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Ultra high frequency radio echo sounding of glaciers Narod, B. Barry 1975

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ULTRA HIGH FREQUENCY RADIO ECHO SOUNDING OF GLACIERS V by B. Barry Narod B . S c , U n i v e r s i t y of B r i t i s h Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOB THE DEGREE OF MASTER OF SCIENCE i n the Department of Geophysics and Astronomy We accept t h i s t h e s i s as conforming to the r e q u i r e d standard The U n i v e r s i t y of B r i t i s h Columbia A p r i l 1975 In present ing th is thes is in p a r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representa t ives . It is understood that copying or p u b l i c a t i o n of th is thes is fo r f i n a n c i a l gain sha l l not be allowed without my wr i t ten permiss ion. Depa rtment The Un ivers i ty of B r i t i s h Columbia 20 75 Wesbrook Place Vancouver, Canada V6T 1W5 i ABSTRACT For determining the t h i c k n e s s of i c e , r a d i o echo sounding of g l a c i e r s i s w e l l e s t a b l i s h e d as a technigue f o r r a p i d g a t h e ring of data. However i t has become evident t h a t r a d i o echo sounder parameters must be t a i l o r e d to meet s p e c i f i c requirements i n order to achieve best r e s u l t s . In p a r t i c u l a r r a p i d sounding of temperate, a l p i n e g l a c i e r s and l a r g e r p o l a r v a l l e y g l a c i e r s c o u l d be surveyed by a r a d i o echo sounder having a very sho r t p u l s e , very wide land response and narrow beam antenna. Such requirements can be f u l f i l l e d by U l t r a High Frequency (300 MHz - 3 GHz) r a d i o echo sounders, improved performance being achieved at the expense of decreased maximum range. T h i s t h e s i s , a f t e r c o n s i d e r i n g previous attempts a t r a d i o echo sounding of g l a c i e r s , with res p e c t to s u r v e y i n g v a l l e y and temperate g l a c i e r s , proposes and d e t a i l s a UHF r a d i o echo sounder o p e r a t i n g a t 840 MHz. Conventional performance i s p r e d i c t e d , and some new experiments, p o s s i b l e because of the sh o r t wavelength, are proposed. Appended to the t h e s i s i s a review and d i s c u s s i o n of problems a s s o c i a t e d with the use of t h e r m i s t o r s as thermometers i n snow or i c e . A procedure i s d e s c r i b e d f o r o p t i m i z i n g the techniques of t h e r m i s t o r s e l e c t i o n and use. i i TABLE OF CONTENTS Abstract . . . . . . . I L i s t Of Tables Iv L i s t Of Figures V Acknowledgements Vi Chapter 1: Introduction 1 1.1 Background 1 1.2 D i e l e c t r i c Propert ies Of Ice 4 Chapter 2: System Design 6 2.1 General Descr ipt ion . . . 6 2.2 Se lect ion Of The C a r r i e r Frequency 7 2.3 System Performance 8 Range 10 2.4 Antenna Design . . . . . . . . . 1 2 Chapter 3: C i r c u i t Design 15 3.1 Transmitter C i r c u i t 17 3.2 Receiver/pulse Generator C i r c u i t . , .18 3.3 Display And Recorder . . . . . . . . . . . . . . . 2 1 Chapter 4: System C a p a b i l i t i e s . . . 2 5 4.1 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 4.2 Maximum Range And Besolution 26 4.3 R e f l e c t i v i t y o f Layers H i t h i n A Glac i e r . . . . 2 8 4.4 P o l a r i z a t i o n 29 4.5 Conclusion 34 Bibliography 36 Appendix 45 i i i 1 I n t r o d u c t i o n ....46 2 Thermistor C h a r a c t e r i s t i c s , 48 3 Bridges And Bridge Power Supply ......52 4 Transmission Line E f f e c t s .....61 5 Evaluation Of A v a i l a b l e Systems (dmnus) ............62 Conclusion 64 Bi b l i o g r a p h y 67 LIST OF TABLES i v 0 Table 2.1: Radar Parameters .7 Table 2.2: System Performance 10 Table 1: D i g i t a l Multimeters ......63 Table 2: D i g i t a l Multimeter E r r o r s ....64 LIST OF FIGURES Figure 2.1 .. 13 Figure 3.1: Radar Interconnection Diagram .16 Figure 3.2: Transmitter Block Diagram . .....17 Figure 3.3: Receiver Block Diagram 19 Figure 3.4: I n t e n s i t y Modulation Recording Block Diagram .23 Figure 3.5: D i g i t i z e r Block Diagram ....24 Figure 1: Generalized Bridge .............................47 Figure 2: Bridge C o n f i g u r a t i o n s ......54 Figure 3: D i g i t a l Multimeter E r r o r s ...64 v i ACKNOWLEDGEMENTS I wish to thank my s u p e r v i s o r , Dr. Garry C l a r k e , f o r h i s patience and guidance during the course of t h i s work. I would a l s o l i k e t o thank Dr. C l a r k e , Dr. R, B. R u s s e l l , the Department of Geophysics and Astronomy, and the Department of Physics f o r f i n a n c i a l support I r e c e i v e d while I was completing t h i s t h e s i s . I am very g r a t e f u l to Dr. Ron Goodman of Calgary f o r h i s i n v a l u a b l e a s s i s t a n c e and advi c e while development of the r a d i o echo sounder progressed. I wish t o acknowledge the s e r v i c e s of the U n i v e r s i t y ' s Computing Center, which supported t h i s t y p e s c r i p t ; and the numerous manufacturers who p a r t i c i p a t e d i n the development of the r a d i o echo sounder. I thank the Department of Geophysics and Astronomy f o r p r o v i d i n g l a b o r a t o r y f a c i l i t i e s f o r t h i s p r o j e c t . I thank a l l of my f r i e n d s among the f a c u l t y , s t a f f and students of the Department, e s p e c i a l l y Mr. Peter Michelow, f o r a l l t h e i r c o n t r i b u t i o n s to t h i s p r o j e c t . F i n a l l y , and e s p e c i a l l y , I wish to thank the N a t i o n a l Research C o u n c i l of Canada which f i n a n c e d the development of both the UHF r a d i o echo sounder and the t h e r m i s t o r r e s i s t a n c e bridge. The r a d i o echo sounder was fi n a n c e d by grant A3479 from the N a t i o n a l Research C o u n c i l to Dr. C l a r k e . The r e s i s t a n c e bridge was f i n a n c e d by grant A4327 from the v i i N a t i o n a l Research C o u n c i l c f Canada a l s o to Dr. C l a r k e . 1 CHAPTER 1 : INTRODUCTION 1.1 BACKGROUND Radio echo sounding of i c e was " s u c c e s s f u l " as e a r l y as 1946 when a i r c r a f t p i l o t s using pulsed radar a l t i m e t e r s ever A n t a r c t i c i c e r e p o r t e d p o s s i b l e f a t a l e r r o r s i n radar i n t e r p r e t a t i o n . In 1955 440 MHz pulsed radar a l t i m e t e r s attempted the f i r s t i n t e n t i o n a l v e r t i c a l t r a n s m i s s i o n through i c e on the 800 f t . t h i c k Ross Ice S h e l f . A l a c k of r e s u l t s induced attempts i n 1958 to probe 500 f t . t h i c k i c e at Wilkes S t a t i o n . Strong echoes combined with s e i s m i c i n f o r m a t i o n provided i n f o r m a t i o n about the propagation v e l o c i t y of el e c t r o m a g n e t i c r a d i a t i o n i n i c e . Further work i n Greenland confirmed the d i e l e c t r i c constant value i n i c e of 3.2 (von H i p p e l , 1954). In 1960 t e s t s were made of a l t i m e t e r s o p e r a t i n g at 110, 220, 440 and 4300 MHz. These shewed that the lowest f r e q u e n c i e s were most s u i t e d to sounding of t h i c k i c e . A summary was r e p o r t e d by flaite and Schmidt (1962). In 1963, the B r i t i s h A n t a r c t i c Survey operated the 35 MHz SPRI Mk I apparatus, the f i r s t radar system designed s p e c i f i c a l l y f o r the use of sounding i c e sheets. The SPRI Mk I sounder had a 40 W r.m.s. t r a n s m i t t e r pulse power, a -93 dBm r e c e i v e r s e n s i t i v i t y , a 10 MHz bandwidth and moncpole antennae (Evans, 1963a). Furt h e r t e s t s by the S c o t t P o l a r 2 Sesearch I n s t i t u t e (SPBI) and the U. S. Army E l e c t r o n i c s Laboratory (DSAEL) determined that s i g n a l a t t e n u a t i o n was reduced at lower f r e g u e n c i e s (Evans, 1963b). During the f o l l o w i n g f i e l d season the Ninth S o v i e t A n t a r c t i c E x p e d i t i o n (Bogorodskiy, Rudakov, T y u l ' p i n , 1965) operated a type-1M4 radar apparatus, with a c a r r i e r freguency of 213 MHz, and a pulse power of 80 Kw r.m.s. Strong echoes were obtained from depths up t o 900 m. The p r o j e c t terminated with the l o s s of the apparatus and the d r i v e r i n t o a crevasse. The next t h r e e years saw expanded use of the SPRI Mk II sounder (500 w pulse power, otherwise same as Mk I) and the SCR 718 r a d i o a l t i m e t e r (440 MHz), i n c l u d i n g a i r b o r n e s u r v e y i n g i n Canada, Greenland and A n t a r c t i c a (Evans, 1966). The SPRI operated a SPRI Mk IV sounder from an a i r c r a f t during the 1969-70 f i e l d season. F l i g h t l i n e s are i n Evans and Smith, (1971). The f o l l o w i n g year the SPRI operated a modified SPRI Mk IV apparatus (modified to 60 MHz) from an a i r c r a f t . B u t t e r f l y plan m u l t i - w i r e d i p c l e antennae were used to maintain a l a r g e bandwidth. A maximum i c e t h i c k n e s s cf 4450 m was recorded (Evans, Drewry, Robin, 1972). In 1973 Davis, H a l l i d a y and M i l l e r r e p o r t e d a Cambridge e x p e d i t i o n attempt t o sound the R o s l i n G l e t s c h e r i n Stauning A l p e r , East Greenland, using a modified SCR 718 r a d i o a l t i m e t e r with a 45° corner r e f l e c t o r antenna. Op to t h i s time a l l r a d i o sounding had been with systems eguipped" with 3 monopole, d i p o l e or two element Yagi antennae. For fr e q u e n c i e s below 300 MHz high gain antennae would be p r o h i b i t i v e l y l a r g e . Sounding i n i c e sheets, however, co u l d be improved by using higher power t r a n s m i t t e r s . Returned power t h a t a r r i v e d l a t e r than the i n i t i a l bottom bounce d i d not a f f e c t the accuracy of the r e c o r d . In v a l l e y g l a c i e r s , wall echoes c o u l d obscure or be mistaken f o r bottom echoes, Davis e t a l (1973) r e c o g n i z e d that i n order to achieve c o n s i s t e n t r e s u l t s r a d i a t e d and r e