacial echo that becomes closer to the surface wave towards the northern end. This feature wi l l be considered first since it can in principle be used as a reference when analyzing other signal features. 6.4-1 Englacial Reflector: Location and Reflectivity The range to the internal reflector is found from figure 6.8 to be 53 m for trace 40 and 35 m for trace 60. Since these traces were recorded 21 m apart and the echo range changes by only 18 m, a line reflector causing this echo would lie at an angle of sin 1 (18/21) or 59° off the survey line. Photographs of the region show that there is a crevasse in roughly this orientation nearby. The result is further supported by comparing the internal echo amplitude of trace 50 with those of the records from the three-day continuous survey. This point is clarified in section 6.4.3. Note that a single reflecting body is an unlikely cause for such a reflection for the reasons explained in the previous section. The reflection coefficient of an ice/air boundary is R — 0.28 from table 2.2. What happens to this coefficient if the reflector is in fact a thin air-filled crevasse? Equation 2.10 can be solved using the following parameters: r\i = 211; na = 377; pia — 0.28; pai — - 0.28; Tia = 1.28; and r a t = 0.72 . The propagation constant is 7 = a + jj3; a « 0 in air and {3 — OJ/V — 0.168 at 8 M H z in air. Solving equation 2.10 for crevasse thicknesses of 0 .5m < x < 1.5m yields reflectivities of (0.057/ - 41°) < pt < (0.127/ - 59°) or — 24 .9dB < \p\\ < —17.9dB. Thus the magnitude of the reflection coefficient is significantly less than for an interface wi th an infinite half plane of air, and the phase Figure 6.8 Profile 5, the close-spacing survey. Notes are as per figure 6.4. Note that these records have been aligned with respect to the bottom echo. Refer to the text for discussion. - 80 -of the echo wil l have been shifted. Ac tua l echoes are too small to accurately reveal this phase shift, but it wil l be shown in section 6.4.3 that such reflectivities are consistent wi th echoes known to originate from a crevasse. It is worth noting in passing that detection of crevasses in this way might help make surface travel over dangerously crevassed terrain safer. Radar frequencies may even be chosen to emphasize crevasses within a certain size range. 6.4-2 Estimation of Attenuation Constant The amplitude of an echo a can be expressed in terms of its range r, the attenuation constant of the medium a, and the reflection coefficient p, by an equation similar to equation 2.5: o = (Kpe~aT^ jr in which K contains all the information regarding trans-mission power and system performance. If two echoes from the same target are recorded at different ranges and the ratio of their amplitudes is taken, the common factors K and p wi l l cancel leaving an expression with the attenuation constant as the only unknown. Tha t is: a-2 rye a r -Arnplitudes a, were found with the aid of figure 6.9a which plots the maximum peak-to-peak amplitude found in given time windows for each trace. The figure caption explains minor processing that was required. Ranges were read from figure 6.8 and then equation 6.1 was solved for pairs of traces chosen to ensure that amplitudes were not contaminated by either the bottom echo or the surface wave signal. As might be expected from the variability of echo amplitudes seen in figure 6.9, the derived a's were also highly variable. The average a over 15 trials was a = 0.0064 wi th a standard deviation of s = 0.0057. This is significantly higher than the expected attenuation constant of about 0.003. The relations following equation 2.5 were used for this estimate, wi th the assumption that the average temperature of Trapridge Glacier 's upper 2 0 m is about - 81 -! 5 0 2 0 0 A) MAX. P - P AM P L . WITHIN C H O O S E N TIME WINDOW a a ' 5 0 < L d ^ 1 0 0 U J 5 0 0 V , B A S A L E C H O : WIND0W = 0 . 7 - 1 . 3 / z S E N G L A C . E C H O : WIND0W = 0 . 4 - 0 . 7 5 /xS J 1 1 I I L 0 1 0 2 0 3 0 4 0 T R A C E N U M B E R 5 0 6 0 B) S O U D = 1 S T MULT. ; D A S H = MOISE L E V E L 4 0 3 5 3 0 a t— • CL 2 5 < 2 0 UJ > :LATI 1 5 U1_J or 1 0 5 SOLID: WIMDOW= 1 . 6 - 1 . 9 0 /xS i i /A A D A S H : WINDOW = 3 . 3 - 3 . 