AID-A276 999 RE

SELECTESMAR 16 1994*fDEM

A Reassessment of the In-SituDielectric Constant of Polar FirnAustin Kovacs, Anthony J. Gow and Rexford M. Morey December 1993

ft 1"5~

The success In using VHF and UHF frequency systems for sounding polar Icesheels has been tempered by an uncertainty In the in-situ dielectric constant e,which controls the efliective velocity V. of an electromagnetc wave propagatingIn an air-Ice mixture. An empirical equation for determining e' vs. density(speciic gravity, p)was proposed In 1968 by Robinetfal. where e= (I + 0.851p)2. However, this expression has Met With uncertainty because wide-angileradar rellraction sounding techniques have produced values of el that are lowrIthan Robin's equation predicts. This report discusses radar sounings made onthe McMurdo Ice Shel, Antarctica, and compares the resuiting e' values withRobin's equationt, labortory measuremenlsontim and ice andol3wexreessionsgiven In the literature for determining e'vs. the specitlc:gravltyof dryfim and lee.Our findings indicate that the form of Robin's equation Is valid. However, ouranalysis also Indicates the expression could be slightly Improved to read e'=(I + 0.845 p)2. Reasons are suggested as to why previous wide-angle radarsounding studies did not reproduce Robin's findings.

Cover~ Radar transceive antenna being tboood from the front of a boommounted to a tracked vehicle. Behind Mf e antenna box Is a disk andsupport leg used to elevate the boom above the snow surface Thisantenna arrangermet was used In 19 74 for proflllng the brine layer inAhe McMurdo Ice Shelf and for crevasse detection during a ftranser inifti Pensacola Mountains, Antoracla, In search of bluelcerfunwaysites.The radar console and recording equipment v.,re locte In the vehicle.(Photo by A. Kovacs.)

For conversion of SI metric units to U.S./Brltlsh customcury units of measurementconsult ASTM Standard E380-89a, StondardPracftceforUse of the nternaonalSystem of Unfts, published by the American Society for Testing and Materials,1916 Race St., Philadelphia, Pa. 19103.

CRREL Report 93-26

US Army Corpsof EngineersCold Regions Research &Engineering Laboratory

A Reassessment of the In-SituDielectric Constant of Polar FirnAustin Kovacs, Anthony J. Gow and Rexford M. Morey December 1993

Accesion For

NTIS CRA&I

DTIC TABUnannouncedJustification ...............

By .........-...................

Dist, ibution I

Availability Codes

Avail and °orDist Special

Prepared forDIVISION OF POLAR PROGRAMSNATIONAL SCIENCE FOUNDATION

Approved for public release; distribution is unlimited.

PREFACE

This report was prepared by Austin Kovacs, Research Civil Engineer, of the Applied Re-search Branch, Experimental Engineering Division, Dr. Anthony J. Gow, Geologist, of the Snowand Ice Branch, Research Division, U.S. Army Cold Regions Research and Engineering Labora-tory, and Rexford M. Morey of Morey Research Company. Funding for this research was pro-vided by the National Science Foundation, Division of Polar Programs, under grants NSF-DPP 74-23654 and NSF-DPP 8004221.

The authors thank Dr. David Morse of the University of Washington, Geophysics ProgramAK-50, and Dr. Kenneth C. Jezek of the Byrd Polar Research Center, Ohio State University, fortheir technical review of the report.

ii

CONTENTSPage

Pr[ o~~eelooool~efac ................................... ...................... ......... ...... ... o.................•.o.H.................. ii

FIntod ci o ....... .............................................................................................................. IField inessun-a t . ...................................................... 5

D su ssi ......................................................................................................................... 12C naclusions . .. ........................................................................................................... 14Literature citd.............ted............................................ 14Appendix A.~ Suppleenwt equaticins for determining the dielectric constant of

an air-ice mi x t ure...................................................... 17Appendix B: TM dielectric constant of a soil-water mixture..................... 21Abstract............................................................................................ 273

ILLUSTRATIONS

Figure

1. Map of the McMurdo Ice Shelf area ......................................................................... 22. Cross section of the McMurdo Ice Shelf along the subsurface radar sounding

prfile line shown in Fgure I ................................................................................. 33. Radar records of McMurdo Ie Shelf along sounding line ........................... 44. Graphic record of 300 MHz radar sounding data showing internal layers in

the mow field below Castle Rock ......................................................................... 65. Example of received radio echo wavelet ................................................................... 76. Field-determined in-situ effective dielectric constant 4e vs. the bulk specific

gravity of McMurdo Ice Shelf firn .......................................................................... 87. Field-determined in-situ effective dielectric constant 4 vs. the bulk specific

gravity of McMurdo Ice Shelf fim .......................................................................... 98. Field-determined in-situ effective dielectric constant e' vs. the bulk specific

gravity of McMurdo Ice Shelf firn .......................................................................... 109. Field-determined in-situ effective dielectric constant 4e vs. the bulk specific

gravity of McMurdo Ice Shelf fim .......................................................................... 1110. Field and laboratory-determined values of the dielectirc constant of firn vs.

specific gravity ......................................................................................................... 1111. Effective radar velocity vs. depth at DYE-3 Greenland .................... 1212. Horizon depth within the McMurdo Ice Shelf vs. radar wavelet two-way

flighttim e ................................................................................................................. 1313. Effective dielectric constant of the fim-ice in the McMurdo Ice Shelf vs.

depth increm ent ....................................................................................................... 13

TABLES

Table

1.1978 McMurdo Ice Shelf station data along traverse from shelf edge toice shelf movement marker 307 ............................................................................. 5