c e i v e d power must be r e s t r i c t e d t o a narrow beam. Using an antenna with 8 dB forward gain they recorded echoes up to 350 m. In 1972, i n a c o n t i n u i n g p r o j e c t , the Department of Energy Mines and Resources, Canada, made soundings on the Athabasca G l a c i e r , A l b e r t a , Canada, with a UHF apparatus developed by R. Goodman. The u n i t f e a t u r e d a 620 MHz c a r r i e r frequency, 3 Kw pulse power and a very high gain corner r e f l e c t o r antenna. R e s u l t s were g e n e r a l l y negative, but very f i n e i n t e r g l a c i e r s t r u c t u r e was de t e c t e d . The f o l l o w i n g year the u n i t was operated on the T r a p r i d g e and Rusty G l a c i e r s , s u r g i n g g l a c i e r s i n the Yukon T e r r i t o r y , Canada, with t o t a l success (Clarke 6 Goodman, 1975; Goodman et a l , 1975). In 1974, us i n g a t r a n s m i t t e r developed by the S t a n f o r d Research I n s t i t u t e , Watts, Meier et a l (1974) made soundings on the South Cascade G l a c i e r , Washington U.S.A. and the Columbia G l a c i e r , Alaska, U.S.A. The apparatus f e a t u r e d a monopulse s i g n a l with 1-5 MHz c a r r i e r frequency and 100 ns pulse length. Successful soundings were made up to 1200 m in temperate ice (Meier £ Watts, private coffimunicaticn) . Its chie f disadvantage was i n i t s antennae conf igura t ion . I t was necessary to use bu t te r f ly ha l f wave dipoles spread cn the g l ac ie r surface. The transmitter and receiver antennae were separated by 50 m. This conf igurat ion precludes continuous p r o f i l i n g due to i t s s i ze and i t s method of deployment. Radio echo sounding has been establ i shed as a p r a c t i c a l method for obtaining i ce thicknesses , with reasonable r e l i a b i l i t y . Sounding i n large polar i ce masses i s most sa t i s fac tory at low frequencies, the lower l i m i t being determined by antenna s ize and communication inter ference . Large temperate i c e masses could be sounded with low frequency monopole sounders. However sounding in smaller val ley and alpine g l a c i e r s , in p a r t i c u l a r temperate or p a r t i a l l y temperate g l a c i e r s , could be success ful ly studied with UflF sounders. These sounders have very narrow antennae beams, very fast r i set imes and short pulse lengths. They w i l l be the most p r a c t i c a l system for continuous p r o f i l i n g over these g l a c i e r s . 1.2 DIELECTRIC PROPERTIES OF ICE 1.2.1 PERMITTIVITY Pure i c e has a r e l a t i v e l y high s t a t i c p e r m i t t i v i t y (approximately 100) (Evans, 1965) and a long re laxat ion time 5 (0.1 ms) due to i t s polar molecules. At radio frequencies of the order of 1 MHz the e f f e c t s of the relaxation spectrum, and i t s corresponding e f f e c t with temperature cn the r e l a t i v e permittivity have v i r t u a l l y vanished. Numerous programs have detemined that above 1 MHz the r e l a t i v e permittivity cf ice i s 3.2±0.2 (Auty S Cole, 1952; Cumming, 1952; von Hippel, 1954). It i s v i r t u a l l y independent of temperature, and i n temperate ice i t i s suspected that water content i s i n s u f f i c i e n t to t cause large variations (Evans, 1965). 1.2.2 LOSS TANGENT In 0°C ice below 300 MHz, ftanS i s v i r t u a l l y constant, and i n spite of the lack of e f f e c t on p e r m i t t i v i t y , power losses are due primarily to the relaxation spectrum. Above 300 MHz infrared absorption becomes evident. At reduced temperatures, the infrared absorption, which i s r e l a t i v e l y temperature i n s e n s i t i v e , i s evident at lower frequencies. Residual absorption from the relaxation spectrum decreases with lower temperatures (Evans, 1965). In temperate i c e , water content can have .widely varying effects on the loss tangent. This i s due i n part to the wide relaxation spectrum of water, but probably B.C. conductivity of water and scattering by water inclusions provide the greatest losses (Evans, 1965; Smith S Evans, 1972). 6 CHAPTER 2: SYSTEM DESIGN 2.1 GENERAL DESCRIPTION In designing a radio echo sounder for sounding in valley g l a c i e r s one has b a s i c a l l y f i v e parameters to work with: c a r r i e r frequency, bandwidth, pulse length, antenna pattern and peak transmitter power. Echo risetime at the receiver i s determined by transmitter, receiver and antenna bandwidth and by the antenna pattern. Maximum range i s determined by the peak transmitter power, the c a r r i e r freguency, and the antenna pattern. Resolution i s affected by pulse length, system bandwidth and antenna pattern The parameters for a system designed at the University of B r i t i s h Columbia are l i s t e d i n table 2 . 1 . The c a r r i e r frequency i s 840 MHz, the bandwidth i s 40 MHz, the pulse length i s 70 ns, the antenna gain i s 19 dE and the peak r.m.s. transmitter power i s 4.1 Kw. 7 2.2 SELECTION OF THE CARRIER FREQUENCY The d e c i s i o n to operate at 840 MHz can be d i v i d e d i n t o two s t e p s . F i r s t , the d e c i s i o n to operate wi t h i n the U.E.F. T.V. band. Secondly, what frequency w i t h i n the band to use. TRANSMITTER PARAMETERS Operating frequency 840 MHz Bandwidth 35 MHz Pulse l e n g t h 70 ns Rise time 18 ns F a l l time 28 ns Peak power 4.1 Kw (66 dEm) R e p e t i t i o n r a t e 25 KHz ANTENNA CONFIGURATION 90° dual d i p o l e corner r e f l e c t o r Gain 19dB over i s o t r o p i c F r o n t / s i d e r a t i o 60 dB VSWR < 1.5 RECEIVER PARAMETERS Bandwidth 40 MHz Dynamic range 97 dB Minimum s e n s i t i v i t y -82 dEm SYSTEM PERFORMANCE S i n g l e antenna > 95 dE Dual antenna 138 dB TABLE 2.1: RADAR PARAMETERS The prime f a c t o r i n choosing a high frequency i s the c o n s t r a i n t that the f i r s t use of the system w i l l be to sound s m a l l i c e c a p s and v a l l e y g l a c i e r s of the Canadian A r c t i c and Northwest, where v a l l e y w a l l echoes n e c e s s i t a t e a high g a i n antenna. VHF or lower f r e q u e n c i e s cannot be operated with a 8 high gain antenna which would be conveniently small for e i ther a e r i a l or surface use. The useful frequency range i s l imi ted to 300 MHz cr higher (Davis, 1973) . Once the dec i s ion has been made to operate within the useful UHF range (300MHz - 1GHz) a s ingle freguency must be se lected . In sounding - 2 0 ° C i ce at these freguencies f tan 6 increases as the second power of the frequency (Walford, 196 8; Bleaney 8 Bleaney, 1957). This i s countered by the antenna gain, i n that for a given aperture s ize gain also goes up as the second power of the freguency, and the ef fects cance l . The advantage of using a higher freguency l i e s in the narrower beamwidth ava i lab le for a given aperture s i z e . The beam w i l l i l luminate a smaller area of the g l ac i e r bed, hence c learer echoes w i l l be achieved. As the temperature increases the va r i a t ion of ftanS with frequency decreases so that at 0 °C ftan6, or attenuation per unit length i s e f f e c t i v e l y constant (0.057dEm _ 1 : Smith 5 Evans, 1972) hence the advantage of going tc a higher freguency due to having a greater gain for a given aperture i s r e a l . The two way gain increases as the fourth power cf the frequency whereas transmission losses decrease only as the second power. The advantage of the narrower beamwidth s t i l l app l ie s , e spec i a l ly considering that the beam w i l l i l luminate fewer sca t ter ing objects whose range i s close to the range of the bedrock (Davis, 1973), Davis (1973) also suggests that 9 s c a t t e r e d power may a c t u a l l y tend to decrease with these higher f r e q u e n c i e s , although evidence f o r t h i s i s l i m i t e d . The f i n a l d e c i s i o n to use 840 MHz r a t h e r than any nearby frequency ( e i t h e r higher or lower) i s economic. 840 MHz ± 20MHz l i e s w i t h i n a common c a r r i e r landbased mobile, and i n t e r i m UHF TV band f o r which hardware i s more e a s i l y a v a i l a b l e . Due t o i t s dual use, t h i s frequency has been set as a break p o i n t i n t r a n s m i t t e r d e s i g n ; any lower frequency would r e q u i r e a l a r g e r , more expensive c a v i t y a m p l i f i e r (R.L. Sepulveda, Microwave C o n t r o l Co,, p r i v a t e communication) . 2.2.1 TRANSMITTER DESIGN At the c a r r i e r frequency s e l e c t e d i t i s more s t a b l e to employ a c r y s t a l frequency generator r a t h e r than use an L-C tank to produce the frequency, as i s the case with more c o n v e n t i o n a l systems such as the SPRI Mk I I . The t r a n s m i t t e r d e r i v e s i t s frequency from a 120 MHz c r y s t a l o s c i l l a t o r , fed i n t o a x7 m u l t i p l i e r . Two stages of a m p l i f i c a t i o n and modulation l e a d the s i g n a l to a c a v i t y t r i o d e R.F. power a m p l i f i e r . Here some of the advantages of the c r y s t a l generated frequency become apparent. It i s much e a s i e r to detune the c h a r a c t e r i s t i c l y high Q of a c a v i t y a m p l i f i e r , g i v i n g the e f f i c i e n t r e s u l t of having a l l of the t r a n s m i t t e d power w i t h i n the r e c e i v e r bandwidth. 10 2.2.2 ANTENNA S TRANSKIT/RECEIVE SWITCH A corner r e f l e c t o r antenna was selected for the prototype conf igura t ion . With a two co l inear dipole driven element the antenna should have s u f f i c i e n t l y high gain and narrow beam width to y i e l d strong echoes with short fading patterns . Concurrently the 9 0 ° s ide lobes should be s u f f i c i e n t l y low that va l ley wall echoes w i l l not obscure bottom echoes when the apparatus i s operated at the ice surface. A c i r c u l a t o r i s used as a passive transmit /receive switch when the system i s operated with a s ingle antenna. 