8 /J.S / M "\ / V \ a „ V / \ 0 1 0 2 0 3 0 J-0 T R A C E N U M B E R 5 0 b11 Figure 6.9 Ampl i tude plots of close-spaced profile. Basal echo: the maxi-m u m peak-to-peak amplitude was found within the time window shown and plot-ted for each trace. A l l others: The linear trend over al l points wi th in the window was found using least squares regression over all points within the window. This trend was removed and the maximum peak-to-peak amplitude then found within the window. In all cases, amplitude units are relative to the maximum dynamic range of the digit izing receiver which is 256; the analogue-to-digital converter currently has a resolution of 8 bits. Conversion to volts at the antenna depends on the gain setting at the time of recording. - 82 -6 ° C . Travel times are great enough to ensure that echoes are not air-path arrivals, so the signals have been acted upon only by features within the ice, or by the effect of travelling very near the ice/air boundary. We must therefore consider which of the assumptions inherent in equation 6.1 have been violated. Fi rs t , propagation is in a non-uniform medium, i.e. is parallel to a surface. A n n a n (1973) considers such a geometry; for distances of more than a wavelength, surface effects are expected to be small . Perhaps more important, the reflector is not an infinite plane. The situation is more like a diffraction problem with energy incident on a line diffractor (the crevasse l ip) . Alternatively, we could consider diffraction from a wedge-shaped body with the ice/air/crevasse corner as the apex, and the energy at grazing incidence along one side of the wedge. Narod and Yedlin (1986) discuss a similar acoustic problem, from which it is evident that both geometrical optics and diffracted wave fields would have to be considered. In the present case, complications due to normal incidence would also have to be included. This is by no means t r iv ia l and is beyond the scope of this thesis. Suffice it to say that solving equation 6.1 assuming only a diffracted wave field ( implying geometrical losses proportional to l / r 3 / 2 rather than l / r ) results in very small attenuation constants, so use of the complete solution is likely to yield answers that are less than the a found above. In other words, we should expect signals returning from such a reflector to be smaller and to decay faster than echoes from an ideal plane reflector. Such behavior would imply a smaller attenuation constant, as predicted above simply from the physical properties of ice. The true attenuation constant can be confirmed only by more detailed consideration of the theory, and through controlled experiments in the field. Reduction of the variabili ty by stacking would also help, a point considered again at the end of this chapter. - 83 -6.4-3 Basal Reflection Coefficient If the internal echo originates from a known reflector, the basal reflection coefficient can be estimated. A ratio can be taken as above using the appropriate values for amplitude, range and attenuation: a. The °''T'piG2 ah Tie °"-ri-pi, where the subscripts i and b denote internal and basal reflector parameters. G accounts for the directionality of the antennas and must be included if the signal path is not perpendicular to the antenna array. It is related to the angle 6, between the signal path and the normal to the antenna in a manner dependent on the type of antenna. From Jordan and Balrnain (1968, section 11.03), COS(r, C O S 0 ) G = 1 2 ' (6.3) sin 0 for a half wave dipole and G = sin 0 for an elemental dipole. For a damped halfwave dipole, the value of G is likely to be between these two, probably closer to the elemental dipole. This factor affects both transmitt ing and receiving antennas, so the recorded echo strength wi l l be reduced by a factor of G2. In our case, the remaining parameters of equation 6.2 are as follows. The two-way travel distances are taken from figure 6.8; the attenuation constants are ab = 0.004 (assuming an average temperature throughout the glacier of —3°C) and a , = 0.003 (average temperature in the glacier's upper 2 0 m is about —6°C); G = 0.805 assuming 0 — 59° as above (the half-wave dipole formula gives this conservative estimate); the two amplitudes ah and ac are found as described