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Gravity and temperature measurements on the Fox Glacier, Yukon Crossley, David John 1969

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GRAVITY AND TEMPERATURE MEASUREMENTS ON THE FOX GLACIER, YUKON by DAVID JOHN CROSSLEY B . S c , Univers i ty of Newcastle-Upon-Tyne , 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of GEOPHYSICS We accept- th is thesis as conforming to the required /Standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u rposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada CD ABSTRACT During the summer of 1968 a gravi ty survey was conducted over the Fox* G l a c i e r , Yukon T e r r i t o r y , for the purpose of f inding ice depths. Choice of the Fox G l a c i e r was as a resu l t of i t s predicted surge, and the survey was part of a long-term analysis of the phys ica l condit ion of the g l a c i e r . Although seismic sounding was attempted, the thinness of the g lac i er prevented successful r e s u l t s . Analys i s of the gravity measurements indicated 88m as the maximum depth; comparison with depths from three d r i l l e d holes showed that the gravi ty resul ts were not ser ious ly in e r r o r . A small near-surface temperature program was completed and the resu l t s ident i fy the Fox as a sub-polar g l a c i e r . This i s not an o f f i c i a l l y accepted name. ( i i ) TABLE OF CONTENTS PAGE -ABSTRACT (i) TABLE OF CONTENTS ( i i ) LIST OF TABLES (iv) LIST OF FIGURES (v) ACKNOWLEDGMENTS (vi) 1. INTRODUCTION 1.1 G lac i er surges 1 1.2 The Fox G l a c i e r region 2 1.3 Other studies 4 2. THE GRAVITY MEASUREMENTS AND THEIR REDUCTION 2.1 Instrumental 5 2.2 Experimental 5 2.3 The s ta t ion data 8 2.4 Instrument d r i f t 9 2.5 Least squares analysis H 2.6 Standard reductions 12 2.7 Terra in correct ions 14 2.8 The reg ional gradient correct ion 17 3. INTERPRETATION OF THE RESIDUAL ANOMALIES 3.1 General theory 22 3.2 Integration method 2 3 3.3 Adjustment of the res iduals 37 3.4 Concluding remarks 38 4. TEMPERATURE MEASUREMENTS 4.1 The equipment 4 0 ( i i i ) PAGE 4.2 Comments on the resul t s 41 4.3 The impl icat ions of temperature measurements 43 4.4 Summary and r e l a t i o n to surges 50 BIBLIOGRAPHY APPENDIX A THEORETICAL RESULTS A . I Prism integrat ion for g r a v i t a t i o n a l a t t r a c t i o n 56 A.2 The d i f f u s i o n of a thermal wave into a g lac i er ,-58" APPENDIX B TABLES OF RESULTS 65 (iv) LIST OF TABLES PAGE 1 F i e l d data for c i r c u i t s 66 2 The s ta t ion data 69 3 Data for least-squares reduction 71 4 Data for least-squares so lut ion 72 5 Correct ions to gravity 73 6 Regional gradient 75 7 Anomalies and depths 76 8 Temperature measurements 78 9 Climate data 80 10 Data for ef fect of accumulation on temperature 81 (v) LIST OF FIGURES PAGE 1 Location of Fox Glac i er 3 2 Glac ier sketch showing gravi ty stat ions 6 3 Gravi ty network 7 4 Plot for d r i f t rate 10 5 Contour map of Bouguer anomalies 18 6 Contour map of res idua l anomalies 21 7 A port ion of the prism network 24 8 Contour map of g lac i er depths 26 9a-9d Transverse depth p r o f i l e s 27 9e Longi tudinal depth p r o f i l e 31 9f Sample of least squares adjustment 32 lOa-lOd Observed and calculated anomalies 33 11 Temperature data 42 12 Estimated c l i m a t i c var ia t ions for the Fox Glac i er 45 13 Ef fec t of accumulation rate 49 14 Ef fec t of snow cover on the penetrat ion of the "63 < annual cold wave (vi) ACKNOWLEDGMENTS I wish to thank the fol lowing people and organisations for the i r ass i s tance . The seismic apparatus was provided./by Dr. W. A. Weeks and the U. S. Army T e r r e s t r i a l Sciences Center (formerly C . R . R . E . L . ) , Hanover, New Hampshire; Dr. J . Tanner and the Gravi ty D i v i s i o n , Dominion Observatory, Ottawa, generously loaned a gravimeter at short not i ce . The I c e f i e l d Ranges Research Project* gave invaluable l o g i s t i c support; spec ia l thanks go to Dr. M. Marcus the d i r e c t o r , and P h i l Upton the p i l o t . Sam C o l l i n s was an excel lent leader at Fox Camp, David Harrison and Patr ick Powell were commendable f i e l d ass i s tants . The help given both by Dr . A. Stanley, Inland Waters Branch, Department of Energy, Mines and Resources, Ottawa, and Dick Ragie was great ly appreciated. F i n a l l y I am.indebted to my supervisor , Dr .G.Clarke , for his in teres t and guidance throughout this" work*. F i n a n c i a l support was obtained from A . I . N . A . and the Nat ional Research C o u n c i l . * Sponsored j o i n t l y by the A r c t i c Ins t i tute of North America ( A . I . N . A . ) and the American Geographical Society . Department of Geophysics, Univers i ty of B r i t i s h Columbia. 1 1. INTRODUCTION This thesis is concerned with gravi ty and temperature measurements made during 1968 on the Fox G l a c i e r , Yukon T e r r i t o r y . The gravi ty survey is the major part of the thesis and i t s purpose was to determine the depth of the g l a c i e r . The temperature measurements were made i n the upper 8m of i c e . It is considered worthwhile to begin with a b r i e f d iscuss ion of g l a c i e r surges. 1.1 G l a c i e r Surges A surging g l a c i e r i s a g l a c i e r which advances, p e r i o d i c a l l y , at a rate much higher than i t s normal flow ra te . An example of a surging g l a c i e r is the Steele G l a c i e r , Yukon, the snout of which advanced about f ive miles during 1966-1967. A c l a s s i f i c a t i o n system for this type of g lac i er has been given by Meier and Post (1968) , and the ir geographical locat ion was discussed recently by Post (1969). Deep crevassing extends over most of the surging g l a c i e r due to t ens i l e stresses at the surface . Because of the fragmented condit ion of the g l a c i e r , surface measurements are d i f f i c u l t and l i t t l e information on the i r phys ica l propert ies is a v a i l a b l e . As a resu l t of a .successful pred ic t ion of the surge of the Steele G l a c i e r , Aust in Post was led to suggest that the Fox Glac i er may surge. For this reason a continuing inves t iga t ion of the g l a c i e r was begun, and the present work forms part of the 1968 program. 2 As a means o f d e t e r m i n i n g g l a c i e r d e p t h , g r a v i t y surveys have o f t e n been used to supplement the more accura te s e i s m i c r e f l e c t i o n method. Attempts t o d e t e c t a s e i s m i c r e f l e c t i o n from the bottom of the Fox were u n s u c c e s s f u l , and i t was con-c l u d e d from the records t h a t the g l a c i e r was l e s s than 150 m t h i c k . The r e l e v a n c e of bedrock p r o f i l e s to the s u r g i n g mechanism depends on the s o l u t i o n of g l a c i e r f l o w , f i r s t t r e a t e d by Nye (1951, 1952) . R e l a t i o n s h i p s govern ing the s l i p r a t e of a g l a c i e r pas t i t s b e d , i c e t h i c k n e s s , and s t r a i n h e a t i n g depend on depth p r o f i l e s or bedrock s l o p e s . For the water l u b r i c a t i o n theory put forward by Weertman (1962) , roughness o f the g l a c i e r bed and b a s a l temperature are i m p o r t a n t . 1. 2 The Fox G l a c i e r Region The Fox G l a c i e r i s l o c a t e d i n a s m a l l v a l l e y between the S t e e l e and Hodgson G l a c i e r s ( F i g u r e 1 ) . Nearby are two s m a l l e r g l a c i e r s , the J a c k a l and the Hyena , which share common m e l t -water dra inage w i t h the Fox . A s i n g l e c i r q u e s n o w f i e l d at the s o u t h e r n end of the Fox i s m i l d l y c revas sed near the v a l l e y w a l l s . The s u r r o u n d i n g t e r r a i n i s mountainous : to the south acros s the Hodgson V a l l e y i s M t . S t e e l e , and to the west l i e s M t . Wood ( F i g u r e 1 ) . A g e o l o g i c s tudy o f the S t e e l e G l a c i e r v a l l e y by Sharp (1943) i n c l u d e d some o f the area to the n o r t h e a s t o f the Fox . The predominant s t r u c t u r e was a basement of Devonian marble o v e r l a i n by four to f i v e thousand f e e t of s t r a t i f i e d T e r t i a r y 3 4 volcanics. Of interest to the history of the Fox i s the morainal evidence found by Sharp for a marked advance of the Steele ending 100-200 years ago; the advance occurred at the same time as s i m i l a r a c t i v i t y on the coastal Alaskan g l a c i e r s . This general g l a c i e r advance, due probably to c l i m a t i c change, appears to be related to the existence of moraines at the foot of the Fox Valley which suggest a simultaneous advance of the Fox, Jackal and Hyena Glaciers at about that time. Further examination of the morainal patterns indicates that since the general advance, the three glaciers have each surged independently at least once. G. Denton (U.S.G.S.) i s investigating the moraine geology in more d e t a i l . 1.3 Other Studies Concurrent with the gravity and temperature measurements, other f i e l d work was undertaken during 1968. Radio echo sounding apparatus was used over the upper portion of the g l a c i e r , but due either to water absorption or improperly working equipment, no useful results were obtained. The movement stakes d r i l l e d into the glacier during 1967 were re-surveyed and the results analysed for g l a c i e r flow ( C o l l i n s , personal communication). Brewer (1969, personal communication) completed mass balance calculations based on snow and ice ablation, and ice-core samples were taken over most of the g l a c i e r by K. West for 0 1 8 / 0 1 6 dating. The hydrology associated with the meltwater drainage of the Fox, Jackal and Hyena Glaciers was undertaken by T. Faber. 5 2. THE GRAVITY MEASUREMENTS AND THEIR REDUCTION 2.1 I n s t r u m e n t a l The ins t rument used i n the survey was a Sharpe G r a v i t y Meter (No. C132) w i t h a f a c t o r y c a l i b r a t i o n cons tant o f 0.10135 m g a l s / d i v i s i o n . As the c a l i b r a t i o n was made i n 1967 and d i f f e r e d by o n l y 0.00005 m g a l s / d i v i s i o n from one done i n 1965, i t was assumed tha t t h i s cons tant was s u f f i c i e n t l y accura te f o r the p r e c i s i o n o f the read ings ( ± 0.001 m g a l s ) . 