2.2.3 RECEIVER AND RECORDER The rece iver has a logari thmic intermediate freguency (I.F.) ampl i f ier as i t s primary component. I n i t i a l l y a photographic X-Y or intensity-modulated recording w i l l be used. In the future i t i s hoped to be able to record the s ignals d i g i t a l l y onto magnetic tapes. 2.3 SYSTEM PERFORMANCE 5 RANGE The smaller more e f f i c i e n t c a v i t i e s ava i l ab le at th i s freguency y i e l d higher peak power, hence greater system performance. Important parameters are l i s t e d in Table 2 .2 . If we assume d i e l e c t r i c losses B of 0.057dEm _ 1 and a bedrock r e f l e c t i o n c o e f f i c i e n t R of -20 dB (Rcbin, Evans, Ba i l ey , 1969; Harr i son , 1972) an antenna gain G of 19 dE and a 11 system performance of 138 dB then the maximum range i s determined by p , received _ G^X^R .. -0.2Dr T~T 10 (1) P. , 64iTr transmitted Peak power 66 dBm Receiver s e n s i t i v i t y --90 dEm Mixer c o n v e r s i o n l o s s -8 dB Maximum system performance 138 dB L i n e a r system performance 118 dB 1 1 R e c e i v e r i s l i n e a r down to -70 dBm. TABLE 2.2: SYSTEM PERFORMANCE The maximum range r i s then 700 m which should be ample f o r sounding many v a l l e y g l a c i e r s . . According to Davis (1973) a c r i t e r i o n f o r s u c c e s s f u l sounding of temperate g l a c i e r s i s p r ( p l a n £ ) = f ( f ^ ) >1 (2) r(scattered) m where R i s the bedrock r e f l e c t i v i t y , assumed t o be -20 dE; C i s the s c a t t e r i n g c o e f f i c i e n t , c a l c u l a t e d to be 0.01 m~l (based on Davis* (1973) a n a l y s i s of the DEMB sounder o p e r a t i n g at 620 MHz); G i s the antenna g a i n , set at 19 dE and 1 i s the pulse l e n g t h i n i c e . In our case R.G-l 0.01 80-1 CK 1 ; 0.01/m^ l W ' ( 3 ) m 12 hence our system should be s u c c e s s f u l at sounding temperate g l a c i e r s . 2 .4 ANTENNA DESIGN There are numerous s t y l e s of antennae which can provide l a r g e bandwidth and high g a i n a t the f r e g u e n c i e s d i s c u s s e d here. Some are capable of very great brcadbanding. The Yagi, p a r a b o l o i d , h e l i c a l and broadside a r r a y are some. However, i n s e l e c t i n g an antenna t o sound v a l l e y g l a c i e r s , forward gain i s not the o n l y c o n s t r a i n t . I g u a l l y important i s the 90° s i d e lobe l e v e l , or the " f r o n t to s i d e " r a t i o . In a v a l l e y , the d i p of the v a l l e y w a l l s r a r e l y exceeds 4 5 0 [ F i g * 2.1]. I f we model a g l a c i e r as f i l l i n g approximately a p a r a b o l c i d a l v a l l e y i t f o l l o w s t h a t over a l a r g e range of d i s t a n c e s from the v a l l e y w a l l , L, the t r a v e l time f o r the t r a n s m i t t e d pulse to reach the v a l l e y w a l l c l o s e l y matches the time f o r t h a t pulse to reach the bed, a t height H below the i c e s u r f a c e (using a v e l o c i t y i n i c e c f 176 m/ s e c ) . S i n c e the s u r f a c e wave i s not n o t i c a b l y a t t e n u a t e d , i n a l a r g e g l a c i e r the v a l l e y w a l l echo may e a s i l y obscure or be confused with the bottom echo. For example the p a r a b o l o i d a l r e f l e c t o r antenna has a f r o n t to s i d e r a t i o of 30 dB. With 0.05 dBm - 1 a t t e n u a t i o n i n i c e the bottom echo w i l l be the same s t r e n g t h as the w a l l echo Valley wall d i p U s g -a H FIGURE 2.1 14 a f t e r only 600 m of two way t r a v e l . In temperate i c e t h i s maximum range decreases r a p i d l y . I d e a l l y the f r o n t to s i d e r a t i o should not be g r e a t e r than one h a l f the system performance i n order tc have pcwer returned from the w a l l s obscured i n system n o i s e . It i s p o s s i b l e to achieve a f r o n t t o s i d e r a t i o of 60 dB by using a corner r e f l e c t o r . T h i s w i l l reduce system performance to 120 dB when operated i n such a v a l l e y . aperture s y n t h e s i s may improve the f r o n t t o s i d e r a t i o s t i l l f u r t h e r , though t h i s technique i s d i f f i c u l t and n e c e s s a r i l y very slew. 15 CHAPTER 2k CIRCUIT DESIGH The radio echo sounder consis t s of f ive units (not including power supply) connected i n the f i e l d only during use. They are the t ransmit ter , c i r c u l a t o r , antenna, rece iver /pulse generator, and d i sp lay . The assembly i s depicted i n Figure 3 .1 . 3.1 TRANSMITTER CIRCUIT The transmitter was b u i l t for U . E . C . by Microwave Control Company, Farmingdale, New Jersey, U .S .A . A block diagram for the transmitter i s shown i n Figure 3.2. The c a r r i e r freguency i s generated by a c r y s t a l o s c i l l a t o r operating at a 120 MHz harmonic. The s igna l i s then ampli f ied by two NPN t r a n s i s t o r s , both operating c la s s A (2N3866). Two more stages of ampl i f i ca t ion buffer the 120 MHz c a r r i e r . The 120 MHz s igna l i s fed to p a r a l l e l x6 and x7 m u l t i p l i e r s which y i e l d 720 MHz s ignals for the l o c a l o s c i l l a t o r , and 840 MHz for the broadcast c a r r i e r . The 720 MHz s igna l passes through a bandpass f i l t e r to the l o c a l o s c i l l a t o r output jack. The 840 MHz c a r r i e r then drives two stages of tuned common base ampl i f i e r s . The f i r s t stage i s gated by the modulator pulse which has been amplif ied from a TTL pulse provided by the external pulse generator. The second stage provides a maximum B. F. power of 20 watts. CIRCULATOR TRANSMITTER SMA SMA LOCAL OSCILLATOR TRIGGER PULSE SMA SMA RECEIVER N N BNC VIDEO BNC ANTENNA BNC DISPLAY TRIGGER BNC VERTICAL SCAN BNC DISPLAY BNC FIGURE 3.1: RADAR INTERCONNECTION DIAGRAM v V W V S M SOLID STATE AMPLIFIER TRIODE AMPLIFIER TIMES 7 MULTIPLIER LOCAL OSCILLATOR OUT PULSE AMPLIFIER TIMES 6 120 MHz AMPLIFIER MULTIPLIER / 720 MHz ' BANDPASS 120 MHz OSCILLATOR TRIODE AMPLIFIER R.F. OUT ISOLATOR SMA TRIGGER IN POWER SUPPLY / 26v REGULATOR e -o 30v IN FIGURE 3.2 RADAR TRANSMITTER BLOCK DIAGRAM h-1 18 The 20 watt R. F. power then passes through a 30 watt i s o l a t o r to a t r i o d e a m p l i f i e r / m o d u l a t c r , which i s a l s o gated by an a m p l i f i e d pulse from the e x t e r n a l pulse generator. The high power modulated R. F, s i g n a l i s then fed f i n a l l y t c a broad band t r i o d e power a m p l i f i e r which d e l i v e r s 4.1 k i l o w a t t s peak R. F. power through an i s o l a t o r to the R. F. output jack. i Power f o r the t r a n s m i t t e r i s drawn from a 28 v - 30 v supply which i s dropped and r e g u l a t e d to 26 v. A l l v o l t a g e s used (up to 4 Kv) are d e r i v e d from t h i s 26 v r e g u l a t e d supply. A d i g i t a l timing c i r c u i t d i s a b l e s the high v o l t a g e s f o r 1.5 minutes a f t e r turnon to allow f o r warmup. I n t e r n a l sensing c i r c u i t s provide f o r immediate shutdown should any s u b c i r c u i t o v e r l o a d , f o r any reason. The shutdown c i r c u i t throws a c i r c u i t breaker which may be r e s e t by a p p l y i n g a p o t e n t i a l t o a p i n on a t e s t jack provided. 3.2 RECEIVER/PULSE GENERATOR CIRCUIT The r e c e i v e r / p u l s e generator was designed and assembled at the U n i v e r s i t y of B r i t i s h Columbia, Department of Geophysics. F i g u r e 3.3 i s a block diagram f o r the r e c e i v e r / p u l s e generator. The r e c e i v e d R. F. s i g n a l passes through a diode switch which i s enabled during the t r a n s m i t pulse when the system i s DIODE SWITCH MIXER R.F. IN LOG I.F. AMPLIFIER VIDEO AMPLIFIER ATTENUATOR SMA LOCAL OSCILLATOR IN PULSE GENERATOR 100 KHz MULTIVIBRATOR SYNCRONOUS DIVIDE BY 4 A i DIODE SWITCH PULSE FORMER TRANSMITTER! TRIG. DELAY TRANSMIT PULSE FORMER FIGURE 3.3 6 C RADAR RECEIVER BLOCK DIAGRAM D 6 BNC VIDEO OUT TRANSMIT TRIGGER 3 " SMA BNC -4 DISPLAY TRIGGER i-1 20 operated i n the single antenna mode. The diode switch i s enabled by an amplified pulse derived from the pulse generator. The R. F. s i g n a l i s then mixed down tc the 120 MHz intermediate freguency, using the 720 MHz l o c a l o s c i l l a t o r provided i n the transmitter. The l o c a l o s c i l l a t o r provides 22 dBm of R. F. power to the mixer. This i s attenuated to 10 dBm, The mixer i s a Mini C i r c u i t s Laboratory model MA-1 with a conversion loss of 8 dB, The I, F. s i g n a l i s then amplified through a logarithmic I. F, amplifier. The amplifier i s an EHG model ICLT12040. It has a center frequency at 120 MHz, a 3 dB bandwidth of 40,1 MHz. I t has a dynamic range of 97 dE and i s l i n e a r l y logarithmic (±1 dB) for 70 dB of i t s range. Its risetime i s less than 20 ns; i t s noise figure i s 10 dE. Its output voltage range i s from 0,017 v at -90 dBm to 2,670 v at +7 dBm. The detected video signal passes through one f i n a l stage of gain which adjusts amplitude and bias for display purposes. The pulse generator provides trigger pulses to the transmitter, diode switch and oscilloscope display. I t i s capable of only a single r e p e t i t i o n rate and pulse length. The r e p e t i t i o n rate i s determined by a 100 KHz TTL multivibrator. The 100 KHz clock pulse then passes through a divide-by-four TTL counter which provides the 25 KEz trigger pulse rate. The counter provides two b i t s cf control information for a proposed d i g i t i z e r . The 25 KHz pulse then 21 drives two monostable TTL f l i p f l o p s . One monostable pulse i s amplif ied and enables the diode switch. The second mcnostable pulse provides a time delay between the diode switch enable pulse and a t h i r d monostable TTL f l i p f l o p . The t h i r d monostable v ibra tor i s adjusted to have a pulse length of 70ns. This pulse provides the modulating s igna l to the transmitter and the t r igger for the osc i l loscope d i sp l ay . The length of the diode switch enable pulse i s adjusted so that the switch and the transmitter disable simultaneously. 