in figure 6.9a; and the magnitude of pi for a i m wide crevasse is \pi\ = 0.09 (—20.1dB). Equation 6.2 was then solved with these parameters for traces 40 through 60 to yield an average basal reflectivity of p~b = 0.42 - M •-( —7.5dB) wi th a standard deviation of »s — 0.05. The result is most, sensitive to G and pi but expected variations of these two parameters can be somewhat constrained. Photographs of the area show that the survey line and crevasse are oriented about 60° to each other. Also , the englacial echo amplitude from trace 50 is approximately four-fifths of that for the same echo from the three-day data set (discussed later) which was recorded at the same location with antennas parallel to the crevasse. This implies a directionality factor G = y/4~/5 = 0.89 which corresponds to an angle between reflector and antennas of about 65° (depending somewhat on whether a half-wave dipole or an elemental dipole is assumed when calculating G). Concerning p t , photographs of the area show that the near by crevasse is indeed about 1 m wide. It should be reiterated here that this average basal reflectivity was found under the same assumptions concerning propagation and reflector geometry as described in section 6.3.2. In fact, the crevasse echo can be expected to decay faster than assumed by equation 6.2, resulting in smaller basal reflectivities than predicted here. On the other hand, equation 6.2 also assumes a specular basal reflector. If the same data were used wi th a model including more realistic glacier beds, higher basal reflectivities would be predicted. These two effects may work towards cancelling each other, but unti l the complete relations are incorporated, the estimates above wil l be used to make tentative glaciological interpretations. These considerations suggest that the glacier bed reflectivity is likely to be around 0.3 to 0.4 ( - 1 0 d B to - 8 d B ) . Table 2.2 shows that this is greater than that of a solid rock glacier bed and less than that of water layers that are thicker than a few millimetres. Porous materials with conductive interstitial water have reflectivities comparable to this result, and so do very thin water layers, or Weertman films. Whatever the bed is, it is probably uniform except for localized anomalies since most profiles have similar echo strengths. A Weertman film requires an impermeable bed (Drewry, 1986) and evidence - 85 -from temperature, dri l l ing, pressure, and other hydrological investigations (Clarke and others, 1984; Clarke and others, 1986; Maxwe l l , 1986; Smart, personal communication) argue strongly against the widespread presence of a Weertman film under Trapridge Glacier . The conclusion then is that the radar data suggest a glacier bed with porosity in the range of 10% to 25% if water conductivity is conservatively estimated at around 1 0 0 / x S c m - 1 . The same reflectivity could occur for lower porosities if water conductivity is higher. 6.4-4 Multiples and Secondary Bottom Echoes Similar ratio calculations can be carried out using amplitudes of multiple arrivals and bot tom echoes. The ratio in this case is * - - * f l _ (6.3) am e oZrpaPb where the 2's occur because the range for the multiple is twice that of the bottom echo; PaPb is required since the multiple is reflected from the ice/air boundary once and from the bottom twice; and at, and am are amplitudes of the bot tom echo and multiple. Surface propagation and diffraction effects are of little concern in this case. Solving for the unknown gives pi = 12.6(a m/af,) when the depth is 71 m, a = 0.004, and pa = 0.28 from table 2.2. For traces at the eastern end, figure 6.9a shows « 180 so that pt, « 0.42 ( - 7 . 