2.2 E x p e r i m e n t a l F i g u r e 2 i s a s k e t c h o f the g l a c i e r showing the p o s i t i o n s o f 66 s takes which had been d r i l l e d i n t o the i c e d u r i n g the summer o f 1967. These s takes served as the b a s i s f o r the g r a v i t y network i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 3. T h i s network c o n s i s t e d of 22 c l o s e d loops which i n c l u d e d , i n a d d i t i o n t o the s t a k e s , 9 survey s t a t i o n s s i t u a t e d on e l e v a t e d rock outcrops around the edge o f the g l a c i e r , and 14 r o c k c a i r n s s e t up on bedrock at the ends of g l a c i e r t r a v e r s e s . The loops are numbered f o r convenience i n comput ing , and the arrows i n d i c a t e the d i r e c t i o n s i n which the loop read ings were t a k e n . Tab le 1 g ives the f i e l d da ta f o r the c i r c u i t s t o g e t h e r w i t h the m i s c l o s u r e and the e l a p s e d t i m e . As the g rav imeter was a s h o r t range ins t rument w i t h a s c a l e w i d t h o f 1000 d i v i s i o n s (about 100 m g a l s ) , s e v e r a l r e s c a l i n g o p e r a t i o n s were n e c e s s a r y to cover the e l e v a t i o n d i f f e r e n c e between the -8000 7000 -6000 + Y 5000 (678) 4000 o H A N K V V * \ \ T V ts \ LEGEND Stations 1-18 are edge cairns or survey points Stations 20-85 are g lac i er stakes UTM coordinates are in meters X=Easting Y^Northing (The numbers in brackets are henceforth omitted) T - a temperature hole . 0 Approx g lac i er edge from map /? '4 (53)7000 8000 Figure 2. G lac i er Sketch Showing Gravity Stat ions . (The numbers do not refer to stakes-see Table 2) Figure 3. Gravity Network. The junctions are i d e n t i f i e d in Table 4. 8 l o w e s t and h i g h e s t s t a t i o n s . I n s u f f i c i e n t t i m e p r e v e n t e d t h e t y i n g o f t h e network t o an a b s o l u t e pendulum measurement i n t h e v i c i n i t y . 2.3 The S t a t i o n D a t a The UTM ( U n i v e r s a l T r a n s v e r s e M e r c a t o r ) c o o r d i n a t e s and e l e v a t i o n above s e a l e v e l o f t h e g l a c i e r s t a t i o n s were d e t e r m i n e d f r o m a t h e o d o l i t e s u r v e y i n 1968 t o an a c c u r a c y o f ±lm f o r t h e UTM c o o r d i n a t e s and about ±0.02m f o r t h e e l e v a t i o n s . The c o o r d i n a t e s and e l e v a t i o n s o f t h e edge s t a t i o n s were o b t a i n e d from a l e s s p r e c i s e i n d e p e n d e n t s u r v e y , w i t h i n ±lm and an e s t i m a t e d ±0.15m r e s p e c t i v e l y . S i n c e t h e main s u r v e y d e t e r m i n e d t h e e l e v a t i o n t o t h e t o p o f t h e s t a k e s , a c o r r e c t i o n was a p p l i e d t o a l l o w f o r t h e h e i g h t o f t h e s t a k e above t h e snow o r i c e s u r f a c e . The s t a k e h e i g h t s were o b t a i n e d f o r t h e d a t e s a t w h i c h t h e g r a v i t y r e a d i n g s were t a k e n by u s i n g a c a l i b r a t e d m e a s u r i n g r o d when t h e g r a v i t y was measured, or by c a l c u l a t i n g t h e h e i g h t f r o m a d i r e c t r e a d i n g a t some o t h e r d a t e and u s i n g t h e a b l a t i o n r a t e a t t h e s t a k e . U n c e r t a i n t i e s i n t h e s t a k e h e i g h t s t h u s f o u n d were due t o measurement e r r o r s and f l u c t u a t i o n s i n t h e a b l a t i o n r a t e ; t h e l o w e r i n g o f t h e g l a c i e r s u r f a c e between g r a v i t y r e a d i n g s on d i f f e r e n t l o o p s was o t h e r w i s e i g n o r e d . T a b l e 2 l i s t s t he UTM c o o r d i n a t e s , s t a k e h e i g h t s , and c o r r e c t e d e l e v a t i o n s f o r t h e g r a v i t y s t a t i o n s . An e s t i m a t i o n o f t h e a c c u r a c y o f t h e s t a k e h e i g h t s i n T a b l e 2 y i e l d e d ±0.03m, so t h a t t h e combined e r r o r s i n t h e s t a t i o n e l e v a t i o n s 9 amount t o ±0.05m f o r t h e g l a c i e r s t a t i o n s and +0.18m f o r t h e edge s t a t i o n s . 2 . 4 I n s t r u m e n t D r i f t A g r a v i m e t e r i s u s u a l l y s u b j e c t t o d r i f t c a u s e d by t h e r m a l f l u c t u a t i o n s , t i d a l e f f e c t s c a u s e d by t h e r e l a t i v e p o s i t i o n s o f t h e Sun, Moon and E a r t h , and m e c h a n i c a l r e l a x a t i o n o f i t s components.. I n t h e i n s t r u m e n t u s e d , t h e r m a l d r i f t was m i n i m i s e d by vacuum s e a l i n g and t h e u s e o f c o m p e n s a t i n g s p r i n g s . ' F r e q u e n t r e s e t t i n g o f t h e i n s t r u m e n t a d j u s t m e n t s p r e v e n t e d e x c e s s i v e z e r o e r r o r f r o m m e c h a n i c a l r e l a x a t i o n . The m i s c l o s u r e s a r e shown p l o t t e d a g a i n s t e l a p s e d t i m e i n F i g u r e 4. The l a c k o f any o b v i o u s c o r r e l a t i o n i n d i c a t e s t h a t any d r i f t was s m a l l compared t o random measurement e r r o r s . As a f u r t h e r c h e c k t h e m i s c l o s u r e s were p l o t t e d on a h i s t o g r a m and t r e a t e d as a 'no r m a l ' d i s t r i b u t i o n ; t h e mean was 0.82 s c a l e d i v i s i o n s and t h e s t a n d a r d d e v i a t i o n was 1.78 d i v i s i o n s . A s s u m i n g t h a t f o r 22 c i r c u i t s t h e m i s -c l o s u r e s s h o u l d be n o r m a l l y d i s t r i b u t e d a bout a mean o f z e r o , a d r i f t r a t e o f 0.24 d i v i s i o n s / h o u r was d e d u c e d , and t h i s gave a s t a n d a r d d e v i a t i o n o f 1.75 d i v i s i o n s . The n o n - a d j u s t e d m i s c l o s u r e s were t h e n t r e a t e d as a n o r m a l d i s t r i b u t i o n a bout a mean o f z e r o t o g i v e a s t a n d a r d d e v i a t i o n o f 1.95 d i v i s i o n s . C o m p a r i s o n o f t h e s e t h r e e r e s u l t s showed t h a t t h e b e s t f i t t o a n o r m a l d i s t r i b u t i o n was g i v e n by a s s u m i n g t h a t t h e r e was no i n s t r u m e n t d r i f t and t h e mean o f t h e o b s e r v e d m i s c l o s u r e s was z e r o . Hence a d r i f t a d j u s t m e n t was n o t c o n s i d e r e d n e c e s s a r y . 10 5 r-V) C o •H </) •H > •H 0) rH etf O rH to o I—I u -1 -2 J_ 3 4 Elapsed Time (hrs) F i g u r e d . Plot For D r i f t Rate 11 2.5 Least Squares Analys is Gibson (1941) gave d e ta i l s of the app l i ca t ion of the least squares p r i n c i p l e to the treatment of data i n the form of a network such as the present survey, and his analysis i s followed here. The f i r s t requirement was to se lect a weighting factor for the readings based on the r e l a t i v e accuracy of the data i n each c i r c u i t . The factor . , 3 / 10  ° \T Elapsed Time x Misclosure was found to give a range of weights from 1 - 3 and assigned the weights roughly i n agreement with est imations , i . e . a short c i r c u i t which closed wel l was considered 'good'. Averaging the weights of two adjacent c i r c u i t s gave the weights associated with arms between junctions as shown in Figure 3. As Gibson showed, the least-squares so lut ion s a t i s f i e s the condit ions that the sum of corrected observations around any c i r c u i t is zero and the sum of correct ions at any junct ion is zero. For the gravi ty network the observed di f ference between junctions was taken as the weighted average of junction differences measured on adjacent c i r c u i t s , with the sign convention that differences measured away from a junct ion were p o s i t i v e . Table 3 contains the weighted averages between junctions and the sums of weighted differences at the junct ions . The normal equations can then be wr i t t en : , 12 7 . 9 g l - 2 .4g 2 - 3 .2g 3 - 2 .3g 4 = -160.49 - 2 .4g 1 + 7 .4g 2 - 2 .1g 3 - 2 .3g y = 702.75 etc . for a l l 22 junct ions . The g's are the unknown gravi ty values at the junct ions . So lut ion of this system of equations resul ted i n the gravi ty values g^ shown i n Table 4; stat ions ly ing between two junctions were treated by d i v i d i n g the adjustment by the number of readings along the l ine and taking weighted averages of such adjustments from adjacent c i r c u i t s . By taking the r . m . s . deviat ion of 48 calculated minus measured dif ferences between junct ions , i t was estimated that the least-squares values were not i n error by more than ± 0.68 d i v i s i o n s (± 0.07 mgals). 2.6 Standard Reductions Adjustments to gravity readings have to be made to allow for the effects of l a t i t u d e , e l eva t ion , topography and var ia t ions i n rock density i n the survey area; the brev i ty of the fol lowing treatment i s in accordance with i t s common usage. A l l reductions were referred to the southernmost s t a t i o n , point ' C l i f f . 2.6.1 - Rock density As noted by Clarke (1967) and others , rock density in the v i c i n i t y of g lac iated areas i s d i f f i c u l t to obtain accurately since access ible rock outcrops tend to be more res i s tant to erosion and hence not t y p i c a l of the subglacier 13 b e d r o c k . For t h i s reason no sampl ing of rock was at tempted f o r d e n s i t y and the commonly quoted va lue o f 2.67 gms/cm was used i n the c a l c u l a t i o n s . For the type o f rock d e s c r i b e d by Sharp f o r the Fox r e g i o n , t h i s d e n s i t y does not seem at a l l u n r e a s o n a b l e . Measurements o f i c e d e n s i t y from the _ 3 s u r f a c e o f the Fox y i e l d e d an averaged va lue of 0 .89 gms/cm but a l l o w i n g f o r i c e compact ion at depth the more commonly used va lue o f 0.90 gms/cm ^ seems b e t t e r . 2 .6 .2 - L a t i t u d e c o r r e c t i o n U s i n g the 1930 v e r s i o n o f the I n t e r n a t i o n a l G r a v i t y Formula : Y = 978049.0 CI + 0.00052884) sin2<f> - 0.0000059 s i n 2 2<fr) mgals f o r a s t a t i o n at sea l e v e l and l a t i t u d e <j>, adjustments were made f o r the l a t i t u d e d i f f e r e n c e between the r e f e r e n c e s t a t i o n and a l l o ther s t a t i o n s . S ince exact l a t i t u d e s were a v a i l a b l e f o r o n l y the survey p o i n t s , l i n e a r i n t e r p o l a t i o n was used to o b t a i n the l a t i t u d e s o f the remain ing s t a t i o n s . The p r o b a b l e e r r o r s f o r t h i s c o r r e c t i o n are n e g l i g i b l e f o r UTM c o o r d i n a t e s known to ± l m , s i n c e ^ - 437.54 m g a l s / d e g r e e , f o r l a t i t u d e 6 2 ° 1 2 ' . Assuming s p h e r i c a l geometry, one ob ta in s ^ = 0.000069 mgals/m f o r the e r r o r i n ground measurements. 2 . 6 . 3 - The f r e e - a i r c o r r e c t i o n A l l o w i n g f o r the v a r i a t i o n o f g r a v i t y i n e l e v a t i o n h from the geoid^ t h i s c o r r e c t i o n i s : 14 jjjj- = - 0.30855 - 0.00022cos2<j, + 0.000144 h mgals/m, (h in km). For reference s ta t ion ' C l i f f th is i s - 0.3083 mgals/m. 2.6.4 - The Bouguer correct ion The Bouguer correct ion allows for the a t t r a c t i o n of an i n f i n i t e slab of rock material between the measurement point and mean sea l e v e l . The correc t ion is 2irGp mgals/m, where G is the G r a v i t a t i o n a l Constant and p the mean rock dens i ty . Subst i tut ion for the assumed values gives a correc t ion of 0.111946 mgals/m. Together with the f r e e - a i r correct ion the t o t a l v a r i a t i o n of gravi ty with e levat ion is - 0.1964 mgals/m. As determined in (2.3), uncerta int ies in the s ta t ion elevations can now be converted to mgals to give ± 0.009 mgals for g l a c i e r stat ions and ± 0.030 mgals for edge s t a t i o n s . Using 901 confidence l i m i t s these errors become ± 0.012 and ± 0.050 mgals re spec t ive ly . The reductions of (2.6) can be found l i s t e d in Table 5. 