3.3 DISPLAY AND RECORDER The i n i t i a l display o sc i l lo scope i s a Tektronics model 475 o s c i l l i s c o p e with a Polaro id f i lm pack. When operated using i n t e n s i t y modulation a ramp generator scans the v e r t i c a l axis on the o sc i l l o s cope , which exposes one frame. The ramp generator cons i s t s of a var iable clock pulse which drives a nine b i t counter, which drives a d i g i t a l to analog converter . Intensity and modulation amplitude are contro l l ed by the video ampl i f i e r . A block diagram appears in Figure 3.4. In addi t ion i t i s hoped eventual ly to be able to d i g i t i z e and record the complete radar record . The proposed d i g i t i z e r w i l l be capable of 1024 channels with 10 ns channel separat ion.the d i g i t i z e r w i l l sample 128 pulses at one time 22 delay and average them. The time delay w i l l then be incremented by 10 ns and the process w i l l c o ntinue. The analog c i r c u i t r y i s based on a sample and hold a m p l i f i e r with 175 MHz bandwidth designed by H. B a l d i s and J . Aa2am-Zangeneih. The output w i l l be e i g h t b i t p a r a l l e l . A block diagram appears i n F i g u r e 3.5. + 6v O EXAR 2240M c l o c k s t a r t e i g h t b i t counter J i stop -4A/V -AAAr v e r t i c a l scan FIGURE 3.4: INTENSITY MODULATION RECORDING BLOCK DIAGRAM ( v e r t i c a l scan) N J C O DATA OUT OUTPUT FLAG data OUTPUT BUFFER data 15 BIT REGISTER clock clear A o 100 KHz IN clock] 15 BIT ADDER X data 8 BIT A/D CONVERTER X 1 BNC / VIDEO IN T 10 ns SAMPLE & HOLD ENABLE DECODER B C 10 BIT SAMPLE & HOLD ZERO DETECT TRIGGER 100 MHz OSCILLATOR 10 BIT ECL TIME DELAY COUNTER T 10 BIT ECL CHANNEL SELECT COUNTER -O D 7 BIT. COUNTER 1 FIGURE 3.5 RADAR DIGITIZER BLOCK DIAGRAM 4>-25 CHAPTER 4: SYSTEM CAPABILITIES 4.1 SYSTEM PERFORMANCE The maximum range of any radar system i s a f u n c t i o n of four parameters: antenna g a i n , frequency, medium a t t e n u a t i o n and system performance. The l a t t e r i s de f i n e d as the maximum r.m.s. t r a n s m i t t e d power d i v i d e d by the r e c e i v e r s e n s i t i v i t y , thus system performance i s a f u n c t i o n of the t r a n s m i t t e r and r e c e i v e r parameters, but i t i s a l s o p o s s i b l y determined by antenna c h a r a c t e r i s t i c s . I t i s p o s s i b l e t h a t there i s s u f f i c i e n t t r a n s m i t t e r leakage power, which may be a v a i l a b l e t o the r e c e i v e r , and could obscure otherwise usable echoes. In the present case t h i s i s a r e a l c o n s i d e r a t i o n when a s i n g l e antenna i s used. I f the ON/OFF t r a n s m i t t e r r a t i o i s only 100 dE and the c i r c u l a t o r i s o l a t i o n i s 2 5 dB, then system performance c o u l d be l i m i t e d to t h e i r sum, 1 2 5 dB. F u r t h e r , i f the antenna i s mismatched so t h a t i t has a r e f l e c t i o n c o e f f i c i e n t g r e a t e r than - 2 5 dB, then the system performance would be degraded s t i l l f u r t h e r . Any attempt to improve system performance by improving r e c e i v e r s e n s i t i v i t y would be wasted. T h i s problem can be avoided by employing two antennae as with the SPRI Mk I I sounder (Evans 8 Smith, 1 9 6 9 ) . It i s r e l a t i v e l y easy t o produce antennae p a i r s with the r e q u i r e d 26 i s o l a t i o n , p a r t i c u l a r l y i f high gain antennae are used. Another, poss ibly less expensive method i s ava i lable for increas ing i s o l a t i o n . Passive or act ive diode switches operated between the transmitter and c i r c u l a t o r can increase the ON/OFF r a t i o by at least 40 dB. The only reguirement cn the switch i s the a b i l i t y to conduct the maximum transmitter power, with minimum lo s s . Switching speed i s net c r i t i c a l as the switch need only be off for maximum range echoes, usual ly several microseconds after the transmitter pulse. 4.2 MAXIMUM RANGE AND RESOLUTION In radio echo sounding i n i ce the bedrock has general ly been modeled as a specular plane r e f l e c t o r with a r e f l e c t i o n coe f f i c i en t of -20 dB. This f igure has been considered conservative (Davis, 1973). Deviations on t h i s model have also been considered (Harrison, 1974). I f the plane model i s assumed then the maximum range i s determined by P O ; received G ^ R . -0.2Dr ... F , " 6 4 ^ 1 0 ( 1 ) transmitted where the l e f t expression eguals the inverse system performance, G i s the free space antenna ga in , A i s the free space wavelength, R i s the bedrock r e f l e c t i v i t y , D i s the loss in dBm - 1 , and r i s the range. In cold i c e , i f the attenuation of the s ignal i s 0.057 d B m - 1 , then the maximum range i s 700 m, with the 27 des c r i b e d apparatus, as st a t e d i n Chapter 2. In temperate i c e the maximum range i s only 210 tn f o r a t o t a l a t t e n u a t i o n of 0.2 dBm-*. I f t o t a l a t t e n u a t i o n i s 0.15 dBm-1 (Ragle e t a l , 1964), then the maximum range i s 280 m. Improved gain due to r e f r a c t i o n at the i c e s u r f a c e may improve the system performance by about 2 dB i n c r e a s i n g the maximum range to 290 m i n the l a s t case. I f p r e c i s i o n i s d e f i n e d as the time f o r echo power to r i s e 3 dB above l o c a l average power, then i t f o l l o w s that p r e c i s i o n i s a constant f r a c t i o n of range. In the present case, p r e c i s i o n i s 18ns-88m/ys _ zoUm of range i n temperate i c e . In c o l d i c e the p r e c i s i o n i s 0.25% of range. (Note: these f i g u r e s are based upon the assumption t h a t the plane r e f l e c t o r i s s u f f i c i e n t l y s p e c u l a r , t h a t f o r the high gain antenna, the plane i s e f f e c t i v e l y i d e n t i c a l to a s p h e r i c a l r e f l e c t o r centered a t the antenna with r a d i u s equal to the r e a l range. The v a l i d i t y of the assumption i s s o l e l y a f u n c t i o n of the antenna gain and beamwidth. If fadin g p a t t e r n s r e s u l t i n g from too broad a beam degrade the echo r i s e t i m e , a d e c o n v o l u t i o n of the echo, i f p o s s i b l e , using the t r a n s m i t t e d p u l s e as a source f u n c t i o n , w i l l r e t u r n t h i s a c c u r a c y ) . 28 4.3 REFLECTIVITY OF LAYERS WITHIN A GLACIER Ha r r i s o n (1973) has shown t h a t the r e f l e c t i o n c o e f f i c i e n t R, f o r random v a r i a t i o n s i n p e r m i t t i v i t y vary with the pulse length i n r a d i a n s L, as R - i ^ r ) L 2 e " 2 L i (5) where l a y e r t h i c k n e s s i s g r e a t e r than the pulse l e n g t h . ^E' i s a step change of the r e l a t i v e p e r m i t t i v i t y e with depth. H a r r i s o n has concluded that i t i s necessary to r e s t r i c t o n e s e l f to the case where the l a y e r t h i c k n e s s i s much l e s s than the pulse l e n g t h . In t h i s case T T 2 L 2 . 2 R - -ft {^fr} (6) m f o r s i n g l e r e f l e c t o r s , and 7 T 3 p L . 2 - k 2 L 2 _ _ m m fAS i e m m . f o r m u l t i p l e r e f l e c t o r s where 1^ i s the l a y e r t h i c k n e s s or s p a c i n g , ^ m i s the wavelength i n i c e , P m i s the pulse length i n i c e and k m i s the wave number i n i c e . H a r r i s o n has a l s o shown that there i s a maximum r e f l e c t i v i t y at l m = 1/^2 where •m A 2 -h & m a v = T7" P m k {—^} (8) max lb mm e In the present case, t h i s reduces to A F 2 R = 0.119 {-^ T} (9) max e 29 at L =2.5 cm. To obtain a power r e f l e c t i o n m -70 dB in t h i s case would require that Ae = 10~3 e It i s clear that UHF radio echo sounders can be to small variations in e over centimeter ranges. 4.4 POLARIZATION 4.4.1 OPTICAL ACTIVITY Optical a c t i v i t y i s usually described as the tendency of transparent matter to rotate the E-vector of plane polarized electromagnetic radiation. The E-vectcr of any radiation traversing o p t i c a l l y active matter w i l l rotate either clockwise or counterclockwise when viewed from the radiation source. With a radio echo sounder, plane polarized radiation enters a g l a c i e r at normal incidence. Any rotation due to op t i c a l a c t i v i t y i n the i c e during the f i r s t t r a n s i t (to the bottom) should equal the rotation due to the return traverse. Since the rotation sense does not change, the t o t a l rotation should cancel. Hence radio echo sounding cannot detect o p t i c a l a c t i v i t y . c o e f f i c i e n t of (10) very sensitive 4.4.2 DOUBLE REFRACTION Double r e f r a c t i o n (also known as birefringence) i s 30 defined as a difference i n r e f r a c t i v e index for radiation with E-vectors normal and p a r a l l e l to a well defined c r y s t a l axis (Jenkins & White, 1957). At v i s i b l e wavelengths the ordinary and extraordinary indices of r e f r a c t i o n in ice d i f f e r by 0.3%. In the i d e a l s i t u a t i o n , with c r y s t a l s having their o p t i c a l axes p a r a l l e l and horizontal, a 90° phase s h i f t of the ordinary and extraordinary rays at 840 HHz could occur i n only 16 meters of two way t r a n s i t ( i t i s necessary to assume that the r a t i o of r e f r a c t i v e indices i s constant with frequency above the relaxation spectrum). However t h i s i s excessively optimistic for two reasons. F i r s t , there i s a tendency for the o p t i c a l axes of i c e c r y s t a l s i n glaciers to a l i g n v e r t i c a l l y (Paterson, 1969). Secondly, and predominantly, nonuniforrcity in axis orientation causes double r e f r a c t i o n to cancel. Consider an orthonormal base vector set, say v e r t i c a l , in the d i r e c t i o n of glacier flow, and horizontal and normal to glacier flow. By d i r e c t i o n cosines the g l a c i e r can be divided into three equivalent thicknesses of ice with pure c r y s t a l axis orientations. The component with v e r t i c a l axes does not exhibit double r e f r a c t i o n and can be ignored. The equivalent thickness of ice available for a f f e c t i n g double re f r a c t i o n i s equal to the difference of the other two components. Hence i t i s necessary to have a very strong prefered horizontal orientation to make double r e f r a c t i o n v i s i b l e . Sounding at frequencies of about 60 HHz, double refraction would require 31 at least 120 m of ice to produce a 90° phase sh i f t . Jiracek (1965) reported that at South Pole Station, using a 30 MHz system, a bottom echo could not be received K i t h antennae broadside and para l le l . Maximum receiver power occurred when the antennae were perpendicular and horizontal. Jiracek interpreted this as a 9 0 ° rotation from the original transmitted pulse. "On the Skelton Glacier , bottom echo amplitude was practically independent of receiving antenna orientation in the horizontal plane." Jiracek interpreted this as a transformation of l iner polarized radiation into near circular polarization by double refraction. 