5 d B ) if a2 ~ 6 is used. This is justified by figure 6.9b which plots the noise level at large time delays, as well as the maximum amplitudes of traces in the time window where bottom multiples are expected. (They are in fact faintly observed at around 1.7/zs in figure 6.8.) Removal of the noise level leaves am « 6 in the region of traces 30 to 60. The value of pt, found in this way reinforces the tentative conclusion that the glacier bed has a relatively high reflectivity. - 8(:i -The remaining prominent features are the strong secondary pulses following the bot-tom echo and the correspondingly strong multiples of these pulses. These are at the western end and correlate well with similar features of profile 2. They also appear to fade after the anomalous trace 21. No explanation has been found for such a trace when the soundings were only 1 m apart so, for the present, it must be counted as an error. The remaining features are too consistent to be dismissed, but they remain unex-plained. Using equation 6 .3, a basal reflection coefficient of pi, — 12.6(am/af,) would give pb = 12.6(15/200) = 0.95. This implies an almost perfect reflector which is physically rather unlikely. Some form of constructive interference might be occurring, but there are insufficient data to speculate further. Figure 6.7 may shed light on the thickness of an ice enclosed, water-filled void that can produce ringing echoes, but such a void would have to resemble a crevasse in size (as argued in chapter 5), and no explanation has been found for the extraordinary strength of the multiples. The possibility of a cavity having been observed is tantalizing but is not supported by results from the dri l l ing program (as yet unpublished). F ina l ly , the filtering experiments described in chapter 3 suggest that a thick layer of debris-rich ice could probably not cause such bottom echoes because the reflection coefficients of ice/rock mixtures are not high enough. More extensive surveys, as noted in the conclusions of section 6 .3, are needed to further elucidate the features observed here, which were assumed to be associated with the connected hole of 1985. 6.5 T H R E E - D A Y D A T A S E T The set of records shown in figure 6.10 were recorded at 20-minute intervals over a period of three days at the same location as trace 50 of the close-spaced survey. Simultaneous recordings of pressure at the glacier bed were made in a manner similar to that reported by Clarke and others (1986), and the intention was to compare these data. Unfortu-nately, the 1986 pressure data are st i l l unobtainable owing to technical problems with - 87 -Figure 6.10 Complete set of raw data collected automatically over three days at dr i l l hole number 28 (see figure 6.1). Increased transmitter triggering delays are observed during cooler periods (see figure 6.11 for times). Towards the end, temperatures dropped steadily during the onset of a storm. One calibration record is visible in the first half of the set, and noisy records in the center are caused by tape reading or wri t ing errors. the appropriate cassette reader. Temporal variations in bed reflectivity can therefore be analyzed only qualitatively in light of hydrology data that were gathered downstream of Trapridge Glacier's terminus and the known concurrent meteorology. The effects of cold temperatures are immediately evident in figure 6.10; triggering of the S C R s was delayed by the cold and in extreme cold (during the onset of a storm on the last day of recording), triggering became erratic so that each pulse was different and the sampling timebase receiver produced useless records. The unreliability of our cassette recorder for this k ind of field application was also made clear. Twice during automatic operation, the system encountered uncorrectable read and/or write errors which left it unable to - 88 -proceed. Jt was restarted when found at the time cassettes were to be changed. This accounts for the gaps in time noted in figure 6.11, which displays the useful data after alignment with respect to the bottom echo. Features immediately evident on this temporal section are as follows. A n occasional noisy trace appears for unknown reasons; those that are unusable have been replaced with blanks. The secondary pulse following the bottom echo is present as in most sections recorded at Trapridge, but it appears to vary in size across the section. The same can be said for the englacial echo, the amplitude of which was used in the previous section. F ina l ly , there is a hint of multiple echoes between 1.5 and 2.0 /xs, also with somewhat variable amplitude. Ampl i tude variations are displayed most conveniently in the plots of figure 6.12. Also shown is a normalized set of amplitudes constructed by dividing the bottom echo