2.7 T e r r a i n Corrections In any survey where the topography near a gravi ty s ta t ion d i f f e r s from a hor i zonta l plane through the s t a t i o n , a correc t ion has to be made for the a t t r a c t i o n of the mater ia l above and below that plane. In mountainous t e r r a i n this a t t r a c t i o n cari.be of the order of several m i l l i g a l s and can become the least cer ta in addit ion to the gravi ty readings. An i n i t i a l inspect ion of the simple Bouguer anomalies at s tat ions on the edge and middle of the Fox suggested that 15 the difference of 2.5 mgals between these stations was the same magnitude as the expected t e r r a i n corrections. The topography surrounding the Fox Glacier consists of high l a t e r a l moraines, those on the lower h a l f of the gl a c i e r being ice-cored to uncertain depth, and glaciers to the south and east occupying deep va l l e y s . The lack of symmetry in the geometric shapes of the te r r a i n precluded two-dimensional integration for the a t t r a c t i o n . Due to the lo c a l i s e d area of the survey, hand computations using the zone system of Hammer (1939) were considered suitable. These corrections were made possible by a 1:10,000 scale map of the Fox and environs provided by the Mapping and Charting Establishment, Canadian Forces Headquarters in Ottawa. The tables included by Hammer for the att r a c t i o n of the zones were too limited to allow for the elevation differences encountered and the tables \^ere extended. In addition the attractions of the zones were computed.for both rock and ice densities to allow for compartments which included both materials. There are several ways of making these corrections, and the method adopted i s given in more d e t a i l . The two sketches below show a gravity station P situated on uneven t e r r a i n , (i) i s at the edge of the gla c i e r and ( i i ) i s on gla c i e r i c e . In both cases the Bouguer correction compensates for rock material up to the datum through P, and the t e r r a i n correction must not remove the anomaly due to the ic e . In case (i) the ef f e c t of the rock above P and the deficiency of the material between the datum through P 16 (i) ( i i ) and the ice surface were both removed as rock. The same correc t ion for the def ic iency below P s t i l l applies for case ( i i ) . The materia l above P now consists of ice and rock and was removed according to the d i f f erent dens i t ies and fract ions ly ing \tfithin a s ing le compartment. It i s c lear that correct ions made i n this way cannot be made without an i n i t i a l assumption about the depth of ice to be removed in case ( i i ) , and for th is reason 50 m was assumed to be the depth of a l l g l a c i a l i c e . Natura l ly the depth of the Fox w i l l d i f f e r from the 50 m allowed in the t e r r a i n correc t ions , however g l a c i a l ice was present on much of the surrounding t e r r a i n . Since the depth of th i s ice was indeterminate i t was decided to take 50 m, obtained by considering the anomaly due to an i n f i n i t e s l a b , as a f i r s t approximation for a l l v i s i b l e i c e . Table 5 shows the t e r r a i n correct ions for zones B - H , the c a l c u l a t i o n of which occupied more than a month of tedious contour reading. Corrections for more d is tant zones were not treated using the zone scheme due to the lack of a su i tab ly scaled topographic map, but instead were incorporated as an add i t i ona l slowly varying component into the reg ional gradient . Zone A was not included because the ground near most stat ions was f a i r l y f l a t . 17 The accuracy o f these c o r r e c t i o n s depends on the accuracy of the map contours and on the p r e c i s i o n w i t h which the e l e v a t i o n d i f f e r e n c e between a g r a v i t y s t a t i o n and the t e r r a i n compartment can be e s t i m a t e d . Hammer e s t imated tha t h i s t a b l e s were accura te t o 0.02 mgals f o r a compartment o f a zone when the e l e v a t i o n d i f f e r e n c e s are a c c u r a t e l y known. In the p r e s e n t case i n a c c u r a c i e s i n the e l e v a t i o n s added a f u r t h e r e r r o r o f 0.01 mgal making a t o t a l o f 0 .03 mgals /compartment . The sum of t h i s e r r o r f o r a l l the compartments i n zones B-H was found u s i n g a random walk assumption i n v o l v i n g 56 s teps of s i z e 0 .03 mga l s . The s o l u t i o n i s e a s i l y found ( e . g . F e l l e r (1957)) and can be expres sed as P ( - x / n $ S n < +x/n) -»• 2n(x) - 1 as n + « where P( ) i s the p r o b a b i l i t y t h a t the sum S n of n random one-d i m e n s i o n a l s teps of u n i t l e n g t h l i e s between ±x> /n , and N(x) i s the normal d i s t r i b u t i o n f u n c t i o n . For 90% c o n f i d e n c e l i m i t s 2N(x) - 1 = 0 .1 and the d e s i r e d sum i s ± 0 . 3 7 mgals f o r a s t a t i o n . T a b l e 5 shows the Bouguer anomalies o b t a i n e d by adding the t e r r a i n c o r r e c t i o n s to each s imple anomaly and F i g u r e 5 shows a contour map of these anomal i e s . 2.8 The R e g i o n a l G r a d i e n t C o r r e c t i o n The f i n a l c o r r e c t i o n to the observed anomalies was an e s t imate o f r e g i o n a l v a r i a t i o n s i n bedrock d e n s i t y , g e o l o g i c s t r u c t u r e , and d i s t a n t t e r r a i n e f f e c t s i n the form o f a 19 reg ional gradient . The mathematical form of th i s gradient can be approximated by a three-dimensional geometric surface of any degree, but to describe non- loca l effects low degree-functions are normally used. In normal geophysical surveying the regional v a r i a t i o n is usua l ly removed e i ther by v i s u a l l y smoothing the data or by g r i d d i n g . In the case of a g l a c i e r the anomalous body i s c l e a r l y v i s i b l e with wel l defined l a t e r a l dimensions, and in theory a good estimate of the regional gradient can be obtained by examining the anomalies at stat ions d i s tant from the ice body. In the present survey, as i s often the case, none of the stations were free of the e f fect of the g lac i er and hence an unbiased estimate of the reg ional gradient was not immediately p o s s i b l e . One can e i ther estimate the gradient from the anomalies at s tat ions near the edge of the g l a c i e r , or treat the anomalies as due to a body of unknown dimensions and apply normal smoothing methods. The l a t t e r system suffers from the disadvantage that the measured gravi ty f i e l d i s l o c a l i s e d over the anomalous body and gridding methods would be biased due to edge e f f e c t s . V i s u a l smoothing permits a cer ta in amount of f l e x i b i l i t y in judging the e f fect of g l a c i e r features , but ana ly t i c methods are pre f erred . The reg ional gradient was obtained by least-squares f i t t i n g of a polynomial to stat ions s i tuated near the edge of the g l a c i e r . By subsequently al lowing for the a t t r a c t i o n of the ice at these stat ions i t would be poss ible to approximate by i t e r a t i o n an unbiased estimate of the gradient . Stations 20 Fox, A l m u t , T e d , Tom and Hank: were survey p o i n t s not i n c l u d e d i n the l e a s t - s q u a r e s a n a l y s i s due to t h e i r u n c e r t a i n t e r r a i n c o r r e c t i o n s . The r e s u l t of f i t t i n g a p o l y n o m i a l o f the form re \ n t n-1 L ' n - r r , F ( x , y ) = aoc + a _oc y + + a r x y + + a N to the 18 survey p o i n t s and edge s t a t i o n s i s shown below f o r n = 1 ,2 , and 3: n=l r . m . s . e r r o r i n p o l y n o m i a l f i t = 1.024 mgals n=2 " " " " 1 1 = 0.582 n=3 " 1 1 *' '* '* = 0.507 " H i g h e r order s were not p o s s i b l e due to an i n s u f f i c i e n t number o f s t a t i o n s . The 18 s t a t i o n s and the v a l u e s o f F ( x , y ) f o r the three v a l u e s of n are g i v e n i n Tab le 6 . Normal ly n=l i s c o n s i d e r e d as a s u f f i c i e n t l y good approx imat ion f o r the r e g i o n a l g r a d i e n t . In t h i s c a s e , however, the r e g i o n a l g r a d i e n t i n c l u d e s d i s t a n t t e r r a i n e f f e c t s which c o n t a i n h i g h e r o r d e r t e rms , so s e l e c t i o n o f n=3 from a bes t f i t seems r e a s o n a b l e . The e x p r e s s i o n f o r the g r a d i e n t i s F ( x , y ) = 0 . 2 6 6 x 3 + 0 . 4 4 4 x 2 y - 0 . 5 7 6 x y 2 - 0 . 0 0 7 y 3 + 1 .478x 2 - 2.565xy + 4 . 2 7 2 y 2 + 20.650x - 1.598y - 136.83 mgals where x , y are the UTM c o o r d i n a t e s o f the s t a t i o n s i n k i l o m e t e r s . The r e s i d u a l anomalies shown i n T a b l e 7 are g i v e n by R . = F C x - . y . ) - g . where g^ i s the Bouguer anomaly at a s t a t i o n i . A contour map of R i s shown i n F i g u r e 6 . 21 Figure 6. Contour Map Of Residual Anomalies. Regional gradient removed. 22 3 . INTERPRETATION OF THE' RESIDUAL ANOMALIES 3.1 General Theory The re s idua l anomalies represent the l o c a l density var ia t ions due to g l a c i a l ice and f luctuat ions in bedrock dens i ty . For p r a c t i c a l reasons these tivo effects become ind i s t ingui shable in any i n t e r p r e t a t i o n , and the accuracy of the agreement between gravity and other methods of depth estimation w i l l r e f l e c t var ia t ions i n the bedrock dens i ty . The estimated uncerta int ies i n the Bouguer anomalies include errors accumulated from least-squares f i t t i n g of the i n i t i a l data, standard reduction e r r o r s , t e r r a i n correct ion e r r o r s , and reg ional gradient e r r o r s . Totals for the f i r s t three of these are 0.45mgals and 0.49mgals for the g lac i er and edge stat ions respect ive ly (90% confidence l i m i t s ) . Errors a r i s i n g from the regional gradient f i t t i n g are d i f f i c u l t to estimate; the r . m . s . error of 0.507mgals r e f l e c t s random errors and the s i m p l i c i t y of the quadratic funct ion . Assuming that these two causes equally contribute to the r . m . s . e r r o r , 0.25mgals might reasonably be added to the sum of the e r r o r s . The accumulated errors amount to 0.72mgals, averaged for the edge and g l a c i e r s ta t ions . On th i s basis an in t erpre ta t ion of the res iduals had to be found which gave ca lculated anomalies within 0.72mgals of the r e s i d u a l s . It i s c l ear from the g lac i er sketch (Figure 2) that a two-dimensional model of the g lac i er would be a poor approximation and therefore a three-dimensional model was 23 sought. The in t erpre ta t ion of gravi ty anomalies i s not unique (e .g . Grant and West 1965), and the problem of f inding a • s a t i s f a c t o r y so lut ion becomes one of adjust ing some model to the res iduals to within the accuracy des i red . For a three-dimensional body of non-geometric shape, the integrated mass effect requires d i v i d i n g the body into simpler shapes which can be handled a n a l y t i c a l l y . The computerised sum of a number of hor i zonta l laminae formulated by Talwani and Ewing (1960) has been widely used, and once the coordinates of the lamina have been obtained the c a l c u l a t i o n is f a i r l y r a p i d . This method has the disadvantage that each time:: an approximation is made to the shape of the body these coordinates have to be redetermined to allow integrat ion to proceed. 