4.4.3 DETECTING DC0BL1 REFRACTION The orthonormal basis with one axis ver t ica l , which maximizes the effective double refracting thickness defines the privileged directions in i t s two horizontal axes. These are the directions in which a l l of the transmitted power is either in the ordinary ray or the extraordinary ray. In these directions double refraction i s not v i s ib le . Bowever upon arr ival at the bedrock the ideal reflector model f a i l s by returning only a component fraction of polarized power instead of maintaining a l l polarization. The remaining reflected power i s returned unpolarized. A receiver antenna based cn dipoles, when rotated cannot distinguish between e l i p t i c a l l y polarized radiation and combined linear and unpolarized 32 radiation. A l l that i s possible i s a determination of the major axis of returned power. If t h i s d i f f e r s from the transmitted axis, then double r e f r a c t i o n has been detected. By rotating the transmitter antenna and repeating the procedure two transmitter antenna orientations should appear where no double r e f r a c t i o n i s evident, i . e . the major receiver power axis coincides with the transmitter pcwer axis. At these positions an estimate for bedrock depolarization can be made. Once t h i s i s known i t may be possible tc estimate the amount of double re f r a c t i o n and hence draw a conclusion about the ice f a b r i c . 4.4.4 FARADAI EFFECT In many substances when plane-polarized radiation traverses i n a d i r e c t i o n p a r a l l e l to an applied magnetic f i e l d , the plane of vibration i s rotated. The amount of rotation Qis proportional to the f i e l d strength fi, and tc the distance traversed L. i . e . 0 = VLH where V, the Verdet constant i s determined by the substance and the wavelength. For water M equals 0.0131 minutes Oersted - 1cm - 1 at the Sodium D l i n e s . In the i n f r a r e d V i s the order of 10~ 3 minutes Oersted _ lcm-* (Jiracek, 1967). When radiation i s r e f l e c t e d back through the medium the f i e l d d i r e c t i o n i s e f f e c t i v e l y reversed, and the rotation due 33 to the second t r a v e r s e adds to the r o t a t i o n due tc the f i r s t t r a v e r s e . T h i s i s u n l i k e n a t u r a l o p t i c a l a c t i v i t y which c a n c e l s e x a c t l y . I f Faraday r o t a t i o n i n i c e due to the l c c a l magnetic f i e l d i s d e t e c t a b l e , i t can be d i s t i n g u i s h e d from double r e f r a c t i o n by o b serving the average angular v a r i a t i o n of r e c e i v e r maximum from t r a n s m i t t e r o r i e n t a t i o n , averaged over a l l t r a n s m i t t e r d i r e c t i o n s . J i r a c e k (1965) has c o n s i d e r e d the magnitude of the Faraday e f f e c t at the South P o l e . He determined that r o t a t i o n i n the i n f r a - r e d would be only 5 ° . Since the Verdet constant decreases with frequency ( J i r a c e k , 1965) the e f f e c t should be n e g l i g i b l y s m a l l , even i n the very t h i c k e s t i c e . 4.4.5 PHOTO-ELASTICITY A t r a n s p a r e n t i s o t r o p i c medium becomes o p t i c a l l y a n i s o t r o p i c when s u b j e c t e d to mechanical s t r e s s . The p r i v i l e g e d d i r e c t i o n s are along the d i r e c t i o n s of the p r i n c i p a l s t r e s s e s . Since p h o t o - e l a s t i c i t y i s o p t i c a l l y i d e n t i c a l to double r e f r a c t i o n , the two e f f e c t s cannot be d i s t i n g u i s h e d . I t i s u n l i k e l y that any i n f o r m a t i o n r e g a r d i n g the i c e f a b r i c can be determined a p o s t e r i o r i from i n f o r m a t i o n gathered by s t u d y i n g the e f f e c t s of a l p i n e or s m a l l v a l l e y g l a c i e r s upon p o l a r i z e d r a d i o echo sounder r a d i a t i o n . A l l that may be p o s s i b l e i s the d e t e c t i o n of one or more of these 34 e f f e c t s , 4.4.6 DIGITAL RECORDS A proposed d i g i t i z e r having 8 b i t r e s o l u t i o n and 10 ns channel s e p a r a t i o n w i l l be used to r e c o r d the r e c e i v e d envelope as provided by the output of the video a m p l i f i e r . 10 ns channel s e p a r a t i o n y i e l d s a Nyguist frequency of 50 HHz so t h a t no r e c e i v e r power w i l l a l i a s i n t o a lower frequency. By deconvolving f a d i n g p a t t e r n s using the t r a n s m i t t e r pulse as a source f u n c t i o n , and averaging over s e v e r a l records gr e a t e r rangy accuracy should r e s u l t and i n t e r m e d i a t e r e f l e c t o r s i n the i c e should become v i s i b l e . Gross bottom roughness may be estimated by observing the spread i n time of r e t u r n e d power from the bottom echo. Of p a r t i c u l a r i n t e r e s t would be the d e t e c t i o n of f i n e i n t e r g l a c i e r s t r u c t u r e near the bedrock. 4.5 CONCLUSION T h i s t h e s i s has presented a b a s i s f o r the design of a UHF r a d i o echo sounder f o r the purpose of s t u d y i n g g l a c i e r s i n mountainous t e r r a i n , S p e c i f i c design parameters have been presented f o r a r a d i o echo sounder to be b u i l t at the U n i v e r s i t y of B r i t i s h Columbia. These parameters have been discus s e d and a c c o r d i n g to normal r a d i o a l t i m e t r y p r a c t i c e s and e n g i n e e r i n g p r i n c i p l e s p r a c t i c a l l i m i t s cf the technique 35 have been proposed. The design has f o l l o w e d as a b a s i s a r a d i o echo sounder b u i l t and operated by the Department of Energy, Mines and Resources, Ottawa, Canada, and Environment Canada, o p e r a t i n g at 620 MHz. He suggest that UHF r a d i o echo sounding w i l l provide a h i g h l y mobile method of sounding the a l p i n e and v a l l e y g l a c i e r s which have p r e v i o u s l y evaded s u c c e s s f u l study. 36 BIBLIOGRAPHY - Auty, R. P., and C o l e , R. H. 1952. D i e l e c t r i c p r o p e r t i e s of i c e and s o l i d D20. The J o u r n a l of Chemical P h j s i c s , V o l . 20, No, 8, p. 1309-1314. B a i l e y , J. T., Evans, S, and Robin, G. de Q. 1964. Radio echo sounding of p o l a r i c e s h e e t s . Nature, V o l . 204, No. 4967, p. 420-421. B a l d i s , H. A,, and Aazam-Zanganeh, J , 1973, High speed s i n g l e event sampler. Reviews of S c i e n t i f i c Instruments, V o l . 44, No. 6, p. 712-714. Beckmann, P., and S p i z z i c h i n c , A. 1963. The s c a t t e r i n g of e l e c t r o m a g n e t i c waves from rough s u r f a c e s . Oxford^ Pergamon Press. Berry, M. 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E l e c t r o m a g n e t i c r e f l e c t i o n from m u l t i l a y e r e d models. P£2£Si^iH3s of the Symposium cn Remote Sensing i n G l a c i o l o a y ~ C a m b r i d g e x September J974, i n p r e s s . ~~ ~ Longhurst, R. S, 1957, Geometrical and p h y s i c a l o p t i c s . London^ Longmans^ Green and Co. Nye, J . F., Kyte, R. G., and T h r e l f a l l , D. C. 1972. Proposal f o r measuring the movement c f a l a r g e i c e sheet by observing r a d i o echos. J o u r n a l of Glaciolocjy, V o l . 11, No. 63, p. 319-325. Oswald, G. K. A. 1974. I n v e s t i g a t i o n of s u b - i c e bedrock c h a r a c t e r i s t i c s . Proceedings of the Symposium on Remote Sensing i n G l a c i o l o g y x Cambridqe x September .1974, i n press. Page, D. F., and Ramseier, R, 0. 1974. A p p l i c a t i o n c f a c t i v e radar techniques to the study cf i c e and snow. 2^ the Symposium on Remote Sensing i n SiSSiSlSSIjt Cambridge x September 1974, i n p r e s s . Paren, J. G. 1970, D i e l e c t r i c p r o p e r t i e s of i c e , Ph.D. t h e s i s , Darwin C o l l e g e , Cambridge. Paterson, W. S. B. 1969, The P h y s i c s of G l a c i e r s . O x f o r d x Pergamon P r e s s . 42 Binker, J . N. 1964. Radio echo sounding and s t ra in rate measurement i n the ice sheet of North-west Greenland; 1964. Polar Record, Vo l . 12, No. 79, p. 403-405. Ragle, R. H . , and others . 1964. Ice cere studies cf Ward Hunt Ice Shel f , by R. H. Ragle, R. G. B l a i r and L. E. Persson. Journal of g lac io loc j j . V o l . 5, No. 37, p. 39-59. Robin, G. de Q , , Evans, S . , Drewry, C. J . , Harr ison, C. E . , and Pe t r i e , D. L. 1970. Radio echo sounding cf the Antarc t i c Ice Sheet. Antarc t ic Journal , V o l . 6, p. 229-232. Robin, G. de Q. , Swithinbank, C. W. M . , and Smith, B. M. E. 1968. Radio echo explorat ion of the Antarc t ic Ice Sheet. IASH Publ ica t ion 86, p. 97-115. Ross i ter , J . R., and others , 1973. Radio interferometry depth sounding: part II - experimental r e s u l t s , by J . R. Ros s i t e r , G. A. LaTorraca, A. A. Annan, C. W, Strangway and G. Simmons. Geophysics, V o l . 38, No. 3, p. 581-599. Smith, B. H, E. 1971. Radio echo studies of g l a c i e r s . Ph.D. thes i s , Cambridge U n i v e r s i t y . Smith B. M. E . , and Evans, S. 1972. Radio echo sounding: absorption and scat ter ing by water inc lus ions and ice lenses . Journal of G lac io loay , V o l . 