ampli-tude by the englacial echo amplitude. This ratio effectively removes signal components that are common to both signals. Evidently, the diurnal variations in basal echo ampli-tude are not related to changes in bed reflectivity because the englacial echo is affected to an almost identical degree. Any visible change in reflectivity caused by pressure or other hydrological events ought to be seen in this ratio plot since instrument and climatological effects should have been removed. Another potentially interesting parameter is the average power level displayed in figure 6.12b. If the excessively noisy traces are ignored (blanks in this plot) there does seem to be a reduction in noise level arriving from sources at greater ranges than the depth. This may be a result of reduced englacial water content, possibly owing to the cooling trend in the weather, or perhaps to the draining of subglacial storage cavities. Such an event would lower the basal water pressure with a resulting decrease in the water table; the degree of interconnection amongst englacial water channels would determine the rate at which this level would drop. Speculative as these ideas are, it is intriguing 1 July 24 11:50 It t July 24 July 25 21:10 00:20 12:30 I 19:08 R e c o r d s o i 2 0 m m In te rvo l s E x c e p t o s N o t e d Figure 6.11 Usable records from figure 6.10 with noisy records zeroed and alignment earned out wj th respect to the leading edge of the bottom echo. Travel-time scale was set using dri l l ing data to obtain depth at this site. - 90 -> A) S E E F I G U R E C A P T I O N FOR E X P L A N A T I O N 120 1 0 0 0 4 0 8 0 T R A C E N U M B E R 1 2 0 B) SQRT OF AV. P W R : WIND0W= 1.1 5 - 1 .5 /US 0 4 0 8 0 T R A C E N U M B E R 1 2 0 Figure 6.12 Ampl i tude plots found as per figure 6.9. Note that traces were recorded 20 minutes apart except for discontinuities noted in figure 6.11. (A) Three peak-to-peak amplitude plots. Basal echo amplitude, a 0 , is uppermost and englacial echo amplitude, ae, is in the middle. A t the bot tom is plotted (a.(,/ae) x 10; mult ipl icat ion by 10 is for plot t ing purposes only. (B) Linear trend over the window was removed (see caption of figure 6.9) and average remaining power wi th in the window was found. Square root of the result was taken to improve plot appearance. - 91 -to note that a drainage event was recorded in the early morning of July 25, both by a water level pulse at the downstream staging recorder and by an anomalous increase in streamwater conductivity (C. Smart, pers. comm., 1986). Pr incipal component decomposition was used to try enhancing subtle variations in this section. Figure 6.13 shows various types of misfit reconstructions which exhibit the following characteristics. Most large-scale variations (or variations in the more com-mon components) apparently occur in the echo amplitude and in the shape of the pulse following the bottom echo (figures 6.13c, 6.13f, and 6.13g). Small-scale variations are emphasized by reconstruction with lower order principal components, and appear to oc-cur at the leading and trailing edges of the main echo ( figures 6.13d, and 6.13e). In most cases, there is little suggestion of variations other than those related to the diurnal changes already discussed. Reconstruction with principal components 3, 4 and 5 (figures 6.13f and 6.13g) have the best potential in this case, showing signal inversions between traces 14 to 24, and 60 to 71. These correspond very well to the periods of falling echo amplitude and probably do not indicate anything more than what can be deduced from the amplitude plots of figure 6.12. A final observation concerns the unexpected variability of signal character. Traces recorded only 20 minutes apart at the same location were expected to be more similar. Improvements might best be obtained by gathering more records at each location and stacking them. If noise is truly random, then the observed signal-to-noise ratio can be improved by a factor of y/n with an n fold stack. W i t h the current system, this would not be difficult, providing that a higher capacity high voltage supply could be obtained for the transmitter, and a faster, more reliable digital storage medium could be obtained to replace the cassettes. In conclusion, it should be noted that, in spite of being able to draw only tentative glaciological conclusions from this experiment, it is the first known set of data recorded - 92 -ECHO ONI Y P C ' S 2 - 3 P C ' S 4 - 6 P C ' S 7-111 P C ' S 3 -4 P C ' S 3 " 5 \ I I I \ 1 1 1 \ I i I I * [.