3.2 Integration Method For the Fox Glac i er an a l ternat ive method of in tegra t ing a depth d i s t r i b u t i o n was attempted, based on the a t t r a c t i o n of a number of t r iangu lar v e r t i c a l prisms. The ver t i ces of each prism at the surface of the g lac i er are the known coordinates of the. gravi ty stat ions and remain f i xed . The z coordinate of a vertex at the g lac i er bed is obtained from an i n i t i a l model, with the depth of a prism taken as the average of three v e r t i c e s . For steeply dipping bedrock this averaging contributes the main source of e r r o r . D iv id ing the g lac i er in th is manner resul ted i n 173 prisms; the main pre-computational task was r e l a t i n g ther~pr-ism vert i ces to the gravi ty s ta t ions . Figure 7 i l l u s t r a t e s a favourable 24 Figure 7. A Port ion Of The Prism Network. Stations created for in tegrat ion are labe l l ed with a cross . 25 aspect of the system; any number of e x t r a s t a t i o n s can be placed around the g l a c i e r edge without adding unknown depths. T h i r t y s t a t i o n were added i n the manner shown i n Figure 7. The c a l c u l a t i o n of the a t t r a c t i o n of a s i n g l e prism i s o u t l i n e d i n Appendix A and i s based on the Talwani and Ewing formula fo r a t r i a n g u l a r lamina. For s t a t i o n s f a r enough away from a prism, a center of mass approximation was used: the minimum radius f o r which t h i s approximation i s v a l i d was determined by t r i a l and e r r o r to be 0.7km ( A . I ) . I n t e g r a t i o n of the g l a c i e r i n t h i s way required an i n i t i a l depth d i s t r i b u t i o n and t h i s was obtained by an i n f i n i t e slab assumption f o r each s t a t i o n . The formula has already been used to obtain the Bouguer c o r r e c t i o n (2.6.4) and here p i s replaced by Ap, the de n s i t y contrast between i c e and rock, so z. = 13.5 R i (meters) (1) where R^ i s the r e s i d u a l anomaly i n m i l l i g a l s . Figure 8 shows the depth d i s t r i b u t i o n r e s u l t i n g from the a p p l i c a t i o n of (1); cross s e c t i o n s at the g l a c i e r traverses (Figures 9a-9d) and a l o n g i t u d i n a l p r o f i l e (Figure 9e) are a l s o shown. Figures lOa-lOd i l l u s t r a t e the i n t e g r a t e d " c a l c u l a t e d " anomalies compared to th-e: r e s i d u a l or "observed" anomalies. The r.m.s. d e v i a t i o n between observed and c a l c u l a t e d anomalies i s 0.67mgal which i s w i t h i n the assumed e r r o r s (0.72mgal). 26 7TJ0TJ 8000 9000 X -» Figure 8. Contour Map Of G l a c i e r Depths. Contour i n t e r v a l i s 10m. 27 *Elevation above sea l e v e l . (m) 2400 r-2300 2200 We W2 Wi 12 ;E r Applies to Figures 9a-9£. 2500, 2400 23001 Figure 9a. Transverse ;Depth P r o f i l e s . Rock cairns are denoted by A. 28 2 50 0 2 400 2300 Figure 9b. Transverse Depth P r o f i l e s . Doubtful lines are dotted. 2300 I We I I i I I I i I W2 28 E 2 E 4 E 6 E 8 E 1 0 Ee Figure 9c. Transverse Depth P r o f i l e s . Figure 9d. Transverse Depth P r o f i l e s . G l a c i e r edge is shown by 4-Figure 9e. Longi tudina l Depth P r o f i l e . V e r t i c a l exaggeration 2.54 Figure 10b. Observed And Calculated Anomalies. We W„ W2 32 E 2 E„ E 6 E 8 E 1 0 E 1 2 E 1 5 >' Figure 10c. Observed And Calcu lated Anomalies. Figure lOd. Observed And Calculated Anomalies. 37 3.3 Adjustment Of The Residuals An adjustment to the depth d i s t r i b u t i o n would normally have been made to reduce the r . m . s . dev ia t ion , but since the i n f i n i t e slab depth d i s t r i b u t i o n gives calculated anomalies which f i t the data , no further adjustment was considered necessary. An adjustment of the depths by ti^ o methods was attempted however, to test the e f f i c i ency of the prism integrat ion procedure. The f i r s t adjustment was obtained using a modified form of (1) where R^ is replaced by A g ^ , the deviat ion of calculated from observed anomalies: z . i s ' I replaced by A z ^ , the desired adjustment. The depths z ^ + A z ^ were used in the integrat ion procedure and the resul t s are shown in Table 7, where the r . m . s . dev iat ion has been reduced to 0.45mgals. An improvement has been eas i l y obtained, but continued appl i ca t ion showed that the convergence was slow. Corbato (1965a), noting th is slowness, has given an appl icat ion of the least-squares approach for improving the f i t . Due to the lack of a manageable in tegrat ion method and the large number of simultaneous equations invo lved , he remarked that a three-dimensional least-squares so lut ion is cumbersome (1965b). An advantage of least-squares technique is that the desired s o l u t i o n , i f i t e x i s t s , i s obtained in a s ingle step. The coe f f i c i ent s in the r e s u l t i n g set of simultaneous equations are p a r t i a l der ivat ives of the res iduals with respect to the depth at each s ta t ion (Corbato,1965a; page 229, equation 5). In the prism integrat ion these p a r t i a l 38 derivat ives can be obtained rather eas i l y since they are re lated to the quantity V the gravi ty anomaly per unit thickness at the base of a prism ( A . I ) . The appl i ca t ion of this procedure required the so lut ion of 70 simultaneous equations, but the resul t s were unstable and phys i ca l l y unacceptable (Figure 9f ) . This was taken to indicate that e i ther the data was inconsistent or that the least-squares parameters had too many degrees of freedom. The value of this in terpre ta t ion procedure is therefore unproved for "real" data . 5.4 Concluding Remarks It i s to be emphasised that the depth d i s t r i b u t i o n obtained by the appl i ca t ion of (1) i s not unique, p a r t i c u l a r l y considering the l imi t s obtained from the error ana lys i s . The depths obtained for the tongue region of the g lac i er are u n r e l i a b l e , but this is due i n part to the small phys ica l dimensions of the tongue and the r e l a t i v e l y large t e r r a i n correc t ions . There i s some doubt about the depths below the ice f a l l s on the west side of the g l a c i e r , e spec ia l ly s ta t ion 20We, and l i t t l e confidence should be placed in the resu l t s for th is reg ion . Prel iminary d r i l l i n g resul ts became ava i lab le (Classen, personal communication) from work completed during the summer of 1969. The predicted versus actual depths are compared below. 39 STAT I ON DEPTHS (m) ( S T A K E NO) G R A V I T Y D R I L L I N G D l F F E R E N C E 12 2 9 . 0 3 1 . 4 - 2 . 4 16 30 .6 27 .0 3 . 6 20 5 0 . 6 4 7 . 9 2.7 40 4. TEMPERATURE MEASUREMENTS During the summer of 1968 a smal l -scale d r i l l i n g program was completed and near-surface temperature p r o f i l e s obtained at stakes 2, 7, 16, and 34 (for locat ion see Figure 2). 4 .1 The Equipment Thermal contamination of the environment is the major source of error in the measurement of g lac i er temperatures. The use of ethylene g lyco l or sa l t so lut ion prevents d r i l l f reez ing , but temporarily raises the hole temperature. On the Fox two mechanical d r i l l s were used, a three- inch SIPRE* coring auger and a one-inch ice d r i l l . Ant i - freeze devices were not used and so d r i l l i n g was made more d i f f i c u l t . In the few instances where a d r i l l could not be freed by force , hot water was used for recovery; this thermal disturbance was considered unimportant. The temperatures were taken within one-inch polyethylene tubing which was placed in a l l the holes . To keep the tubing water-free , the bottom was sealed with wooden plugs. A copper-constantin thermocouple was connected to a standard Wheatstone Bridge; a melting slush mixture on the g lac ier surface was the zero reference bath. The thermocouple was ca l ibra ted against a mercury-in-glass thermometer with a range of -10°C to + 1 0 ° C , and a s a l t / i c e mixture provided * Snow, Ice and Permafrost Research Establishment. 41 the temperatures required below zero. Two ca l ibra t ions within a week produced s imi lar r e s u l t s , and a c a l i b r a t i o n constant of 0.036 +0.002 m i l l i v o l t s / d e g C was deduced over the range of the thermometer. During f i e l d measurements, precautions were taken to minimise the ef fect of sunlight on the reference bath temperature and frequent n u l l i n g was performed. M i l l i v o l t values were read from the Wheatstone Bridge at depth spacings of 0.5m or l e s s , and recorded when a stable value was thought to have been reached. Hourly measurements over a period of 18 hrs for the hole at stake 7 indicated that the temperatures had s t a b i l i s e d within 12 hrs of d r i l l i n g . The resu l t s shown i n Table 8 are probably only accurate to 0.2deg C . Figure 11 shows a plot of these resul t s for each hole . 4 .2 Comments On The Results (i) At stake 32 there was a f i r n cover of about a meter; the temperature p r o f i l e indicates that the thermal gradient is smooth from the surface and through the f i r n / i c e in t er face . Comparison with the p r o f i l e s at holes with no f i r n cover confirms that the snow has an insu la t ing ef fect on the ice beneath. ( i i ) Comparison of the July 10th and August 16th p r o f i l e s for stake 7 shows that the top few meters of ice had warmed by about a degree. ( i i i ) The 8 meter hole at stake 7 indicates that the g l a c i e r Figure 11. Temperature Data. 43 temperature remains f a i r l y constant at about - 4 . 