11, No. 61, p. 133-146. Strangway, D. W., Simmons, G . , LaTorraca, G . , Watts, R . , Bannister , L . , Baker, R . , Redman, J. C . , and Ross i ter , J . R. 1974. Radio-frequency interferometry - a new technigue for studying g l a c i e r s . Journal of Glacioloc], V o l . 13, No. 67, p. 123-132. 43 Swithinbank, C. 1968. Radio echo sounding cf A n t a r c t i c g l a c i e r s from l i g h t a i r c r a f t . IASH P u b l i c a t i o n 79, p. 405-414. Swithinbank, C. W. M. 1972. F i e l d work. Radio Echo Sounding by the B r i t i s h A n t a r c t i c Survey. Polar Record, Vo l . 16, No. 102, p. 411-412. Von H i p p e l , A. 1954. D i e l e c t r i c m a t e r i a l s and a p p l i c a t i o n s . New Y o r k x Technology Press and Wiley, p. 12, p. 301. Waite, A. H. J r . 1966. I n t e r n a t i o n a l experiments i n g l a c i e r sounding, 196 3 and 1964. Canadian J o u r n a l of E a r t h S c i e n c e s , V o l . 3, No. 6, paper 17, p. 887-892. Waite, A. H. , and Schmidt, S. J . 1962. Gross e r r o r s i n height i n d i c a t i o n from pulsed radar a l t i m e t e r s o p e r a t i o n over t h i c k i c e or snow. Proceedings cf the I n s t i t i u t e of Radio E n g i n e e r s , V o l . 50,~No.~ 6~ p. 1515-1520. Walford, M. E. R. 1964. Radio echo sounding through an i c e s h e l f . Nature.* V o l . 204, No. 4956, p. 317-319. Walford, M. E. R. 1965. Radio echo sounding cf p o l a r i c e masses. Ph.D. t h e s i s , Cambridge U n i v e r s i t y . Walford, M. E. R. 1968. F i e l d measurements of d i e l e c t r i c a b s o r p t i o n i n A n t a r c t i c i c e and snow at very high f r e g u e n c i e s . J o u r n a l of G l a c i o l o g y , V o l . 7, No. 49, p. 89-94. . Walford, M. E. R. 1972. G l a c i e r movement measured with a r a d i o echo t e c h n i q u e . Nature, V o l . 239, p. 93-95. Watts, B. D., England, A. W., Meier, M. F., and V i c k e r s , R. S. 1974. Radio echo sounding of temperate g l a c i e r s at f r e g u e n c i e s of 1 to 5 MHz. Proceedings of the Symposium on Remote Sensing i n G l a c i o l o g y ^ Cambridge^ September J974, i n press. 44 Weber, J . R., and Andrieux, P. 1970. Radar sounding of the Penny Icecap, B a f f i n I s l a n d . J o u r n a l of G l a cj. elegy, V o l . 9, No. 55, p. 49-54, 45 APPENDIX Some c o n s i d e r a t i o n s on the s e l e c t i o n and use of t h e r m i s t o r s f o r the purpose of making a b s o l u t e temperature measurements i n snow or i c e . 46 1 INTRODUCTION In g e n e r a l , t h e r m i s t o r s , when used as temperature measuring d e v i c e s , are used s i n g l y or i n p a i r s i n some impedance net, t h a t net being d r i v e n by some power supply, and a l s o having an output, which i s monitored by a d e t e c t o r . Frequently the t h e r m i s t o r i s placed at the end of a transmission l i n e ( F i g . 1). Errors i n p r e c i s i o n and accuracy enter from numerous sources: from the t h e r m i s t o r i t s e l f , from the power supply or i t s c o n f i g u r a t i o n , from the the d e t e c t o r , impedance net or t r a n s m i s s i o n l i n e . The measurement of temperature can only be as good as the p r e c i s i o n standard a g a i n s t which the t h e r m i s t o r was c a l i b r a t e d . I f i t has been assumed t h a t the t h e r m i s t o r c h a r a c t e r i s t i c w i l l f i t a t h e o r e t i c a l curve, then the accuracy can be no b e t t e r than the q u a l i t y of that f i t . Of n e c e s s i t y one must assume that a given t h e r m i s t o r w i l l be s t a b l e over the long term, although i t i s known that t h i s i s not n e c e s s a r i l y the case; environmental f a c t o r s such as s t r e s s or moisture may a f f e c t a t h e r m i s t o r ' s behaviour, and over a p e r i o d of time a thermistor»s s t u c t u r e may change. Preaging can reduce these e f f e c t s , however they cannot be e l i m i n a t e d . I f a t h e r m i s t o r i s r e c o v e r a b l e f c r r e c a l i b r a t i o n a f t e r i t s p e r i o d of use, i t may be p o s s i b l e to monitor some cf these e f f e c t s . P O W E R S U P P L Y V V I N T E R F A C E CB R I D G E ) D E T E C T O R T R A N S M I S S I O N L I N E F I G U R E 1: G E N E R A L I Z E D B R I D G E 48 I t i s the i n t e n t of t h i s paper t c examine i n s t r u m e n t a l parameters, and t o d i s c u s s how they may be used or determined, i n order to optimize the p r e c i s i o n with which the r e s i s t a n c e cf a given t h e r m i s t o r i n a f i x e d s i t u a t i o n , can be determined. These parameters i n c l u d e : t h e r m i s t o r s e l f - h e a t i n g , nominal t h e r m i s t o r r e s i s t a n c e , t r a n s m i s s i o n l i n e r e s i s t a n c e and reac t a n c e , impedance net or brid g e c o n f i g u r a t i o n , type c f bridge power supply, and g u a l i t y of the d e t e c t o r . T h i s examination a p p l i e s e q u a l l y to both c a l i b r a t i o n systems and f i e l d s i t u a t i o n s s i n c e both c o n d i t i o n s can be completely d e s c r i b e d . 2 THERMISTOR CHARACTERISTICS 2.1 THERMISTOR SEIF-HEATIUG I f we assume t h a t a t h e r m i s t o r has s p h e r i c a l symmetry, and t h a t the ambient temperature of the surrounding i c e (or snow) i s constant at T, then the steady s t a t e s o l u t i o n of the heat equation shows t h a t the temperature of i c e c l o s e to the th e r m i s t o r can be no g r e a t e r than T + 4 , k ? r < D x c e where P i s the power d i s s i p a t e d i n the t h e r m i s t o r , K ± c e i s the thermal c o n d u c t i v i t y of i c e (assumed t c be constant with T) and r i s the r a d i u s from the c e n t e r of the t h e r m i s t o r . Let 49 AT. = -7—7^ (2) i c e 4frk. r i c e and l e t AT+T be the temperature as i n d i c a t e d by the r e s i s t a n c e c f the t h e r m i s t o r . I t f o l l o w s t h a t AT > AT. I . = . , P (3) i c e ' mm 4 7 r k. r . i c e min where r m l n i s the r a d i u s of the i c e c l o s e s t t c the t h e r m i s t o r ; i n e f f e c t the r a d i u s of the t h e r m i s t o r . Owing to the f a i l u r e of our s p h e r i c a l approximation i n (1) and t c the great v a r i e t y i n s t r u c t u r e and shape of t h e r m i s t o r s , i t s h a l l be assumed here t h a t the r e l a t i o n i n (3) i s an e g u a l i t y , where r m-£ n must now be a t y p i c a l r a d i u s . Manufacturers of t h e r m i s t o r s g e n e r a l l y provide f i g u r e s f o r t h e i r t h e r m i s t o r s t h a t i n d i c a t e the a b i l i t y of the device to d i s s i p a t e power i n t o the surrounding medium. T h i s • D i s s i p a t i o n C o n s t a n t 1 which s h a l l be c a l l e d E c , i s s p e c i f i c a l l y d e f i n e d as the amount of power r e g u i r e d to r a i s e the temperature of the t h e r m i s t o r 1°C above the ambient temperature. More c o n v e n i e n t l y from (3), i n i c e D = 4TTk. r . (5) c i c e mm 50 Equation (4) c l e a r l y depends on the environment of the t h e r m i s t o r . Manufacturer's f i g u r e s are u s u a l l y given f o r the t h e r m i s t o r i n s t i l l a i r . In i c e Dc i s at l e a s t a f a c t o r of three g r e a t e r [Fenwal D-1; Eg. ( 5 ) ] , and although i n c r e a s e s i n It w i l l improve the measurement p r e c i s i o n , a f a c t o r cf three i n D c r e s u l t s i n no more than 1.5dB improvement i n p r e c i s i o n . Hence f o r the examples used here, s i n c e D c i s g e n e r a l l y d i f f i c u l t t o measure or c a l c u l a t e , manufacturers' f i g u r e s w i l l be used. 2.2 THERMISTOR SELF-HEATING WITH WATER LAYER I f the temperature of the i c e i s s u f f i c i e n t l y c l o s e to the melting p o i n t that before reaching steady s t a t e the temperature of the t h e r m i s t o r reaches the melting p o i n t a l a y e r of water w i l l form arround the t h e r m i s t o r . Since the thermal c o n d u c t i v i t y of water i s much s m a l l e r than that of i c e , the t h e r m i s t o r w i l l tend to s e l f - h e a t g r e a t l y . T h i s e f f e c t has been demonstrated i n attempts t c measure the thermal c o n d u c t i v i t y of i c e by using a thermal d r i l l cable as a l i n e heater, and attempting t c observe the l o g a r i t h m i c r i s e cf temperature with time. I f too much power i s s u p p l i e d to the c a b l e a water l a y e r forms before the l c g a r i t h m i c approximation becomes v a l i d . In another case, i n temperate i c e , the i c e cannct conduct power away from the t h e r m i s t o r . The o n l y a v a i l a b l e s i n k i s i n 51 the i c e melt, hence steady s t a t e w i l l never be approached. However a f t e r s u f f i c i e n t time the ice/water boundary should be s u f f i c i e n t l y d i s t a n t and l a r g e , t h a t i t may be modelled as s t a t i o n a r y . In t h i s case D = 4 TT k r . (6) c water mm v ' a l s o i f too much power i s a v a i l a b l e , induced water c u r r e n t s may cause f l u c t u a t i o n s i n the t h e r m i s t o r temperature. Any system which must c o n s i d e r t h i s case should be designed so that t h i s e f f e c t i s too s m a l l to be measurable. 2.3 THERMISTOR RESISTIVITY GRADIENT Th e r m i s t o r s have negative thermal c o e f f i c i e n t s of r e s i s t i v i t y , which s h a l l be c a l l e d Bp. For most t h e r m i s t o r s RT - -0.05°C - 1 (7) and t h i s f i g u r e w i l l be used i n a l l of the examples i n t h i s paper. 