+H-HH"J I \ 1 h - H 1 > t H H < J M A) C) D) E) F) G) MEAN S T P C K Figure 6.13 Results of reconstruction wi th principal compo-nents derived from traces 11 to 109 of figure 6.11. (A) The raw data; bottom echo only. (B) Mean stack across all 99 traces. (C) to (G) Reconstruction using only those principal components that are noted above each figure. - <):s -automatically over an extended time period. Readings taken at 20-minute intervals show distinct diurnal variations assumed to be caused by ambient temperature affecting S C R trigger t iming and switching speed. The problems encountered are not insurmountable, and temporal radar data of this type may prove to be useful when taken in conjunction wi th other glaciological and hydrological data. - 9.1 -C H A P T E R VII S U M M A R Y j have addressed theoretical and practical considerations concerning the application of impulse radar echo sounding to the geophysical investigation of glaciers. Theoretical dis-cussion was begun by noting the wide range of values possible for electrical parameters of glacier materials. Table 2.1 summarizes these, and table 2.2 gives representative re-flection coefficients for several possible reflectors of electromagnetic waves. Evidently, it should be possible to determine the type of glacier bed from the echoes, but in practice, exact reflectivities are not easily obtained. The modelling experiments discussed in chap-ter 3 suggest that finer structure of the glacier bed may be resolvable, but again, only large variations in physical features are likely to be noticeble in changes of echo character. Appl ica t ion of digital signal processing techniques such as the Karhunen-Loeve transform may help separate the finer structure from large-scale signal features, but some care is required in applying and interpreting such methods. The U B C impulse radar instrument was found to operate satisfactorily, given that it is a prototype. The major requirement is for a triggerable transmitter that is stable and temperature-compensated. A n alternative and perhaps more practical solution to the t iming problem would be to generate a signal at the transmitter to inform the receiver of the exact time of pulse emission. A further important hardware modification would replace the cassette with a more robust memory, perhaps solid-state random access mem-ory. Also , portable computers are being considered for control and data manipulation in the field. The automatic data collecting facility has great potential for temporal studies - 05 -of glacier dynamics, and if the current system can be speeded up, wi l l also help make depth profiling more efficient. Interpretation of impulse radar data is greatly facilitated by including reference sig-nals in the records. Quantitative analysis tends to be unreliable without having some known response with which to compare interesting signals. Future work may involve the use of fixed radar reflectors in the air or perhaps down crevasses, to be used as t iming and amplitude references. The field work presented also emphasizes the difficulties of interpreting sparse data. This is a common problem throughout geophysics, and until the advent of lightweight digital technology, particularly evident in radio echo sounding of small glaciers. Instruments such as the one described in this thesis, especially if they can gather reliable data at high rates, wi l l certainly help alleviate this problem. Signals that have interacted with the ice/air interface were shown to be difficult to use. Neverthless, I employed echoes from a crevasse to help conclude that bottom echo amplitudes suggest a wet, porous glacier bed. Some anomalous features were discussed, but not adequately explained. Subglacial cavities capable of draining dr i l l holes were perhaps observed, but this is st i l l only speculative. Future work wi th the U B C impulse radar wi l l involve gathering concurrent geophysical and hydrological data for comparative studies of these and other features. Final ly , it should be noted that the high quality of the 1986 data is partly due to successful operation of the equipment, but that local conditions were also an important factor. 