7 ° C below a depth of 4m, although this behaviour could not have been ant ic ipated from the shalloiver holes . I f the deep temperatures at stake 7 are correct the minimum g lac i er temperature may wel l be i n the region of - 5 ° C ; warming towards the g lac i er bottom is to be expected due to geothermal heat ing. (iv) Temperatures determined on the Jackal and Hyena Glac iers are shown i n Table 8. The measurements are sparse, but these g lac iers show signs of being sub-polar . From the point of view of surge mechanisms, the three -g lac ier system could show common surge c h a r a c t e r i s t i c s i f temperature is a. f a c t o r . 4.3 The Implications Of Temperature Measurements Although the depth of the temperature holes only represents the upper 10% of the g l a c i e r , some general remarks can be made concerning the temperature of the whole g l a c i e r . Some idea of the annual climate in the Fox Glac i er region is required before the factors inf luencing the temperature of a g lac i er can be discussed. 4.3.1 - Climate Meteorological stat ions in the Yukon T e r r i t o r y are sparsely s i tuated and none are in the St . E l i a s Mountains. Although a weather record for the Fox was kept for the months of July and August, there i s no d i r e c t information concerning the climate for the rest of the year . The meteorological data accumulated at the nearest two a l l - y e a r s ta t ions , A i s h i h i k and Snag, and displayed in Table 44 9 is taken from Kendrew and Kerr (1955) . A crude extrapolat ion from A i s h i h i k and Snag, using the suggested temperature gradient from Kendrew and Kerr of 1°F per 330ft, gives yearly means of - 2 3 ° F , - 2 9 ° F at the a l t i tude of Fox Camp. The authors pointed out that th is gradient w i l l be too steep due to the tendency for cold a i r to accumulate in the val leys where the data are c o l l e c t e d . Marcus (1964) reported a yearly set of meteorological data for the Juneau I c e f i e l d region in southern Alaska and found the temperature gradient between the i c e f i e l d and Juneau a irport (at sea level) was seasonably dependent. On average the gradient for this region was about h a l f that quoted from Kendrew and Kerr , and an extrapolat ion of the A i s h i h i k and Snag data using the gradients obtained by Marcus gave the monthly v a r i a t i o n shown in Figure 12. This determination of the Fox climate assumes more than can be j u s t i f i e d , but i t seems the best that can be achieved with such sparse data. Comparison of the observed monthly means at the Fox Glac i er for Ju ly and August indicates that the extrapolated means are about 5 degrees too h igh . With the assumption that this dif ference is constant throughout the year, the seasonal temperature v a r i a t i o n at the Fox G l a c i e r can be approximated by a s inusoid of mean -15 + 5°C and an amplitude of 20 + 5 ° C . For the Fox Glac i er there are no d i r e c t observations of winter snowfal l , so an estimate was made based on the mass 45 10 _ o -• • 10 Yearlv mean A i s h i h i k Yearly mean Snag 20 30 ~ 5> 40 J Jan Mar May July Month -+ Sept Nov Dec Figure 12. Estimated Cl imat i c Var ia t ions For The Fox G l a c i e r . Extrapolat ions are from Snag O , and A i s h i h i k / . Observed means are 03 . 46 balance resul ts of Brewer (1969) . The projected yearly 1 2 accumulation obtained by Brewer was 1.7x10 gm of snow of . 3 density 0.5gm cm , and from the map of the g lac i er sketched 1 0 2 in Figure 2 an estimated area of the Fox was 5x10 cm . The snowfall averaged over one year was thus deduced to be 0.7m. 4 . 3 . 2 - General Remarks The thermal h i s tory of a g lac i er i s pert inent to temperature measurements. The past surges of the Fox G l a c i e r obviously involved appreciable thickness changes during the surge c y c l e , and even assuming a constant external c l i m a t e , these f luctuat ions i n the phys ica l state of the g l a c i e r indicate that the temperature p r o f i l e s are time dependent. Considering large ice masses l ike the Greenland and Antarc t i c ice sheets Wexler (1959) has shown that due to the very slow conduction of heat i n ice and rock, large ice masses can only reach a quas i -equi l ibr ium s tate . Hence a l l temperature ca lcu la t ions should i d e a l l y consider the duration of the assumed boundary condi t ions . In p a r t i c u l a r geothermal heat flow, basal shear, the accumulation and ablat ion of ice at the surface , long term c l imat i c changes, annual temperature v a r i a t i o n s , and, i n the case of small va l l ey g l a c i e r s , the conduction of heat through the rock w a l l s , are relevant to the discuss ion of the thermal regime. In the case of surging g lac iers these factors may assume an important status in the complete descr ipt ion of the phys ica l state of the g lac i er before a surge. 47 4.3.3 - Penetration Of The Winter Cold Wave Some ca lculat ions of the ef fect of the penetration of the annual temperature f luctuat ions into a g l a c i e r treated as a s emi - in f in i t e medium are given in Appendix A. For the case of a homogeneous h a l f space (ice) , the equations given i n Carslaw and Jaeger (1959) were applied d i r e c t l y . In the treatment of the composite s o l i d (snow upon ice) further appl icat ion of the heat flow equation was necessary. If the Fox Glac i er were at the pressure melting point throughout (close to 0°C for a th in g l a c i e r ) , i t would be classed as temperate. A temperature wave of amplitude 50°C at the surface , greater than the amplitude of the annual cold wave, has an amplitude of 2 1 . 5 ° C at a depth of three meters and 2 . 8 ° C at 8m, assuming no snow cover. A year- long cover of one meter of snow reduces these amplitudes to 2.5 and 0 . 5 ° C re spec t ive ly . It is very u n l i k e l y that a temperate g lac i er would have a temperature of -5°C at a depth of 8m due only to the winter cold wave, and therefore the Fox should be c l a s s i f i e d as a sub-polar g l a c i e r . Benf ie ld (1952) considered modifications to the amplitude of the cold wave due to the accumulation of snow at the surface blanketing the cold wave. He deduced that i f the rate of accumulation during the winter is s u f f i c i e n t to ra i se the snow surface at a rate comparable to the v e l o c i t y of penetration of the cold wave, then the amplitude of the cold wave f a l l s off more slowly with depth than i n the absence of 48 accumulation. Comparison of the estimated snowfall and penetration rate for the Fox show that an accumulation rate _6 _ 1 of one meter a year (3x10 cm sec ) i s an order of magnitude ; .6 _ I lower than the penetration rate (54x10 cm sec ) for snow; .6 .1 for ice the discrepancy is greater , 0.3x10 cm sec and .6 .1 68x10 cm sec re spec t ive ly . Thus this ef fect can be ignored. 4.3.4 - The Effect Of Ice Movement On Temperature P r o f i l e s As the f i r n becomes compacted and moves down into the g lac i er in the form of i c e , the temperature of th is moving ice w i l l have an effect on the thermal gradient . Robin (1955) discussed th is downward movement in terms of the rate of accumulation of new i c e . The surface of the g lac i er i s assumed to remain at constant e l evat ion , but any v e r t i c a l column of ice i s taken to be spreading in cross sect ion uniformly throughout the g l a c i e r . The expression derived for the temperature at depth h above the base of the g l a c i e r (or ice sheet) i s given by Robin as:-where H is the thickness of the i c e , q i s the geothermal heat _2 . 1 flow (1.2ycals cm sec ) and A is the accumulation ra te . For g lac iers 50m and 100m thick the resul t s are shown numerically in Table 10 and graphica l ly in Figure 13 for d i f f erent values of A. For an ice accumulation rate less than .1 50-100cm yr there is neg l i g ib l e perturbat ion of the geothermal gradient . Since the accumulation rate i s varying Figure 13. Ef fec t Of Accumulation Rate. A=0, 50 , 100 , 500 cm yr" for (1), (2) , (3), and (4) r e s p e c t i v e l y . 50 monthly and even becomes negative in summer due to a b l a t i o n , the accumulation ef fect i s smaller than suggested above. 4.3.5 - S tra in Heating The survey resul ts for 1968 and 1969 were compared by C o l l i n s to assess the surface ve loc i ty of the Fox. The flow rates obtained were of the order of one meter a year which is about the accuracy of the UTM coordinates , hence i t appears that the g lac i er i s v i r t u a l l y stagnant. Since g lac iers have been shown to behave in a manner adequately described by the theories of p l a s t i c flow, the basal v e l o c i t y and s t r a i n rate should be n e g l i g i b l e . S t r a i n heat ing , usual ly smal l , can thus be discounted. 4.4 Summary And Relat ion To Surges There are some aspects of the temperature regime of the g lac i er which are as yet unknown. The penetration of the annual f luctuat ions at the surface was considered for conduction and s o l i d convection only, but the effects of the summer ablat ion and the heat carr ied down into the g lac i er by perco la t ing meltwater and sub-surface streams remains d i f f i c u l t to assess. I f the relevent data were avai lable a gradual change in the c l i m a t i c environment ( including changes in geothermal heat flow) could be treated in terms of thermal gradients within the i c e . A poss ible c a l c u l a t i o n would be the treatment of a one-dimensional slab of ice with a heat f lux at one face and an accumulating boundary with a constant 51 or varying temperature at the other. The ro le of f luc tuat ing temperature p r o f i l e s in providing tr igger mechanisms for g lac i er surges has often been mentioned (e .g . Robin 1955,1968), e spec ia l ly in conjunction with the mechanism of g l a c i e r s l i d i n g as proposed by Weertman (1968). No sa t i s fac tory method, however, has been proposed for r a i s i n g the basal temperature, aside from q u a l i t a t i v e references to changes in the geothermal heat floxv, surface accumulation and basal flow r a t e . Further , as Nielsen (1968) has pointed out, some g l a c i e r surges suggest that mechanical i n s t a b i l i t i e s are present; for example t r ibutary g lac iers often advance after the parent g lac ier has surged. It is possible that the d i v e r s i t y in s ize and normal flow rates of surging g lac iers may indicate involvement of more than one tr igger mechanism. 