2.4 TIME CONSTANTS The 'time constant' of a t h e r m i s t o r , as d e f i n e d by some manufacturers i s the time r e q u i r e d f o r a t h e r m i s t o r tc change i t s temperature 63% of the amount of temperature change of a value impressed upon i t i n a st e p change [Fenwal EMC-5]. For 52 a given t h e r m i s t o r t h i s may vary from f r a c t i o n s c f seconds to minutes [Fenwal D-1] as a f u n c t i o n of environment. For steady s t a t e temperature measurements a more u s e f u l time constant would be the time r e g u i r e d f o r a t h e r m i s t o r t c reach 63% of #T above T, from the i n i t i a t i o n c f power, but because of the e f f e c t s of environment on Dc and hence AT, and a l s o c o n s i d e r a t i o n o f the f a c t t h a t the twc co n s t a n t s as defin e d here are probably c l o s e l y r e l a t e d , the l a t t e r time constant i s almost c e r t a i n l y i n d e t e r m i n a b l e , e s p e c i a l l y when the t h e r m i s t o r would be deployed i n a bore ho l e i n i c e . The best t h a t should be s a i d about a t h e r m i s t o r being used to measure a steady s t a t e temperature i s that the temperature i t measures i s between T and T+AT, both as d e f i n e d b e f o r e . I t i s necessary then t h a t the al l o w a b l e e r r o r due to s e l f - h e a t i n g must be the f u l l value of T, and that i n most cases t h i s w i l l not be reduced. 3 BRIDGES AND BRIDGE POWER SUPPLY. 3.1 POWER SUPPLY TYPES In t h i s paper only two kinds of power supply w i l l be considered. They are f i r s t a D.C. supply, and secondly an A.C. supply of angular freguency u . Further i n t h i s paper they w i l l be shown to be both o p t i m a l when compared tc pulsed 53 supplies. 3.2 BRIDGE TYPES The simplest type of resistance measuring device consists of a current source driving the unknown resistance. A voltmeter then measures the voltage drop accross the resistance (Fig. 2A), A measure of the signal available i s dV/dR. In t h i s case S i - * <« Thermal noise voltage i s proportional tc provided we assume that the thermistor i s an i d e a l Johnson ncise generator. Signal to noise r a t i o i s thus proportional to i//R. A l l analog ohmmeters and d i g i t a l chmmeters work i n t h i s fashion. The d i f f i c u l t i e s involved i n taking t h i s approach i s that with analog meters, they r a r e l y have enough dynamic range cr precision to be useful, and with d i g i t a l meters long term l i n e a r i t y and short term thermal s t a b i l i t y are generally not good enough so that o v e r a l l accuracy approaches the resolving c a p a b i l i t y of the instrument. This i s particulary the case when d i f f e r e n t instruments are used for c a l i b r a t i o n and f i e l d measurements. Null detectors have the advantage that they do not require the dynamic range or l i n e a r i t y of the •chmmeter* type cf instrument. However, they may s t i l l be thermally 54 FIGURE 2: BRIDGE CONFIGURATIONS 55 s e n s i t i v e , ana they cannot be used f o r ' i n s t a n t * measurements. T h i s i s a problem i f continuous measurements i n time ever a l a r g e temperature range are r e g u i r e d . For making s i n g l e measurements of steady s t a t e temperatures, n u l l d e t e c t o r s are we l l s u i t e d . F i g u r e s 2B and 2C show two p o s s i b l e c o n f i g u r a t i o n s . The c h i e f d i f f i c u l t y i n implementing a system g e n e r a l i z e d by the type i n Fi g u r e 2E l i e s i n p r o v i d i n g an accurate low impedance v o l t a g e r e f e r e n c e v B/2 e x a c t l y h a l f of the primary b r i d g e supply (In a l l cases v B r e f e r s t o the B.M.S. V o l t a g e ) . F i g u r e 2C r e p r e s e n t s a Sheatstcne bridge with the f o u r arms e q u a l . In F i g u r e 2B v dV = _B dR 4R and noise voltage i s times s m a l l e r than i n case A. S i g n a l to n o i s e v o l t a g e r a t i o i s then p r o p o r t i o n a l t c VB / 8T 3 " I f power d i s s i p a t e d i n the t h e r m i s t o r i s the same i n both cases V 2 i 2 R = 7 J - ( 1 0 ) and s i g n a l to nois e r a t i o s may be compared. I t f o l l o w s that S/U v o l t a g e r a t i o f o r case A i s ^2 times g r e a t e r than f o r case B, and i s two times g r e a t e r than f o r case C ( F i g . 2C). 56 D i f f i c u l t i e s i n c o n s t r u c t i n g r e l a t i v e l y n o i s e l e s s c u r r e n t and voltage sources would l i k e l y counter the advantages c f case A or B over case C. For t h i s reason, and f o r ease i n c a l c u l a t i o n s , case C w i l l c o ntinue to be used. 3.3 BRIDGE AND DETECTOR RESOLUTION Let A T * be the d e s i r e d temperature r e s o l u t i o n . Then M = A T * R T (11) where A R i s the necessary r e s o l u t i o n i n terms of r e s i s t a n c e . From (9) and (11) I?- = — * — (12) A V A T * R T where A v i s the r e q u i r e d v o l t a g e r e s o l u t i o n cf the d e t e c t o r . Johnson noise power from the bridge i s i d e a l l y Pn = Y= 4kTB (13) where V n i s n o i s e v o l t a g e , k i s Boltzmann's constant, T i s i n degrees K e l v i n , and B i s the bandwidth of the d e t e c t o r . A convenient measure of the q u a l i t y of the d e t e c t o r may be d e f i n e d as S = ^ = n o i s e f i g u r e (14) n V n where AV now r e p r e s e n t s the d e t e c t o r ' s best r e s o l v i n g a b i l i t y R e c a l l from (10) that 57 V P = -2— 4R From (10), (12), (13), and (14) s 2 PR„ A T * = (1 6 ^ X15) T But from (4) P = A T D (16) c A minimum of the sum of A T and A T * occurs at A T * A M - T T - = A T (17) It follows that AT = ( ^ 4 ^ ( 1 8 ) c T AT* = (32XT)1/3 (19) c T AT + AT* = ( 1 0 8 S n 2 k T B ) l / 3 ( 2 Q ) D K m c T Equations (18), (19) and (20) are useful for determining the optimum resolution of any system as the parameters approach the i d e a l . More r e a l i s t i c a l l y i t would be convenient to have an expression for the optimum in terms of the detector resolution Ay. From (13), (14), (18), (19) and (20) 58 AT = ( A V2 1/3 (21) RB CR T AT* = ( 8AV2 1/3 (22) AT + AT* = ( (23) From (21), (22) and (23) d e t e c t o r parameters and power l e v e l s may be o p t i m i z e d , and o v e r a l l a c c u r a c i e s known. Consider f o r example a t h e r m i s t o r with D c = Imwoc - 1 which s h a l l be operated a t 10K^. Suppose our d e t e c t o r has an i n p u t noise v o l t a g e of ivv . Then Here s i g n a l power has been assumed to be egual t o n o i s e power, G e n e r a l l y i t would be d e s i r a b l e t o have s i g n a l t c noise r a t i o s cf a t l e a s t 10dB. Then 3.4 D.C. BRIDGES I f a D.C bridge i s used with a good d e t e c t o r [ e g . ANALOG DEVICES chopper amp. Model 261K] i t would have input n o i s e on AT + AT* = 0.001°C AT + AT* - 0.0023°C 59 the order of 1vv P-P with a bandwidth to 10Ez. Since a reasonable response time i s d e s i r a b l e , a bandwidth c f 5 Hz i s minimal. Input n o i s e voltage d r i f t of 0.1VV°C - 1 would boost e f f e c t i v e input v o l t a g e noise to about 3.5W. T h i s would boost a usable A v to 12PV, and i n our example AT + AT* = 0.0054°C T h i s may be co n s i d e r e d a p r a c t i c a l l i m i t i n g accuracy f o r a t h e r m i s t o r with D c = 1 mwoc - 1 and B = 10Kfi, when d r i v e n by a D.C. system. Other d i f f i c u l t i e s i n v o l v e d i n using a D.C. system a r i s e from thermal voltage o f f s e t s , and from the p r o x i m i t y of 50 Hz or 60 Hz sources. The f i r s t may be helped by s e l e c t i n g a chopper s t a b i l i z e d d e t e c t o r or s i m i l a r d e t e c t o r designed f o r thermal immunity. The second, which may be l a r g e enough to obscure measurements i n s p i t e of a sharp r o l l o f f should be helped by using good s h i e l d i n g and grounding (the most l i k e l y mechanism would be that the t r a n s m i s s i o n l i n e , a c t i n g l i k e an antenna, would provide s u f f i c i e n t common mode s i g n a l to overload the d e t e c t o r i n p u t ) . 3.5 ft, C. EBIDGES I t i s p o s s i b l e t o get a m p l i f i e r s which operate at audio f r e q u e n c i e s , t h a t have c o n s i d e r a b l y l e s s i n p u t noise voltage per u n i t bandwidth than D.C. a m p l i f i e r s . Detectors, e i t h e r phase-locked, or simple, are e a s i l y designed. Bandwidths may 60 be l i m i t e d to l e s s than 100 Bz, which w i l l keep input noise voltage w e l l below the best a v a i l a b l e D.C. d e t e c t o r s . For systems where extremely high p r e c i s i o n i s necessary, the designer may c o n s i d e r using an a.C. voltage source t c feed h i s b r i d g e . However, new design problems accompany the c h o i c e of an A.C. source. The o p e r a t i n g frequency should be kept as low as p o s s i b l e . The reason i s tw o f o l d : f i r s t , s i n c e a lew bandwidth i s d e s i r a b l e , a low c e n t e r frequency would minimize the need fo r a l a r g e Q; second and predominant, the e f f e c t s of s t r a y reactance i n the b r i d g e , and p a r t i c u l a r l y i n the t r a n s m i s s i o n l i n e to the t h e r m i s t o r would be minimized. Belcw 100 Hz f l i c k e r noise predominates and a l l the d i f f i c u l t i e s c f D .C. b r i d g e s ensue. 3.6 OPTIMUM BRIDGE SUPPLIES I t i s p o s s i b l e to use a pulsed power supply or seme ether form of i n t e r m i t t e n t supply. However i n no case can one improve on e i t h e r a pure D.C. or pure sine wave source i f one c o n s i d e r s the s i g n a l to noise r a t i o . T h i s can be shown as f o l l o w s . S i n c e a l l measurements must be of f i n i t e d u r a t i o n we can assume t h a t the power supply p a t t e r n r e p e a t s r e g u l a r l y . Consider i t s F o u r i e r decomposition. The maximum s i g n a l to noise r a t i o occurs when a l l the s i g n a l power i s confi n e d to the minimum bandwidth; i . e . i n one component. Any attempt cf 61 spreading the s i g n a l power among more than one component n e c e s s a r i l y i n c r e a s e s the r e q u i r e d bandwidth of the d e t e c t o r and thus i n c r e a s e s n o i s e . Hence a s i n g l e component, sine wave or pure D.C. i s o p t i m a l . 