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R . 1981, Time Sequence Analysis in Geophysics, The University of A l -berta Press, Edmonton, Canada, 480p. Kel le r , G . V . 1967, Applications of Resistivity Methods in Mining and Groundwater Ex-ploration Programs, In M i n i n g and Groundwater Geophysics, 1967, Proceedings of the Canadian Centennial Conference on M i n i n g and Groundwater Geophysics, N ia -gara Falls, Canada, 1967, E d . L . W . M o r e y . M a x w e l l , M . 1986, Basai Processes in Surging Glaciers, Unpub. P h D . Thesis, University of Br i t i sh Columbia . - 98 -Morey, R . M . 1974, Continuous Subsurface Profiling by Impulse Radar, Proceedings of Engineering Foundation Conference on Subsurface Explorat ion for Underground E x -cavation and Heavy Construction, Aug . 11-16 1974, Henniker New Hampshire. New York : American Society of C i v i l Engineers, p. 213. Morey, R . M . and Kovacs, A . 1985, Analysis of Wide-Angle Reflecton and Refraction Measurements, U.S. Cold Regions Research and Engineering Laboratory, C R R E L Special Report 85-5, Workshop on Permafrost Geophysics, Golden, Colorado, 23-24 Oct 1984, Editors: J .Brown, M . C . M e t z , P.Iloekstra. Narod , B . B . and Clarke, G . K . C . 1983, UHF Radar System for Airborne Surveys of Ice Thickness, Can . J . Earth Sci. 20, No . 7 , 1073-1086. Narod , B . B . and Yedl in , M . J . 1986, A Basic Acoustic Diffraction Experiment For Demon-strating the Geometrical Theory of Diffraction, A m . J . Phys. 54, No.12, 1121-1126. Olhoeft, G . R . 1978a, Electrical Properties of Permafrost, Proceedings of the T h i r d Inter-national Conference on Permafrost, July 10-13, 1978, Edmonton, Alber ta , Canada, V o l . 1, p.128. Oswald, G . K . A . 1975, Investigation of Sub-ice Bedrock Characteristics by Radio-Echo Sounding, Journal of Glaciology, 15, No.73, 75-88. Paren, J . G . 1970, Dielectric Properties of Ice, Unpub. P h D . Thesis, University of C a m -bridge. Post, A . and LaChapel le , E . R . 1971, Glacier Ice, University of Toronto Press, Toronto, Canada , 178p. Prager, B . T . 1983, Digital Signal Processing of UHF. Radio-echo Sounding Data from Northern Ellesmere Island, Unpub. M S c . Thesis, University of Br i t i sh Columbia , 88 pages. R C A Corporat ion. 1977, User Manual for the CDP1802 COSMAC Microprocessor. R C A Solid State, U S A . R o b i n , G . deQ. Evans, S. and Bailey, J .T . 1969, Interpretation of Radio-echo Sounding in Polar Ice Sheets, Philosophical Transactions of the Royal Society, Series A , 265, 437-505. Rose, G . C . and Vickers, R .S . 1974, Calculated and Experimental Response of Resistively Loaded V Antennas to Impulsive Exitation, Int. J . Electronics, 37 261-271. St. Amant , M . and Strangway, D . W . 1970, Dielectric Properties of Dry, Geologic Mate-rials, Geophysics 35, N o . 4, 624-645 Sellman, P . V . Arcone, S .A. and Delaney, A . J . 1983, Radar Profiling of Buried Reflectors and the Groundwater Table, U . S . Cold Regions Research and Engineering Labora-tory, C R R E L Report 83-11. Shen, L . C . and K i n g , R . W . P . 1965, Correction to the Cylindrical Antenna with Nonre-Hecting Resistive Loading by Wu and King, I E E E Trans, on Antennas and Propa-gation, A P - 1 3 , No .6 , p.998. - 99 -Sheriff, R . E . and Geldart, L . P . 1982, Exploration Seismology, Vol.1; History, Theory and Data Aquisition, Cambridge University Press, Cambridge, U . K . 253p. Smi th , B . M . 1971, Radio Echo Studies of Glaciers, Unpub. P h D . Thesis, University of Cambridge Smi th , B . M . and Evans, S. 1972, Radio Echo Sounding: Absorption and Scattering by Water Inclusions and Ice Lenses, Journal of Glaciology, 11, No .61 133-146. Sverisson, M . Johannesson, JE. and Bjornsson, H . 1980, Radio-echo Equipment for Depth Sounding of Temperate Glaciers, . Journal of Glaciology, 25, No .93, 477-486. Ulr iksen, C . P . F . 1982, Application of Impulse Radar to Civil Engineering, Unpub. P h D Thesis, L u n d University of Technology Walford, M . E . R . and Harper, M . F . L . 