52 BIBLIOGRAPHY 53 BENFIELD A . E . The ef fect of accumulation on temperatures within a snowfield. Journal of Glacio logy 2 250 (1952). BREWER T. Summary of Fox Glac i er mass balance study 1968. Personal communication. (1969) . CARSLAW H.S . and JAEGER J . C . Conduction of heat in s o l i d s . Oxford Press . (1959) . CLARKE G . K . C . Geophysical measurements on the Kaskawulsh and Hubbard g l a c i e r s , Yukon T e r r i t o r y . A r c t i c Inst i tute of North America Technical paper No 20. (1967) . CORBATO C . E . A least-squares procedure for gravi ty i n t e r p r e t a t i o n . Geophysics 30_ (2) 228 (1965a). - - Thickness and basal conf igurat ion of Lower Blue G l a c i e r , Washington, determined by gravimetry. Journal of Glaciology 5_ (41) 637 (1965b) GIBSON M.O. Network adjustment by least squares- a l t e r -native formulation and so lut ion by i t e r a t i o n . Geophysics 6 (2) 168 (1941) . GRANT F . S . and WEST G . F . Interpretat ion theory in applied geophysics. Ch. 8 210 (1965) McGraw-Hi l l . HAMMER S. Terra in correct ions for gravimeter s ta t i ons . Geophysics 4 184 (1939). KENDREW W.G. and KERR D. The climate of B . C . and the Yukon T e r r i t o r y . (1955) Edmond C l o u t i e r . Ottawa. MARCUS M.G. Cl imate -g lac ier studies in the Juneau I c e f i e l d region, Alaska . (1964) Univers i ty of Chicago Press . MEIER M. and POST A. What are surges ? (prel iminary dra f t )* NIELSEN L . E . Some hypotheses on surging g l a c i e r s . Geo l . Soc. Am. B u l l . 79_ 1195 (1968). NYE J . The flow of g lac iers and ice sheets as a problem in p l a s t i c i t y . Proc. Roy. Soc. (A) 207_ 554 (1951) The mechanics of g lac ier flow. Journal of Glaciology 2 82 (1952). POST A . D i s t r i b u t i o n of surging g lac iers in western North America. Journal of Glaciology 8 (-53) 229 (1969) . 54 ROBIN G.de Q. Ice movement and temperature d i s t r i b u t i o n in g lac iers and ice sheets. Journal of Glaciology 2_ 523 (1955) . I n i t i a t i o n of g lac i er surges.* SHARP R. Geology of the Wolf Creek area, S t . E l i a s Range, Yukon T e r r i t o r y , Canada. B u l l . Geol . Soc. Am. 54_ (5) 625 (1943) . TALWANI M. and EWING M. Rapid computation of g r a v i t a t i o n a l a t t rac t ion of three-dimensional bodies of a r b i t r a r y shape. Geophysics 2_5 203 (1960). WEERTMAN J . Catastrophic g lac i er advances. Internat ional Assoc iat ion of S c i e n t i f i c Hydrology. Symposium of Obergurgl: V a r i a t i o n i n the regime of e x i s t i n g g l a c i e r s , p.31 10-18 Sept. (1962). Water l u b r i c a t i o n mechanism of g l a c i e r surges.* WEXLER H. Geothermal heat and g lac i er growth. Journal of Glaciology 3 420 (1959). * These papers were presented at a "Symposium on the causes and mechanics of g lac i er surges". St . H i l a i r e , Quebec, Canada. September 1 0 - l l t h (1968) . APPENDIX A THEORETICAL RESULTS 56 A.1 Prism Integration For Gravitational Attraction According to the formulation of Talwani and Ewing, the v e r t i c a l component of the g r a v i t a t i o n a l attraction per unit thickness of a thin horizontal triangular lamina, evaluated at a point P i s : -where z is the depth of the lamina below P. The symbols have the same meaning as in the paper by Talwani and Ewing. The contribution of the f i r s t term i s zero i f P i s over one of the vertices of the lamina. The t o t a l attraction of a prism extending from z=0 to z=H i s obtained by evaluation of the i n t e g r a l ( '' g = 1 V(z) dz , using numerical methods. For s i m p l i c i t y Simpson's rule was used in the form g = g. ( V l + 4V2 + V 3) where V j , V 2, and V 3 are the values of V(z) obtained from ( 1 ) at the depths 0 , H/2, and H (shown below). 57 Increasing the number of V s was not found to change g by a s i g n i f i c a n t amount because in a l l cases the depth of the prism was less than, or comparable to, the distance from the prism to P. For stations P s u f f i c i e n t l y far from a prism, the evaluation of g was carried out using a center of mass approximation to adequate accuracy. The v e r t i c a l a t t r a c t i o n of a prism treated in this way is given by G A p z . d where A i s the area of the triangular face and d=(z 1+z 2 +z 3)/6= The results obtained by comparing the whole-glacier anomaly at two representative stations i s shown below for values of D , the distance at which the approximation formula was used. RADIUS D A N O M A L I E S (mgals) A P P R O X I M A T E COMPUTER (km) S T A T I O N S T A T I O N TIME PER S T A T I O N A B (sees) 0.0 0 .217 0 .473 0.7 0.1 0.217 0 .473 0.7 0.5 1.9^0 2 .778 1.3 0.7 1.941 2.782 2.0 1.0 1.942 2.783 3.0 10 .0 1.942 2.783 8.0 A distance of 0.7km for D appears to be a good compromise between accuracy and speed of integration. 58 A.2 The Di f fus ion Of A Thermal Wave Into A G l a c i e r The problem has been s i m p l i f i e d to the extent that the wave is applied at the surface z=0 of a s e m i - i n f i n i t e medium. The input i s assumed a harmonic function of time and can be expressed as:- T Q = A c o s ( u f c - 0 By Fourier Analysis any desired input can be treated by the superposit ion of such waves, i f p e r i o d i c i t y can be assumed. Two cases are considered, ca l l ed models I and I I , and the treatment i s r e s t r i c t e d to the steady state so lut ion in which the surface f luctuat ions have been applied since t = - » and the medium was i n i t i a l l y at zero temperature. The fol lowing symbols are used and the values have been taken from Carslaw and Jaeger (1959):-- i 0 .1 .1 K^thermal conduct iv i ty of snow, 0.00025 ca l sec C cm 1&2~ n I T ii i c e , 0.0053 ,, 2 _ l <i= ,, d i f f u s i v i t y snow, 0 .0050 cm sec *• 2 — I I i i I I i c e , 0.0115 ,, ,, _1 .8 .1 f = frequency of input wave, 1 cycle yr (3.171x10 sec ) 2 .1 The thermal d i f f u s i v i t y of average rock is 0.0118 cm sec The object of the treatment i s to determine the e f fect of a snow cover on the d i f f u s i o n of the annual winter cold wave into a g l a c i e r , to decide whether the temperatures measured on the Fox were due to the cold wave. A.2.1 - The Glac ier As An In f in i t e Half -Space. Model I The boundary conditions are 59 2 . - <*> • T - 0 and the method used follows exactly that described in Carslaw and Jaeger. Assuming a so lut ion of the form T . U « L ( W F C - 6 ) , „.«>£*) and so lv ing the d i f f u s i o n equation with the above boundary conditions leads to the so lut ion T- A Cos fab - 6 - I f i i ) where u>= 2r,fand J f c j g Subst i tut ion of the values for l^.and f gives a wave diminishing in amplitude as / ^ e " " 0 ' 2 ^ * ' and with a phase lag of I Z days, for z in meters. Since i n pract ice the d i f f u s i v i t i e s of ice and rock are s i m i l a r , the presence of the i ce / rock interface below the g lac ier should not d is turb the so lut ion by a s i g n i f i c a n t amount. A.2.2 - The Glac i er As A Layered Half Space. Model II Model I would serve as a good approximation for a g lac i er provided the thermal propert ies of ice were constant with depth and not too d i f f erent from the underlying bedrock. Most g l a c i e r s , however, have a f i r n cover which may be many meters t h i c k . For this reason Model II considers the ef fect of a layer of snow of constant depth over a g lac i er throughout the h i s tory of the i c e . The boundary between ice and snow is assumed perfect thermally, and is located at a depth d below the surface . 60 The boundary conditions for this problem are:-and they express the continuity of heat and temperature across the f i r n / i c e interface. To obtain a solution i t i s f i r s t assumed one can write • it<Ofc-~fc) . Solution of the d i f f u s i o n equations at 1 «• a t > I i ? k ^ f c leads to the expressions^ ^ ^ / T g ) .» 6|e»|.^ Jf) With the application of the boundary conditions the following set of equations result where < ^ « [ & andcy i = These expressions were solved to obtain A|} A 2 ^  6j a*Uto give the expressions for u and v:-61 ( l+Sa^' ) ^ where Now (2) and (3) involve the amplitude and phase of the thermal wave; to separate the amplitude part from the phase part u and v are treated as complex amplitudes:-where Cj c (flli24 b, 2)'' 1 , 4>i' ^urchin 0>i/a.) elfc. The expressions for T^ and T^ are thus "IT - c, cos (u>fc-e -+ It remains to write the f u l l so lu t ions : -w h e r e P,,A^ **a P a a ft(l4s)eQ* j . <je& Xr cons,4V C M ( $ , + ( * ; U = 14 Tu*R Sin S, 4 YSin (s,4-Q,) 62 Subst i tut ion of (4) and (5) into the d i f fus ion equations i s found to sa t i s fy the boundary condi t ions . Figures 14a and 14b show the amplitude C and the phase $ of the thermal wave p lo t ted against depth and obtained by evaluating (4) and (5) for d=10cm and one meter. A comparison is given by p l o t t i n g the values obtained from Model I . It i s s u f f i c i e n t to note that the amplitude of the di f fused wave is strongly affected by a shallow snow cover to a distance of 5-10d below the surface . The phase lag i s not great ly affected by a shallow snow cover, and 10m is the approximate depth of the coldest temperature to be expected, h a l f a year after the passing of the winter cold wave. 63 lcm 2 cm 5cm 8 cm 0.1m t-0 ,2m o . 5m 0 ,8m lm 2m 5m 8m 10m 20m (1) Model I (2) Model I I , d=10cm (3) Model I I , d=lm. JL JL _L 0 0.2 0.4 0.6 0.8 Fract ion of amplitude at surface Figure 14a. Ef fect Of Snow Cover On The Penetration Of The Annual Cold Wave. Amplitude r e s u l t s . 1.0 6 4 0 . 8mh lmL (1) Model I (2) Model II , d=10cm, (3) Model I I , d=lm. 50 100 Phase lag (days) 150 200 Figure 14b. Ef fect Of Snow Cover On The Penetration Of The Annual Cold Wave. Phase r e s u l t s . APPENDIX B TABLES OF RESULTS 66 C I R C U I T A H A N K TOM T E D I A # T=3, M=0.82 S T A T I O N A 2E 0.! 1 2 3 4 5 6 6 E 0 A 1=6, M=-1.85 A 6E ! 6|0 . 5 6 7 7 E 0 . 5 A T = 2 . 2 5 , M = - 0 . 7 3 T = 4 . 2 5 , M=0.20 T A B L E 1 F I E L D D A T A F O R C I R C U I T S R E A D I N G 2 4 9 . 4 3 : 1 9 8 . 5 2 5 6 0 . 3 2 611 .78 6 2 1 . 6 5 6 2 8 . 5 8 8 6 4 . 0 0 9 1 6 . 6 3 8 7 2 . 6 2 8 0 6 . 0 2 7 6 7 . 1 7 7 3 4 . 3 7 7 0 2 . 1 2 6 8 5 .90 6 8 9 . 8 8 6 2 6 . 6 7 6 3 1 . 4 3 6 9 3 . 4 2 6 8 8 . 2 0 7 0 5 . 2 2 6 7 7 . 4 0 6 5 5 . 1 0 6 3 0 . 7 0 A 631 .87 7 E 0 . 5 666 .13 7 678 .10 6 705 .62 6w 0 m 5 722 • 52 7 W 0 . 5 688 .50 10 620 .75 12We 502 .60 12W2 521 .83 12Wj 533 .35 12 543 .35 12Ej 559 • 50 A 632 .07 C I R C U I T S T A T I O N R E A D I N G 12 5 4 3 . 1 3 1 4 4 5 9 . 4 3 5 16 413.10 12W2 521 .73 12WX 533-65 12 5 4 3 . 4 2 T = 2 , M=0 .29 12 5 4 3 . 6 2 12E l 5 6 0 . 8 2 l6Ee 429.15 6 16E 2 431 .72 16EX 4 1 8 . 9 0 16 4 1 4 .75 1 4 4 6 0 . 9 3 . 12 5 4 4 . 6 8 T = 2 . 2 5 , M=1.06 16 4 1 4 . 3 7 l6El 418.30 1 6 E 2 430 .92 7 18 3 5 8 . 5 2 l 6 w x 3 8 8 . 4 8 16 4 1 4 . 1 5 T=1 . 7 5 , M = - 0 . 2 2 12W2 5 2 2 . 4 5 12We 5 0 4 . 1 3 l 6 w e i 325 .77 8 l 6 w 2 353.75 l6Wj 389 .32 16 415-53 1 2 W 2 353.75 T = 2 . 5 , M=1.30 l6Wj l 6 w 2 I6we! 2 OWe 20W2 20Wi 20 3 8 8 . 5 2 354.77 3 2 6 . 3 8 267-33 314 .18 3 1 3 . 0 3 3 0 7 . 5 5 " S c a l e c h a n g e i n c i r c u i t . S T i s e l a p s e d t i m e ( h r s ) , M i s m i s c l o s u r e . The r e a d i n g s a r e i n s c a l e d i v i s i o n s 67 T A B L E 1 (continued) C I R C U I T S T A T I O N 18 3 6 0 . 