4 TRANSMISSION LINE EFFECTS 4.1 TRANSMISSION LINE RESISTANCE Presumably i t i s p o s s i b l e t c determine the r e s i s t a n c e of the t r a n s m i s s i o n l i n e being used, or at l e a s t get an estimate well w i t h i n the r e q u i r e d accuracy. T h i s may then be c o r r e c t e d f o r when determining the a c t u a l t h e r m i s t o r r e s i s t a n c e . I f a t h r e e or f o u r wire t r a n s m i s s i o n l i n e i s used, the problem can be e l i m i n a t e d e n t i r e l y . 4.2 TRANSMISSION LINE REACTANCE In an A.C. b r i d g e , i t i s d e s i r a b l e to know what the maximum t r a n s m i s s i o n l i n e c a p a c i t a n c e C i s which w i l l s t i l l permit a nul l of amplitude v. I f C i s s u f f i c i e n t l y s m a l l , then i t s e f f e c t i s to phase s h i f t the c u r r e n t , amplitude changes being second o r d e r . The c o n s t r a i n t on C i s a)RC < ^ (24) B I f the d e t e c t o r i s phase-locked then 62 ^ o b s e r v e d — / / R j ioC a c t u a l (25) To a f i r s t approximation AR = R - R = f ( c o R C ) 2 (26) a c t u a l o b s e r v e d 2 ' provided the transmission l i n e i s short (this error w i l l usually be s u f f i c i e n t l y small that an estimate of C w i l l y i e l d a correction AR of s u f f i c i e n t accuracy). 5 EVALUATION OF AVAILABLE SYSTEMS (DMM.S) On the basis of (16) and the r e l a t i o n cf A T * tc P (from (13) (14) and (15)) AT* = (27) Rt7PR~ It i s possible to evaluate and compare measurement systems for a given R and Dc. The following d i g i t a l multimeters have been evaluated as thermistor measurement systems with respect to thermistor selfheating, displayed p r e c i s i o n , guaranteed accuracy, each when used with a FENHAL GB34P2 thermistor - 10K < R < 15K, D c = Imwoc-i. 63 FLUKE MODEL 8 100A FLUKE MODEL 8000A DANAMETER 2000 DATA PRECISION 245 SYSTRON DONNER 7205 SYSTRCN DONNER 7050 SYSTRON DONNER 7005 TABLE 1: DIGITAL MULTIMETERS Table Two l i s t s pertinent data. CONCLUSION Present technology can e a s i l y y i e l d a device for measuring thermistor resistances within 0.01°C, however the value of achieving t h i s resolution of absolute temperature measurements can be guestioned. In deep boreholes, where the thermistor resistances are used to i n f e r both absolute temperatures and temperature gradients, the thermistors are not recoverable and long term s t a b i l i t y l i m i t s the accuracy possibly tc only 0.4°c (Muller S Stolton, 1953) although 0.08<>c i s more common [Fenwal- TI-1] and0.02<>C i s possible (Beck, 1956). 64 Ar Errors in Temperature Measurement vs..Power to a FENWAL GB34P2 Thermistor, for Seven Digital Voltmeters The diagonal line represents thermistor self-heating. The thick error bars represent the meter resolution. The thin error bars represent the meter accuracy. The numbers in circles indicate the points plotted from Table 2. FIGURE 3: DIGITAL "MULTIMETER ERRORS 65 UNIT RANGE POWER AT AT* ( 1 ) AT* (2) FLUKE 8100A 1 2 K f i 120yW 0 . 1 2°C 0.002OC 0.02OC CD 1 2 0 Kfi 13yW 0.013«c 0 . 0 2 « C 0 . 2 ° C DATA PRECISION 245 20Ktt 1, 3mW 1.3«c 0 . 0 0 2 « C 0. 1 °C DANAMETER 2000 ® 20Kfi 140yW 0 . 1 4 ° C 0.02OC 0. 04 OC FLUKE 8000A 20Kfi 120yW 0.120C 0 . 0 2 ° C 0.06OC ® SYSTRON DONNE R 7050 150Kfi 1. 2yW 0 . 0 0 1 ° C 0. 2°C 0 . 2 8 ° C SYSTRON DONNER 7205 130Kfi 1.2yW 0 . 0 0 1 « C 0.002OC 0 . 0 1 ° C 13KR 120yW 0 . 1 2 ° C 0 . 0 0 0 2 « C 0 . 0 0 1 ° C SYSTRON DONNER 7005 ® 130Kfi 30yW 0 . 0 3 ° C 0 . 0 2 « C 0 . 0 4 O C 13Kfi 3mW 30C 0 . 0 0 2 ° C 0.004OC TABLE 2: DIGITAL HULTIKETER ERRORS Data l i n e s followed by numbers in c i r c l e s are graphed for comparison in Figure 3, AT*(1) i s the re so lu t ion determined by the number of ava i lab le d i g i t s . AT* (2) i s the e f fec t ive guaranteed accuracy of the meter. In shallow experiments such as snow pack s tudies , or permafrost de tec t ion , f ine temperature re so lu t ion i s not required s ince i n one case the temperature var ia t ions are gross and nonl inear , and i n the l a t t e r the experimenter general ly wishes only to detect subfreezing temperatures, not to estimate them. The greatest value in achieving f ine resolut ion of thermistor res i s tances l i e s f i r s t i n thermistor c a l i b r a t i o n s (it i s poss ible to achieve 0.03$ accuracy ea s i ly and rapidly) and in experiments where temperature transients are measured. Thermistor measurement technique i s an important considerat ion in any temperature measurement system where 66 optimum accuracy i s r e q u i r e d . E r r o r s due to t h e r m i s t o r s t a b i l i t y , r e f e r e n c e temperatures, and measurement are comparable i n magnitude. As the q u a l i t y of t h e r m i s t o r s and thermometers improve, so should the techniques of t h e r m i s t o r use. 67 BIBLIOGRAPHY Baxa n d a l l , P. J . 1968. Noise i n t r a n s i s t o r c i r c u i t s , part 1. Wi£§lgss World, November 1968, p. 388-92. Ba x a n d a l l , P. J, 1968. Noise i n t r a n s i s t o r c i r c u i t s , p a r t 2. Wireless World, December 1968, p. 454-59. Beck, A. 1956. The s t a b i l i t y of t h e r m i s t o r s . J o u r n a l of S c i e n t i f i c Instruments, V o l . 33, p. 16-18. Beck, A. E. 1963. L i g h t w e i g h t borehole temperature measuring eguipment f o r r e s i s t a n c e thermometers, J o u r n a l c f S c i e n t i f i c Instruments, V o l s . 40, p. 452-47" Bosson, G., Gutmann, F., and Simmons, 1. M. 1950. A r e l a t i o n s h i p between r e s i s t a n c e and temperature of t h e r m i s t o r s . J o u r n a l of A p p l i e d P h y s i c s , V c l . 32, No. 2, p. 1267-68. " Carslaw, H. S., and Jaeger, J . C. 1959. Conduction c f heat i n s o l i d s , second e d i t i o n . Oxford Clarendon Press. C l a r k e , G. K. C , and Goodman, R. (In press) Radio echo sounding and i c e temperature measurements i n a surge type g l a c i e r . J o u r n a l of G l a c i o l o g y . Classen, D. F., and C l a r k e , G. K. C. 1972. Thermal d r i l l i n g and i c e temperature measurements i n the Rusty G l a c i e r ( i n B u s h n e l l , V. C. and Ragle, R. E. Ed. I c e f i e l d Ranges Research P r o j e c t . S c i e n t i f i c R e s u l t s . V o l . 3. New York, American G e o g r a p h i c a l S o c i e t y ; Montreal A r c t i c I n s t i t u t e of North America, p. 103-16). Doucet, Y., and Guignard, J . P. 1952. E s s a i d ' i n t e r p r e t a t i o n de l a l o i ~ d o n n a n t l a r e s i s t a n c e des " t h e r m i s t o r s " en f o n c t i o n de l a temperature. Academie des Sciences-Ccmptes Rendus, V o l . 234, No. 19, p7 1856-58." 68 G a r f i n k e l , C. I. 1974. How to match readouts to temperature t r a n s d u c e r s . E l e c t r o n i c s , v o l . 47, Ho.. 24, p. 117-123. G r e e n h i l l , E. B., and Whitehead, J. R. 1949. An apparatus f o r measuring s m a l l temperature changes i n l i g u i d s . J o u r n a l of S c i e n t i f i c Instruments, V o l . 2 6, p. 92-95. H a r r i s o n , W. D. 1972, Temperature of a temperate g l a c i e r . J o u r n a l of G l a c i o l o g y , V o l . 11, So. 61, p. 15-29. J a r v i s , G. T. (unpublished) Thermal s t u d i e s r e l a t e d to surging g l a c i e r s . (M.Sc. T h e s i s , U.B.C. 1973). J a r v i s , G. T., and C l a r k e , G. K. C. (unpublished) The thermal regime of Tra p r i d g e G l a c i e r and i t s relevance to g l a c i e r s u r g i n g . Jessop, A. M. 1964. A lead-compensated t h e r m i s t o r probe. J o u r n a l of S c i e n t i f i c Instruments, V o l . 41, p. 503-504. Jessop, A. M., and Judge, A. S, 1974. Temperature measurement i n boreholes f o r the mining i n d u s t r y . d i v i s i o n of Seismology^ E a r t h P h y s i c s B r a n c h x Department of Energy^ Mines and Resources^ Ottawa^ Canada. l e t z t e r , S., and Webster, ft. 1970. Noise i n a m p l i f i e r s . IJEJ Spectrum, August 1970, p. 67-75. ~ L l i b o u t r y , L. 1971. P e r m e a b i l i t y , b r i n e content, and temperature of temperate i c e . J o u r n a l of G l a c i o l c g y , V o l . 10, No. 58, p. 15-29. Misener, A. D., and Thompson, L. G. D. 1952. The pressure c o e f f i c i e n t o f r e s i s t a n c e of t h e r m i s t o r s . Canadian J o u r n a l of Technology, V o l . 30, p. 89-94. M u l l e r , R. H., and S t o l t o n , H. J . 1953. Use of t h e r m i s t o r s i n p r e c i s e measurements of s m a l l temperature d i f f e r e n c e s . A n a l y t i c a l Chemistry, V o l . 25, No. 7, p. 110 3-06. 69 Paterson, S. B. 1972. Temperature d i s t r i b u t i o n i n the upper l a y e r s of the a b l a t i o n area of Athabasca G l a c i e r , A l b e r t a , Canada. J o u r n a l of G l a c i o l o g y , V o l . 11, He. 61, p. 31-41. S t a l e y , R. C. 1952. Performance c h a r a c t e r i s t i c s of Sanbcrn rod t h e r m i s t o r s . American M e t e o r o l o g i c a l S o c i e t y B u l l e t i n , V o l . 32, No. 2, p7~ 67-727" S t u a r t , J . R. 1973. An approach to audio a m p l i f i e r design, part 1. W i r e l e s s World, August 1973, p. 387-91, S t u a r t , J, R, 1973, An approach to audio a m p l i f i e r design, part 2. Wireless World, September 1973, p. 439-46. S t u a r t , J . R. 1973. An approach to audio a m p l i f i e r d e s i g n , part 3. W i r e l e s s World, October 1973, p. 491-94. T e c h n i c a l Note: Thermistor Manual. FENWAL ELECTRON ICS, INC., EMC-5. T e c h n i c a l Note: [ T h e r m i s t o r ] S t a b i l i t y and R e l i a b i l i t y C h a r a c t e r i s t i c s . FENWAL ELECTRONICS, INC., TC-1. T e c h n i c a l Note: C o n s i d e r a t i o n s i n the t e s t i n g cf t h e r m i s t o r s . FENWAL ELECTRONICS, INC., TD-2, EM-34/ R e v i s i o n 2. 

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