1981, The Detailed Study of Glacier Beds Using Radio Echo Sounding Techniques, Geophys. J . R . As t r . Soc. 67 485-514. Walford, M . E . R . Kennett , M . I . and Holmlund, P. 1986, Interpretation of Radio Echoes From Storglaciaren, Northern Sweden, Journal of Glaciology, 32, No.110, 39-49. Watts, R . D . and England, A . E . 1976, Radio-echo Sounding of Temperate Glaciers: Ice Properties and Sounder Design Criteria, Journal of Glaciology, 17, No.75, 39-48. Watts, R . D . and Wright, D . L . 1981, Systems for Measuring Thickness of Temperate and Polar Ice from the Ground or from the Air, Journal of Glaciology, 27, No .97, p.459-469. Wong, J . Rossiter, J .R . Olhoeft, G . R . and Strangway, D . W . 1977, Permafrost: Electrical Properties of the Active Layer Measured in situ, Can . J . Ear th Sci . 14, p.582. W u , T . T . and K i n g , R . W . P . 1965, The Cylindrical Antenna With NonreBecting Resistive Loading I E E E Trans, on Antennas and Propagation, A P - 1 3 , No.3 , 369-373. - 100 -System Depth precision Maximum depth Data storage Time to gather one record Time to store one record Automatic data collection Weights (no batteries) Transmitter Peak pulse output Pulse rise time Pulse recovery Repetition rate Internal triggering delay Power requirments Antennas A P P E N D I X 1: Instrument Specifications 0.82 in 841 m 1320 bytes per record 52 records per cassette 4s 40s Programmable — 1 to 255 min intervals receiver unit — 5.1 kg transmitter — 0.4 kg antennas — 1.2 kg eacli 1200 V into antenna 40 ns from 37% to 100% of V,,,^ time constant is approximately 30/is 250 Hz 0.8 (is at 24°C idling — 95 ma at 18 V pulsing at 250Hz — 280ma at 18 V Broadband (resistiveiy damped) halfwave dipole h = 5m 8.4 MHz in ice 15MHz in air Ru = 300 ft Construction: Wire and carbon resistors are installed inside 1 in sections of plastic pipe. Sections can be screwed together to form antennas with required centre frequency and damping characteristics. Type Dipole arm length Centre frequency Damping coefficient Receiver Uni t Input impedance Total voltage gain Attenuator Sensitivity at maximum gain Amplitude resolution Bandwidth Number of samples per record Sampling interval CPU Memory Clock speed Inputs and outputs Power requirements Note: All digital circuits 3.6kft 150 divide by factors of 1, 2, 4, 20 or 100 LSB = 0.26 mV at rcvr. antenna 8 bits 46 MHz 1024 9.76 ns RCA CDP1802 4 kbyte of ROM 1.25 kbyte of RAM 2.0 MHz hex keypad 8 digit LED display oscilloscope driver RS-232C serial interface digital read/write cassette Min. (system idling) — 450ma at 18 V Max. (momentary) — 1800ma at 18 V Gathering data — 960 ma at 18 V use CMOS technology. 3 r • 1200-12F o o o 0 o 0 0 o o 1 c n o - n - n m 1000 10FF 1400 — — H F F 1300 1100 -13FF . z 0 0 c n c n r o o _ 2 o o c n c n r o 4068 -11FF CD a> 0 ,18 5 3 ,4001 <z oo 4001 "TrT ID CO g> o _ C oo O c o c c oo —1 c n c n r o cr O c i C- OO —1 c n c n r o i 4022 o ^ C oo ^0 O So ") • t> i C O GO SI o -1 '.S,\ }.< < f ~J ^ >• I * * 5 -^o -I el ? n * 1 t o , ox I -3 c& - (* m m * -^L £1 i i i J T» i « r- o *A 0 si si n u I a s -J c- < 3 M o r <t -r bOj bl 1 >o, 2>-To jM > r v -v J i J. r "n 2' ?| U i j ? 1 $ 1 ci T vl l/\ *5 « - ^ K * t* * V V V V V Y V Y V •i * •« n 0 V\ £ t£ j V\ - M r- rl - * "> "J V Y V Y V Y W V d •v. 3 §§SS*»*5 I IS |3-»\ U " «• J w * 2 ? !? ! r 5 R fl ^ J (! S ? » S n Y Y Y v VYYY Y a » s. 0. £ ^  c >" A A $ 0 * * « S U 8 6613 * a ; * v t> 0- i "4 I jT '. , > A <l A « r( H Y Y Y Y Y Y Y Y Y » > £ - t 3| 0 N 1 p n r W -T 1 A w n S 5 * 0 a ia § iisi Y Y Y Y Y V Y Y V 4«, : i; c ^ i »i ^ 3 s * 2 a 13 • > M A « »A > f? R P C h h n f « y v v v Y Y Y Y Y 1 5 « a ^ 2l3 £ ^ J s s Q o: K u < A '"9/SW - " " / V v --'•AV -^ • / • / -CM I C4 > CO : B r4 A A A A A A A A H u v | u J u II j -I -* ^ o r - V v — W V — — v w — —'Wv— — W V -A t-ji.' i 'a 7 otf ; „<J - A A A A A A A <. 5 "» L o I "2 E A >100; K <y 7 W »x<r "1 -t) A A A A A A A A ' * * * )1 ^ » » C J- ^ ^  ~ „ -•ro Jo 2?<r an + s * l <a i ~* t 901 oi — — W v -— w H W , A-^ V A — - A A A , — - / V W » I o •/irY" > -A 3: 3 X c 7" o ic? a m if > i — "1 "i 2 H 0 -n Itl 4 T> -1 71 7» H ft »\ 0 •0 m > rn rn > > 75 > 

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