8 5 16W1 390.15 T= 3 . 2 5 , M=1.63 18 3 5 7 . 0 2 20 3 0 3 . 3 3 20EX 300 .02 10 20E 2 2 9 5 . 6 8 20E 3 2 9 8 . 0 0 20Ee 281.43 l8Ee 346 .47 18 3 5 7 . 3 8 r=3-25 M= 11 T=5, M=0 20 22 24 24w2 24wtt 12 24we DON 2 OWe 20W2 20WX 20 T= 5 - 5 , M=2.08 READING C I R C U I T I S T A T I O N 20 3 0 6 .20 22 2 5 7 . 3 7 24 190 . 6 8 24E 2 1 5 3 .05 2kEh 131 .60 24E 6 7 4 . 5 8 24Ee -16 . 3 3 20Ee 2 8 8 .18 2 O E 3 300 • 6 3 20E 2 2 9 9 . 5 2 20Ej 3 0 3 . 5 8 20 306 . 6 0 13 24E 6 2 8 E 6 2 8 E 8 2 8 E 1 0 2 8 E e ALMUT 24E 6 6 6 5 . 4 5 6 1 4 . 6 2 546 . 9 5 5 3 3 . 6 8 4 7 0 . 6 3 3 5 9 . 8 0 3 2 8 . 6 8 6 2 5 . 9 8 6 7 4 . 6 2 6 7 3 . 7 0 6 6 7 . 5 3 438.00 381.48 319.78 282.52 232.62 107.58 440 .02 T=2.5, M=2.02 14 T= 2 . 5 , 24 26 28 2 8 E 2 28E4 2 8 E 6 24E 6 24E,, 24E 2 24 M=2 .70 1 2 W e FOX 15 l6we 2 I 6 w e i 1 2 W e T= 5 . 2 5 , M=0.91 16 T=4, M= 24 26 28 28w 2 28w„ 28we 24we 24'W^  2 Aw 2 24 -1.22 28 401.78 30 333 .12 32 302 .65 32W2 295 .18 17 32W,, 265 .78 32We 256 .72 28we 279 -30 2 8w u 357.02 28w 2 410.68 28 406 .08 T= 3 . 7 5 , M=4.30 6 8 TABLE 1 (concluded) CIRCUIT STATION READING 2 8 4 0 3 . 6 2 28E 2 406 .55 2SEk 4 0 9 . 4 3 28E 6 3 9 1 . 6 7 2 8 E 8 3 2 7 . 0 7 1 8 3 2 E 8 1 9 1 . 2 8 3 2 E 6 2 6 8 . 1 5 32Ek 2 6 2 . 5 2 32E 2 2 9 2 .40 32 3 0 5 . 7 7 3 0 3 3 6 . 3 8 2 8 4 0 5 . 2 5 T = 3 . 5 , M= 1 . 6 3 2 8 E 8 7 9 5 . 8 7 2 8 E 1 0 7 5 8 . 6 5 28Ee 7 0 8 . 8 5 3 2 E 1 5 4 9 9 . 4 5 PHI L 3 2 8 . 2 8 3 4 E 1 2 5 7 5 . 6 7 19 3 2 E 1 2 6 1 7 . 6 5 3 2 E 1 0 6 1 0 . 7 7 3 4 E 1 0 5 6 7 . 5 8 36E 8 5 9 6 . 5 8 3 4 E 8 5 7 8 . 1 0 32E 8 664 . 2 0 28E 8 7 9 7 . 2 0 T = 3 . 5 , M= 1 . 3 3 7 8 9 . 1 0 7 7 5 . 0 7 7 9 4 . 9 3 8 0 9 . 7 7 8 3 5 . 3 2 7 8 7 .40 CIRCUIT STATION READING 3 2 6 2 7 . 3 5 3 4 605 . 2 7 3 6 5 8 6 . 6 3 3 6 E 2 5 6 1 . 1 0 36Ek 5 1 7 . 3 7 21 3 6 E 6 4 4 5 . 3 8 3 4 E 8 4 2 6 . 2 0 32E8. 511 .77 3 2 E 5 5 8 7 . 7 8 5 8 0 . 1 7 3 2 E 2 6 1 1 . 1 0 32 6 2 5 . 1 5 T= 3 , M = - 2 . 2 0 3 2 6 2 3 . 9 2 3 4 6 0 2 . 0 7 3 6 5 8 2 . 9 7 3 6 w 2 5 1 9 . 2 3 22 CLI FF 442 .68 3 6 We 5 5 0 . 1 0 32We 5 7 6 . 8 2 32W 4 5 8 9 . 5 8 32W2 6 1 8 . 5 3 \ 3 2 6 2 7 . 8 0 T= 4 , M = 3 . 8 8 A rock c a i r n set up by Weber i n 1967. 69 TABLE 2 THE STATION DATA STATION "EASTING -NORTHING "STAKE "CORRECTED REMARKS e.g. NO LABEL HEIGHT ELEVATION station type 1 A 7546 .66 7041 .87 _ 2155.77 SURVEY 2 12We 7208 .66 6 5 4 3 . 3 9 - 2204 .26 EDGE 3 l6Ee 7893.11 6376.57 - 2249 .39 M 4 l 6 W e 2 7063 .95 6002.18 - 2358 .85 T l 5 l8Ee 7 9 8 6 . 6 1 6125 .28 - 2287 .30 n 6 20Ee 8098 .88 5977.51 - 2322 .28 11 7 DON 7283 .58 5607 .04 - 2449 .75 SURVEY 8 24Ee 8 6 2 6 . 9 9 5682 .61 - 2471 .74 EDGE 9 24We 7265 .94 5243 .75 - 2447 .02 ii 10 28Ee 9064 .06 5604 .68 - 2523 .40 t t 11 28we 7373.25 4756 .13 - 2493 .96 11 12 32We 7466 .96 4397.94 - 2499 .42 n 13 PHIL 9452 .80 4751.48 - 2663 .35 SURVEY 14 36We 7647.21 4169 .39 - 2508.04 EDGE 15 CLI FF 8 0 5 9 . 9 0 3971 .13 - 2 5 4 6 . 3 6 SURVEY 16 3 2 E 1 5 9 3 8 5 . 4 5 5145 .12 1 .53 2597 .49 GLACIER/EDGE 17 #1 #7690.00 #7890.00 - #2010 .00 EDGE 18 6w 0 # 5 7 4 3 3 . 1 5 7246 .56 #4.42 2 1 0 9 . 6 0 GLACIER/EDGE R 7552.48 6 9 7 8 . 5 3 - 2162 .47 NOT USED FOX 6980 .70 6371 .72 _ 2409 .94 SURVEY ALMUT 8799.83 5808 .49 2 5 7 2 . 4 7 1 1 HANK 8 3 6 1 . 8 0 7497.16 2 3 5 8 . 2 9 T l TOM 7 8 4 1 . 5 1 7 3 7 6 . 2 9 - 3186.24 II TED 7 8 8 3 . 6 2 7531 .34 _ 2161 .89 11 28WL. - - 2 .80 - NO DATA 20 3 6 E 5 8737.52 4429 .45 2.04 2 5 5 0 . 9 6 GLACIER 21 34 8122.52 4493 .62 2 .18 2471 .58 u 22 3^E 8 8 8 3 1 . 6 5 4757.47 2 .05 2 5 5 9 . 4 9 23 3^E 1 0 9017.34 4830 .01 2 .52 2564 .65 24 3^E 1 2 9210 .25 4 8 8 1 . 7 8 1 .83 2565 .43 25 32W„ 7696 .82 4540 .35 #2 .45 2485 .22 26 3 2 W 2 7 8 8 3 . 0 6 4612 .20 2.04 2464 .94 n 27 32 8066 .95 4681 .63 2 .60 2460 .24 n 28 3 2 E 2 8247 .52 4746.93 2 .96 2469 .16 29 32E, , 8 4 2 6 . 6 7 4812 .06 2 .26 2486 .59 30 3 2 E 5 8606 .03 4875.13 2 .29 2493 .82 „ 31 3 2 E 8 8 7 7 8 . 6 2 4936 .20 2 .79 2525 .49 32 3 2 E 1 0 8963.42 5003 .37 2 .55 2547 .00 33 3 2 E 1 2 9215 .05 5 0 8 7 . 7 6 2 .34 2552 .40 34 ":20We 7412 .86 5758.46 - 2 3 1 0 . 8 0 GLACIER/EDGE 35 30 8010 .08 4874 .59 2 .72 2448 .51 GLACIER 36 28w2 7770.97 4975 .65 2 .52 2416 .83 37 28 7954.84 5 0 6 5 . 9 9 3.11 2 4 1 9 . 8 5 38 2 8 E 2 8131 .72 5151 .88 2 .56 2419 .67 39 2 8 E h 8315 .38 5239.12 2 .50 2423 .60 „ 40 2 8 E 5 8501.41 5 3 2 7 . 8 3 2.64 2 4 3 8 . 9 3 41 2 8 E 8 1 8683.74 5419 .14 2 .65 2469 .25 70 TABLE 2 (concluded) STATION EASTING NORTHING STAKE CORRECTED REMARKS NO LABEL HEIGHT ELEVATION 42 2II" 8853 .35 5503 .83 2 .07 2491 .25 GLACIER 43 7902 .23 5256 .90 2.70 2380 .43 n 44 24w\ 7466 .17 5321 .49 2 .77 2386 .07 45 24w, 7654 .06 5386.11 2 .37 2 3 4 7 . 7 3 n 46 24 2 7 8 4 7 . 4 3 5446 .96 3 . 6 7 2347 .86 47 24E - 8035.17 5585 .29 2 .92 2370 .70 48 24E^ 8226.19 5569.11 2 .65 2389.00 M 49 24E 6 8422 .75 5633.52 3 .26 2417 .74 50 22 7784 .13 5666 .61 3.87 2317 .30 51 20W2 7542 .47 5800 .27 3.06 2286 .21 52 20W j 7637.65 5828.59 2.68 2287 .48 M 53 20 7732.06 5859.46 2 .34 2 2 9 2 . 8 9 54 20E l 7826.41 5890.74 2 .52 2298 .33 55 20E 2 7918.81 5919 .54 2.17 2303 .94 M 56 20E 3 8013 .82 5950 .26 1.45 2309 .23 57 18 7672.91 6050 .69 2 .55 2268 .02 n 58 l6wei 7 3 3 7 . 8 3 6119 .45 - 2279.02 GLACI ER/EDC 59 l6w 2 7435.61 6163 .71 1 .95 2265.04 GLACIER 60 I6w, 7526 .13 6205 .30 2 .34 2251.44 61 16 7616.06 6247 .37 3.15 2245 .76 62 l 6 E j 7705 .66 6290 .24 3 . 2 8 2245 .68 63 16E 2 7795 .85 6331 .13 3 .14 2244 .31 64 14 7534 .87 6432.46 3-52 2219 .13 65 12W2 7302.28 6571 .36 3 . 6 5 2192 .22 66 12W! 7 3 9 6 . 5 7 6599 .20 3 .42 2185 .32 67 12 7496 .56 6630 .34 2 . 8 6 2183 .35 68 12E, 7592 .34 6658 .44 1.91 2179 .63 69 10 7472.16 6830 .58 4 .29 2152 .63 11 70 3 6E 2 8 3 6 0 . 7 9 4 3 4 4 . 9 9 2 . 9 4 2500.15 71 8 7428.03 7028 .50 2137 .96 FELL OVEF 72 7w 0.s 7401 .52 7133 .34 2'.08 2123.92 GLACIER 73 7 7450.18 7124 .29 2 .42 2129.62 74 ? E 0 . 5 7499 .94 7115 .00 2 .37 2135 .49 t . 75 36E; 8 5 5 0 . 5 0 4386.70 2 .06 2520 .80 n 76 6 7476.01 7222 .22 2.22 2117 .98 M 77 6 E 0 . 5 7526 .33 7209.42 1.65 2123.14 u 78 7576.08 7195.62 2.13 2121.36 „ 79 5 7503 .79 7317 .36 1 .91 2102 .13 M 80 4 7532 .40 7414.08 1 .96 2082 .37 81 3 7520.84 7538 .19 : 2 .80 2060 .20 82 2 7593 .39 7781.82 1 2.10 2029 .08 83 2E 0.5 ' 7646 .43 7769.42 i 0 .93 2031.05 f 84 36w, 7995 .36 4258.16 ! 2 . 8 0 2509 .34 85 36 . 8178.96 4303.55 I 3 . 0 8 2483 .57 „ : Values are in metres. # Some doubt about these figures. } : This s ta t ion may rest on ice or bedrock. 71 T A B L E 3 DATA FOR L E A S T - S Q U A R E S REDUCTION WEIGHTED AVERAGES N C T I O N J U N C T I O N AVERAGE V A L U E 1 2 -74.38 1 3 -47.25 1 k 72.57 2 3 27 .65 2 7 203 .02 4 5 16.58 4 8 131.67 5 6 21.61 5 9 130.00 6 7 18.89 •6 9 108.49 7 11 178.65 8 9 15.09 8 12 71.31 9 10 25.84 10 11 62 .90 10 12 29.77 11 15 59.05 12 13 75.95 12 Ik 53-54 13 Ik -22 .60 13 16 . 208 .60 l4 15 40.82 m 17 116 .62 15 18 266.18 16 17 -115-19 16 19 207.40 16 21 56.44 17 18 186 .65 17 22 152.75 18 23 90.91 19 20 -87.10 19 27 112.27 20 21 -63.09 20 24 134.97 21 22 -13.16 22 23 126.19 22 25 99.34 23 26 22.58 24 25 -113-93 24 27 66.98 25 26 48.60 25 28 40 .82 26' 28 -6.15 27 28 -141.25 SUM OF WEIGHTED D I F F E R E N C E S AT J U N C T I O N S NCTIOiN SUM 1 -160 .49 2 702 .75 3 91 .59 4 75 .26 5 293 .34 6 200 .99 7 -21 .26 8 37 .97 9 -467 .81 10 87 .44 11 -492 .48 12 -38 .88 13 159 .78 14 153 .78 15 150 .41 16 -178 .54 17 398 .28 18 -353 • 31 19 -250 .64 20 177 .27 21 -7 .81. 22 70 .63 23 -238 .93 24 -211 .51 25 121 .94 26 - 6 7 .34 27 -366 .67 28 134 .22 72 TABLE 4 DATA FOR LEAST-SQUARES SOLUTION STATION JUNCTION NO. GRAVITY" STATION JUNCTION NO. GRAVITY 1 651.26 24E e -286 .97 2 E0 5 5 9 8 . 5 7 24E 6 16 -196 .02 607 .31 24E1+ -140.04 3 540.77 24E 9 -119.33 4 5 0 1 . 9 8 24 2 17 -82.10 5 469 .24 2 4w2 -94.48 6 E 1 425 .34 2 4w^ -156 .57 420 .44 2 4w e 18 - 2 6 9 . 8 9 2 437.05 26 -147.83 6 W 0 5 453 -88 28E e 19 -403.19 7E ' 0 5 397.11 2 8 E 1 0 28E 8 - 3 5 2 . 7 7 3 409 .09 20 -314 .96 7 W 0 5 419.80 28E® 21 -251.15 A * 1 363.03 28E, -232 .79 8 384.00 28E, -234.18 R 349.10 28 22 - 2 3 5 . 9 6 9 369 .06 28w 2 -230.77 10 351 .98 2 8w e 23 -361.23 1 2 E i 4 290.73 30 -304.69 12 5 274.19 32E 1 5 32E 1 2 -612 .72 12W, 164.33 - 4 9 4 . 9 3 12W2 6 252 .63 3 2 E 1 0 -501.93 12We 7 233.77 32E 8 32E 6 24 -449 .49 14 190.86 - 3 7 2 . 9 6 FOX -210.54 32E 4 - 3 7 9 . 4 9 l 6 E e 8 159.40 32E 2 - 3 ^ 8 . 9 9 16E 2 160 .96 32 25 -335.19 1 6 E , 16 148.22 32W2 - 3 4 3 . 4 3 9 144.58 32W,, -372 .40 l 6 w : l 6 w 2 10 118.21 32We 26 -383.23 83.42 PHI L -784 .03 l6Wej 16W62 11 55.20 3 ? E 1 2 3^E 1 0 - 5 3 6 . 7 8 -88.94 -545 .28 l 8 E e 77.50 3^E 8 -535.29 18 12 8 8 . 3 7 3 4 8 -357.17 20Ee 13 12.51 3 6E 6 27 -516.41 20E 3 29 .49 36Ek \ -44.70 20E 2 27.74 3 6E 2 1 -401.25 20E r 20 31 .96 36 | 28 -375 .99 14 35 .14 36w 2 ! -440 .00 20WX 20W2 41 .36 36w e | -409.68 i 42 .83 C L I F F 1 -516.82 20We 15 -4.42 22 -14 .74 - Scale d i v i s i o n s , a r b i t r a DON -301.36 ALMUT ! [• -528.35 o r i g i n . 73 T A B L E 5 C O R R E C T I O N S T O G R A V I T Y -S T A T I O N I N P U T C O R R E C T I O N S B O U G U E R A N O M A L Y L A T I T U D E j E L E V A T I O N jB O U G U E R T E R R A I N A N O M A L Y 1 118 .39 2 .70 - 1 6 6 . 6 2 60 . 6 0 3.37 14 .02 2 E 0 . 5 113.04 2 . 6 0 1 -158 . 6 0 57 . 6 9 3.84 13.38 1 1 3 - 9 3 2 . 6 1 i - 1 5 9 . 3 4 57 . 9 6 3.39 13.35 3 107 .19 2 . 4 4 \ -149.61 1 54.42 3 .18 12.73 4 103 . 2 6 2 . 3 6 -142.80 ! 51.94 3.04 13.08 5 9 9 . 9 4 2 . 2 9 ' - 1 3 7.48 I 50.01 2.85 13 .02 6 E X 9 5 . 4 9 2 .21 - 1 3 0 . 8 0 1 47 . 5 8 3 .14 13 . 20 6 E 0 . 5 95.00 2 . 1 6 -130 . 2 5 f 47.38 2 . 9 0 12 .86 6 9 6 . 6 8 2.23 -131.84 47.96 2.75 13-31 6 w 0 . 5 9 8 . 3 8 2 . 2 5 ! -134.42 48 . 8 9 2 . 8 1 13.43 ?E0 5 9 2 . 6 3 2.16 -126.45 46 .00 2.81 12 . 8 3 7 9 3.84 2 .16 i - 1 2 8.25 46.65 2.62 12 .40 7 W 0 . 5 9 4 . 9 3 2 .17 l - 1 3 0 . 0 1 47 . 2 9 2.79 12.83 A 8 9 . 1 7 2 .11 -120.21 43 .72 2.97 13.56 8 9 1 . 3 0 2 .10 -125.51 45.65 2.68 12 .03 R 8 7 . 7 6 2 .06 - 1 1 8.14 42 .97 2 . 8 8 13.41 9 8 9 . 7 8 2 .03 -112 .34 4 4 . 5 0 - -10 8 8 . 0 5 1.96 -121.17 4 4 . 0 8 2 .96 11 . 9 2 1 2 E l 8 1.84 1.85 -112.86 41.05 3 .01 11.20 12 8 0 . 1 7 1.83 -111.71 40.64 2.81 1 0 . 0 7 12Wj 7 9 . 1 7 1 . 8 1 -111 .11 40 .42 2.90 9.57 12W2 7 7 . 9 8 1.79 - 1 0 8 . 9 9 39.64 3 . 3 2 1 0 . 1 8 12We 7 6 . 0 7 1.64 -105 .28 38.30 4.57 12.03 14 71.72 1.70 -100 . 7 0 36 . 6 3 2 .71 8.67 FOX 31.04 1.65 -41.98 15.27 - -l 6 E e 6 8 . 5 3 1 . 6 6 -91.39 3 3-24 2.97 11.71 1 6 E 2 6 8 . 6 9 1 . 6 3 - 9 2.95 33.81 2 . 3 6 10 . 2 9 I 6 E . 67.40 1.60 -92.53 3 3 . 6 6 2.39 9 . 3 3 16 6 7 . 0 3 1.57 -92.51 33-65 2 . 4 4 9.05 l6w x 6 4 . 3 6 1.54 -90.76 3 3 . 0 1 2.49 7.57 l6w 2 6 0.84 1.51 -86.57 31.49 2.54 6.79 l6wei 58.00 1.48 - 8 2 .27 29.93 2 .72 6.87 l6we 2 4 3 . 3 6 1.40 -57 - 7 0 2 0 . 9 9 4.84 10.10 l 8 E e 6 0.24 1.48 -79.72 2 9 . 0 0 2.58 10 . 6 1 1 8 6 1 . 3 4 1.43 -85 . 6 6 31.16 2 .22 7.63 20Ee 5 3 . 6 5 1.38 - 6 8 . 9 6 25 . 0 8 2 .34' 10.74 20E 3 5 5 . 3 7 1.34 -72.97 26 . 5 5 2 .09 9.69' 20E 2 5 5 . 1 9 1.34 -74 .60 27.14 1.95 8.34 20E! 5 5 . 6 2 1 . 3 2 -76 . 3 3 27 . 7 7 , 1.81 7.54 20 5 5 . 9 4 1 . 3 0 - 7 8.00 28.37 1 . 7 7 6.79 20WX 5 6 . 5 7 1.28 -79.67 28.98 I 1.94 6 . 5 5 20W2 56.72 1 . 2 6 - 8 0 .06 29.12 ; 2 . 3 2 6 . 8 5 20We 5 1 . 9 3 1 . 2 3 -72 .49 26.37 ' 2.94 7 . 5 2 22 5 0 . 8 9 1.17 1 - 7 0.49 25.64 1 . 7 7 6.64 74 TABLE 5 (concluded) STATI ON INPUT CORRECTIONS |BOUGUER ANOMALY LATITUDE! I ELEVATION BOUGUER TERRAIN ANOMALY DON 2 1 . 8 4 1.13 - 2 9 . 7 3 10 .81 5 .73 7 .53 ALMUT } - 1 . 1 7 1.27 8 . 0 4 -2 .92 4 .92 7 . 6 0 2 4 F e 23-30 1.18 -22 .96 8.35 3 . 1 2 1 0 . 6 3 24E 3 2 . 5 1 1.15 - 3 9 . 5 8 14 .40 1.49 7 . 6 8 24E 6 38.19 1 . 10 i -48 . 42 1 7 . 6 2 1.35 7 .63 24EU 40.29 1 .05 -54 .05 19 .66 1.2-9 6 .13 242 i 4 4 . 0 6 1.02 - 6 1 . 0 8 22.22 1 . 4 6 5 . 6 4 2 4W2 42 80 0 .97 - 6 1 . 1 2 22.23 1.66 4 . 6 1 24Wf4 ( 36'.51 0 .93 - 4 9 . 3 2 17 .94 2 .18 6 .39 24we ; 25.03 0 .87 - 3 0 . 5 7 1 1 . 1 2 2 .86 7 .57 26 I 37.40 0 .88 - 5 1 . 0 6 18 .57 l • 13 5 .16 2B E e I 11 .52 1 .13 -7 . 24 2 .63 2 .16 7 . 9 5 28E10 1 6 . 6 3 1 .06 -16 .96 6.17 1 .30 6.09 28E8 ! 20 .46 1.00 - 2 3 . 7 3 8.63 1 .31 5 . 6 8 28E6 i 2 6 . 9 3 0 .93 - 3 3 . 0 6 12 .03 1.11 6 . 0 8 28E4 f 2 8 . 7 9 0 .87 - 3 7 . 7 7 13 .74 1.00 4 . 8 9 28E2 I 2 8 . 6 5 0 .81 - 3 8 . 9 8 1 4 . 1 8 ' 1.01 4 .05 28 ! 2 8 . 4 7 0 .75 - 3 8 . 9 3 1 4 . 1 6 1 . 0 1 3 .97 2 8W2 : 2 8 . 9 9 0 .68 - 3 9 . 8 6 14 .30 1.06 4 . 0 1 28w e 15.77 0 .53 -16 . 12 5 .87 1.40 6 . 8 9 30 I 2 1 . 5 0 0 .61 - 2 9 . 8 3 1 0 . 8 5 0 .96 2 .87 32E15 i - 9 . 7 2 0 .80 15 .73 -5 .72 5.15 4 . 6 4 32E12 i 2.22 0 .76 1.86 -0 .68 2 .16 4 .80 32Eio I 1 .51 0 .70 0 .20 - 0 . 0 7 1 .68 2 .61 32E8 | 6 . 8 2 0 .65 -6 .42 2 .34 1.65 3 .74 32E6 1 4 . 5 9 0 .61 - 16 .17 5 . 8 8 1 .33 5 .02 32Ek I 13.92 0 .57 - 1 8 . 3 9 6 .69 1.00 2 .66 32E2 S 1 7 . 0 1 0 .52 -22 .75 8 . 6 4 0 . 84 2 .22 32 ! 1 8 . 4 1 0 . 48 -26 .50 9 . 6 4 0 .72 1.79 32W2 i 17 .57 0 .43 -25 .05 9 . H 0 .82 2 .03 32W+ !' 1 4 , 6 4 0 .38 - 1 8 . 8 1 6 . 8 4 0 .92 3 . 2 1 3 2 W e ; 13.54 0 .29 - 1 4 . 4 4 5 .25 1.68 5-75 PHIL i - 2 7 . 0 8 0 .52 ! 36 .00 - 1 3 . 1 0 9 .54 4 . 8 4 34E12 I -2.02 0 .62 i 5 . 8 7 - 2 . 1 4 2 .44 3 .54 34EIO | - 2 . 8 8 0 .58 5 .63 - 2 . 0 5 2 .06 2 .18 34ES } - 1 . 8 7 0 .53 4 .04 - 1 . 4 7 1.96 2 .13 34 t 16 . 18 0 .35 - 2 3 . 0 1 8.37 0 . 8 3 2 .02 36E6 | 0.04 0 .13 1.42 - 0 . 5 2 1.86 2 .50 36E^ • 7 .31 0 .28 - 7 . 8 6 2 .86 1 .62 3 . 6 5 36E2 I 11 .71 0 .25 -14 . 22 ! 5 .17 1 .28 3 .70 36 i 1 4 . 2 7 0 .22 - 1 9 . 3 2 1 7 . 0 3 , 4 . 1 4 1.22 2 .98 36W2 I 7 .79 0 .19 - 1 1 . 3 9 1.53 1 .88 3 6 w e 1 0 . 8 6 O . I 3 - 11 .79 j 4 . 2 9 2 .42 5 . 6 5 CLI FF | - - 5 . 9 7 5 .97 " Values in m i l l i g a l s , re ferred to C l i f f . 75 T A B L E 6 R E G I O N A L G R A D I E N T S T A T I O N BOUGUER VALUE OF P O L Y N O M I A L A N O M A L I E S " n=l n=2 n=3 :: 1 13.56 12.84 13 .12 13.15 2 12.03 11.78 11.46 11.85 3 11.71 10 .86 11.83 11.56 4 10 .10 10 .47 9.38 9.46 5 10.61 10 .13 11.31 11.15 6 10 .74 9.67 10.95 10 .89 7 7.53 9 .28 8.96 8.74 8 10.63 8.52 9.4 3 9.73 9 7-57 8.34 7 .70 7 .41 10 7.95 8.01 7.56 7.89 11 6.39 7.00 6.45 6.25 12 5-75 6 .00 5-56 5-52 13 4.84 5.51 4.75 4 .32 14 5.65 5.27 5.45 5 .60 15 5-97 4.46 5-95 6.21 16 4.64 6.58 5.43 5.51 17 14 . 0 2 14.95 14.37 14 .00 18 13.43 13.45 13.46 13.88 In m i l l i g a l s . 76 TABLE 7 ANOMALIES AND DEPTHS STATION RES I DUAL DEPTH Z ANOMALY DEPTH S ANOMALY ANOMALY FROM FROM ADJUSTMENT FROM R" R : : Z » A Z " j Z + A Z " 1 0.02 _ -0.03 _ -0.05 2Eo.5 -0 .72 9 . 6 - 0 . 4 4 0 .7 [ - 0 . 6 6 2 -1.05 14.1 -0 .20 9.7 i - 0 . 3 3 3 -1 . 55 20 .8 -0 . 5 5 9 . 4 i - 0 . 8 5 4 -0 .90 12.1 -0 .43 3 . 5 | -0.64 5 -0.84 11.3 -0 .50 2 .3 | - 0 . 6 7 6Ei -0 .21 2.8 -0.27 -1.2 -0.30 6EO . 5 -0 .70 9.4 - 0 . 5 7 0 .8 1 - 0 . 6 5 6 -0.41 5.5 -0.61 -2.9 -0.63 6wo. 5 -0 .45 - -0.15 - ! -0.16 7E0 . 5 -0 . 5 8 7 .8 -0 .56 -1.0 I -0.66 7 -0.84 11.3 -0 .76 -0.8 -0 .91 7W0 . 5 -0.82 11.0 -0 .62 1.0 -0 .75 A 0.41 - -0.03 - -0.05 8 -1.29 17.3 -0 .58 6 . 4 -0.82 10 -0.84 11.2 - 0 . 7 8 -1.3 - 0 . 9 3 12El -1.06 14.2 - 0 . 5 5 4 .4 - 0 . 7 3 12 -2 .16 29.0 -1.64 2 .8 - 1 . 9 5 12W1 - 2 . 5 8 3 4 . 5 -2.55 -5 . 5 -2.99 12W2 -1.84 24.7 -1.23 4 .9 -1.48 12We 0.18 - 0 . 3 5 -0 .47 I 4 e -3-07 41.1 -2.00 8 .2 -2.46 16 E„ -0.15 - -0.27 - -0 . 3 6 16 E ! -1.25 16.7 -0 .87 1 .7 -1.12 16EI -2 .13 28.6 - 1 . 3 9 5 . 8 -1.70 16 -2 .28 30.6 -2.61 -9-7 -3 .01 l6wi -3-58 48.0 -3 .02 7 .5 1 - 3 . 4 9 16W2 -4 .13 5 5 . 3 -3.31 11.0 -3 -93 l 6 w e i -3 .74 50.1 -2 . 5 8 15.5 -3-14 I6we2 0.64 _ - 0 . 4 5 -0 .57 l 8 E e -0 .54 - - 0 . 7 8 -0 .86 I 8 e -3-30 44 .2 -2 .56 9 .9 - 2 . 8 9 20E -0 .15 - -0.42 | - 1 . 3 3 I - 1 . 8 - 0 . 3 8 20E3 -1.20 16 .0 ! -1.27 2 0E2 -2 .49 3 3 . 4 -2 .34 2.1 -2 .30 20E1 -3 .19 42 .7 -3-32 -1 .7 - 3 . 3 6 20 - 3 - 7 8 50.6 -3.16 8 . 3 -3 .28 20W1 -3.80 51.0 -4 .22 -5 .6 -4 .31 2 0W2 -3 .24 4 3 . 5 -3 .14 1.4 -3 .28 20WP -2.13 28.6 - 1 . 8 9 3.2 -2.14 22 - 2 . 6 8 ! 35-9 - 3 - 3 4 - 9 . 0 -3 .20 -0.19 DON -1.21 • -0.16 77 TABLE 7 (concluded) STATION RESIDUAL DEPTH Z ANOMALY DEPTH ANOMALY ANOMALY FROM FROM ADJUSTMENT FROM R R Z . AZ Z+AZ 24E e 0 . 9 0 _ -0.21 _ -0 .25 24E 6 -2.46 33.0 -2 .68 7.1 -2 .00 24E 4 -2 .63 3 5 . 3 - 3 .06 -5.7 -2 .98 2 4E, -4.01 5 3 . 8 - 3 - 9 6 0.7 - 3 . 8 6 24 -4 .17 55-9 - 3 . 7 8 5 . 3 - 3 . 6 5 24w2 -4.64 62 .2 -4.93 - 3 . 9 -4.46 24W4 -2 .09 28.0 - 3 . 3 3 -16.6 -2.44 24we 0 .16 - -0 .80 - -0 .57 26 -4 .31 57-7 -4.87 -7.6 -4 .62 2 8 E e 0 .06 - -O.56 - -0.59 2 8 E 1 0 -2 .72 3 6 . 5 -2 .26 6.1 -2 .57 2 8 E 8 - 3 . 6 6 49.0 -3.14 7.0 - 3 . 4 9 28E 6 - 3 . 5 5 4 7 . 6 - 3 . 6 3 -1.0 - 3 . 7 2 28E„ - 4 . 8 0 64.4 -4.45 4.7 -4.48 28E 2 -5.46 73.2 - 5 . 5 9 -1.7 -5.66 28 -5.14 6 8 . 9 -4.74 5.4 -4.64 28w2 -4.46 5 9 . 7 - 5 . 4 5 -13 .2 -4.55 2 8 w e 0 .14 - -1.13 — -0.90 30 - 5 . 8 6 7 8 . 6 - 5 . 6 7 2 .5 - 5 - 7 6 3 2 E 1 5 -0 .87 - -0 .37 - 0 . 3 2 3 2 E 1 2 -1 .79 24.0 -2.22 - 5 . 8 -2 .12 3 2 E 1 0 - 5 . 1 8 6 9 . 4 - 3 . 8 3 18.0 -4.13 3 2 E 8 - 4 . 6 2 61 .9 -4.26 4.9 -4.58 3 2 E 6 - 3 . 6 6 49 .0 - 4 . 3 8 -9 .7 -4.67 3 2 E ^ -6.12 82.1 -5.21 12 .3 -5.64 3 2 E 2 - 6 . 4 4 8 6 . 4 - 5 . 9 7 6.3 -6.40 32 - 6 . 5 4 87 .6 - 5 . 4 5 14.6 - 5 . 7 4 32W2 - 5 . 7 4 7 6 . 8 -6 .07 -4.5 | -6 .15 32Wlt - 3 . 7 6 50 .4 -4.64 -11 .7 i -4.41 32We 0 .23 - -0 .79 - -0 .79 PHI L 0 .52 — -0 .73 : — ! -0 .61 3^E 1 2 -2 .75 3 6 . 9 -4.04 -17.3 | - 3 . 5 9 3 ^ E 1 0 -5.05 6 7 . 7 - 5 . 8 5 -10.6 < -5.77 34E 8 - 5 . 7 1 7 6 . 5 -4.13 21.1 ( -4 .64 3 4 8 - 5 . 8 8 78.8 - 5 . 6 1 3.6 1 -6 .02 3 6 E G -4.82 64.6 - 3 . 2 7 20 . 8 ? - 3 . 9 4 36E^ - 3 . 9 4 5 2 . 8 - 3 . 4 5 -0 .5 I - 3 . 9 8 3 6E 2 - 3 - 9 2 52.6 -3.41 1.6 1 - 3 . 8 1 36 - 4 . 4 4 5 9 . 5 -3.61 5.2 1 -4 .06 36w 2 -5.12 68.6 -4.02 7 6 1 -4.55 36We 0 .05 _ -0.31 j -0 .36 CLIFF -0.24 - -0 .95 ! -1 .13 Depths in meters, anomalies in m i l l i g a l s . 78 T A B L E 8 TEMPERATURE MEASUREMENTS HOLE AT STAKE 2 Measured August 16th Surface e levat ion 2029m No snow cover DEPTH R E A D I N G T E M P E R A l m mV deg C 0.50 - -1.00 0 .008 -0.0 1.50 0 .026 -0.7 2.10 0 .046 -1.3 2 .50 0.083 -2.3 3 .00 0.107 -3.0 3.50 0.123 -3.4 4 .00 0.138 -3.8 4 .50 0 .160 -4.4 HOLE AT STAKE 7 Measured July 7th Surface e levat ion 2130m No snow cover DEPTH READING TEMPERATURE m mV deg C o .60 -1.00 0 .042 -1 .2 1.40 0 .095 -2 .6 2 .40 0 .157 -4 .4 3.00 0 .197 -5 .5 Measured August 12th 0 .80 - -1 .30 0 .038 -1 .1 1 .80 0 .092 -2 .6 2 .30 0 .113 -3 .1 2 .80 0 .135 -3 .8 3 .30 0 .145 -4 .0 3 .80 0 .168 -4 .7 4 .30 0 .164 -4 .6 4 .80 0 .165 -4 .6 5 • 30 0 .161 -4 .5 5 .80 0 .165 -4 .6 6 .30 0 .163 -4 .5 6 .80 0 .168 -4 .7 7 • 30 0 .170 -4 .7 7 .80 0 .166 -4 .6 HOLE AT S T A K E 16 Measured August 8th Surface e levat ion 2246m No snow cover D E P T H | R E A D I N G m mV 0 .15 0 .40 0 .65 0 .90 1.15 1.40 1.65 1.90 2.15 2.40 2 .65 2 .90 3.15 ! 3 .40 TEMPERATURE deg C 0 .001 0.009 0.035 0 .054 0 .071 0.096 0 .119 0.133 0 .146 0.159 0 .168 0.182 0 .192 -0.0 -0.2 -1.0 -1.5 -2.0 -2.7 -3.3 -3.7 -4.1 -4.4 -4.7 -5.1 -5.3 HOLE AT S T A K E 34 Measured August 4th Surface e levat ion 2472m Sno\\r cover 96 cm DEPTH m READING mV TEMPERA deg C 0.15 0 .014 -0.4 0 .40 0.034 -0.9 0 .65 0 .040 -1.1 0 .90 0.053 -1.5 1.15 0.061 -1.7 1.40 0 .074 -2.0 1.65 0.092 -2.6 1.90 0.105 -2.9 2 .15 0.123 -3.4 2.40 0.131 -3.6 2 .52 0.135 -3.8 79 TABLE 8 (concluded) HOLE IN SIDE OF JACKAL GLACIER D r i l l e d h o r i z o n t a l l y , 73 ft v e r t i c a l l y below surface Measured July 12th DEPTH READING TEMPERATURE m mV deg C 3 .00 0.176 -4.9 Measured August 15th 2 .35 0.109 - 3 . 0 HOLE IN TOP OF JACKAL D r i l l e d v e r t i c a l l y Measured July 21st DEPTH READING TEMPERATURE m mV deg C 2.70 0 .112 - 3 . 1 HOLE IN SIDE OF JACKAL D r i l l e d h o r i z o n t a l l y , 2m above bedrock Measured August 15th DEPTH READING TEMPERATURE m mV deg C 1 . 4 3 0 .050 - 1 . 4 HOLE IN SIDE OF HYENA GLACIER D r i l l e d h o r i z o n t a l l y , 3m above ground l e v e l Measured August 15th DEPTH READING TEMPERATURE m mV deg C 0 . 9 0 0 . 0 2 7 - 0 . 8 80 T A B L E 9 C L I M A T E DATA S t a t i o n : - A I S H I H I K (61 3 7 ' N , 137 31 MV. E levat ion 3170m) MONTH MONTHLY TEMPERATURE C O R R E C T I O N P R O J E C T E D OF YEAR MEAN G R A D I E N T TO MEAN TEMPERATURE AT F deg F 1 deg F per deg F deg F deg C (-) ft J A N -1 751 -5 -6 -21 FEB -1 717 -6 -7 -22 MAR 14 556 -7 7 -14 APR 33 501 -8 15 -9 MAY 41 545 -7 34 1 J U N 50 583 -7 43 6 J L Y 53 608 -7 46 8 AUG 49 603 -7 42 6 S E P 41 597 -7 34 1 OCT 28 557 -7 21 -6 NOV 6 656 -6 0 -18 DEC -4 639 -6 -10 -23 mean= -7. Stat ion :- SNAG (62 22'N, 140 24 MV. E levat ion 1925m) J A N -14 751 -7 -21 -29 FEB -10 717 -7 -17 -27 MAR 11 556 -9 2 -17 APR 25 501 -10 15 -9 MAY 45 545 -10 35 2 JUN 53 583 -9 44 7 J L Y 57 608 -9 48 9 AUG 52 603 -9 43 r 0 SEP 41 597 -9 34 1 OCT 24 557 -9 13 -11 NOV -3 656 -8 -11 -24 DEC -15 ; 639 -8 -23 -31 6°C mean= - 1 0 . 2 ° C 81 T A B L E 10 DATA FOR E F F E C T OF ACCUMULATION ON TEMPERATURES H E I G H T h ABOVE G L A C I E R BASE (m) G L A C I E R T H I C K N E S S H=100m G L A C I E R T H I C K N E S S H = 50m Ae=eLJ-eu FOR H . n *A=0 A=50 A=100 A=500 A 6 = 6 1,-e T, FOR . H . n A=0 A=50 A=100 A=500 0 10 20 30 40 50 60 70 80 90 100 0.23 0.45 0.68 0.91 1.14 1.36 1.59 1.82 2 .04 2.27 0 .23 0.45 0 .68 0 .91 1.14 1.35 1.59 1.79 1.95 2 .09 0.23 0 .45 0.68 0 .91 1.14 1.32 1.47 1.58 1.68 1.76 0.23 0 .45 0 .63 0.75 0 .81 0.85 0.86 0.87 0.87 0.87 0.23 0 .45 0.68 0 .91 1.14 0.23 0.45 0.68 0.23 0.45 0.68 0.91 0.90 1.14[ 1.04 0 .23 0.44 0.55 0 .60 0 .62 A is accumulation rate in cm yr 

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