2. McMurdo Ice Shelf depth increment data ............................................................... 7

iio

A Reassessment of the In-Situ Dielectric Constant of Polar Fire

AUSTIN KOVACS, ANTHONYJ. GOW AND REXFORD M. MOREY

INTRODUCTION and gt' = real part of the magnetic permeability4E = realeffective (bulk) dielectric constant

Since 1948, when Steenson (1951) first used a (e = effective (bulk) conductivity.100-MHz pulse radio sounding system to estimateice thickness on the Seward Glacier in Alaska, "ra- Since the conductivity of dry polar firn and ice isdioglaciology" has been extensively used for mea- extremely low, the effective pbase velocity of high-suring the depth of polar ice sheets. Success in using frequency electromagnetic waves can be deter-sounding systems operating at VHF and UHF fre- mined fromquencies stems in part from the generally very fa-vorable electromagnetic properties of polar fire and Ve = C (2)ice, which allow for deep penetration at these fre- where c is the velocity of an electromagnetic wave inquencies. ahvacis 0.3 v tn etThe relative complex permittivity •r of an air-ice a vacuum, 0.3 m/ns.

If the two-way vertical travel time t of a transmit-mixture can be described by the Debye expression ted wavelet traveling from the surface to the ice bot-

• -tom (or from some internal horizon) and back isCr = Er - J~ r = Er + Crs-r (1) measured, then this time may be used to estimate

1 + j o" the distance D to the reflective boundary from

where e' = the relative real part of * (or the dielec- D - tc=_ t Ve (3)tric constant) 21-e 2

r" = the loss factor or imaginary part ofE!El = the relative static dielectric constant To accurately make this distance determination, Ee

= the relaxation time for the site must be known. 4 can be determinedo) = the angular frequency. when t and D are known as follows:

In this report the variation in the dielectric constant 4e =I2kD2 . (4)vs. firn density or specific gravity is discussed, as 12(this value governs the propagation speed of an Since D is seldom known, this equation is of limitedelectromagnetic wave transmitted from VHF and se D is and is ensity profilimiteUHF sounding systems into polar firn and ice. The available he f ir t ait ies possible to estimate a foraloss tangent, tan 8, is represented by " /e and for epolar firn and ice is typically >> 0.1 given depth increment based on the mean intervalAn electromagnetic wave propagates through density and a laboratory-determined e' value for

An eldiewitrmagnefeticave proagte s v ith.ouh this mean density.firn and ice with an effective phase velocity Ve of To circumvent these requirements, borehole in-

Ve = ()/p terferometry and widE angle radar reflection tech-niques have been used to determine D or ,. Thesewhere 5 is the phase constant determined by methods have been widely discussed by Bentley

(1979), Jezek and Roeloffs (1983), Bogorodsky et al.(1985) and others. However, Jezek and Roeloffs

g,• C' 12 +~ 2 \1/2 1Wi (1983) state that "collectively, these experiments are1)= !! 1 + 1 inconclusive." It has been found that Ve determined

202 (E from wide-angle reflection sounding measurements

tends to be too high, and the resulting low value for n = - = 1 + 0.851p.

r is not in agreement with laboratory determina- Vetions of e' made on fire and ice of the same density.System timing error and curved ray paths are two of Since n 2 = £e in the radio-radar frequency range ofthe possible reasons given for the observed discrep- interest, thenancies (Jezek and Roeloffs 1983).

The lack of agreement between laboratory-deter- e = (1 + 0.851 p) 2 . (5)mined Er values and the various radar field resultshas brought into question the validity of Robin's The form of this exponential expression is hereafter(Robin et al. 1969, Robin 1975) borehole radar inter- referred to as a refraction tyj - -quation.ferometry measurements, from which he proposed During their study of the -mne infiltration zonean empirical equation relating the index of refrac- in the McMurdo Ice Shelf, Antarctica (Fi& 1), Kovacstion n to the firn-ice density, which is henceforth ref- and Gow (1975) and Kovacs et al. (1981, 1982) usederenced as the specific gravity p for the purpose of two impulse radar sounding methods to profile themaking his and subsequent equations dimension- depth variations, lateral continuity and "inland"ally correct: boundary of seawater infiltration into the ice shelf

30' Ford 36.

Rack

McMURDO ROSL

SOUND ISL 4N 3N

ca.01:'Rac 5N2N(&19)

. i, 202 IN/

-77-50S al *; 1" / 0 jb, " z 0C,04 (Jan.m 19 Is

\ Profile Line 2S

station IWJon, 19771 Limit of rineI IShelf Edged.. __ Infillrotion

a'207 ~ lt~W 208

I ( .- '6SMcMURDO ICE SHELF 7S relief

Long r wide aef aanto seo neoor isla0nid

,e! Moroine 9S n WSBonds 21 os

// /

/(1 /€mme4 fI /I

rD - 0

LA

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EI

8 /x

C1

0,0

4 900 0cv v ( OD t0

(W) 813 w) tide

0 -3

o .111N

N

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j

(Fig. 2). One method previously discussed (Kovacs FIELD MEASUREMENTSet al. 1982) used a fixed separation, dual-antennaconfiguration in which one antenna was a trans- A Geophysical Survey Systems impulse radarceiver (colocated transmitter-receiver antenna) and system was used in the field study. The transceiverthe second antenna was a receiver only. The dual- antenna, when smow-coupled, transmitted a broad-antenna methodology used is discussed in Kovacs band wavelet with a center frequency of about 100and Morey (1979). With this radar sounding meth- MHz. The vertical two-way travel time of the wave-od, Ve, D and ee were determined for the firn be- let from the snow surface to various subsurface an-tween the snow surface and the brine infiltration nual accumulation layers and the top of the brinelayer. The depth of the brine layer was determined infiltration zone in the McMurdo Ice Shelf was re-by direct borehole measurements one year after corded in real time on a graphic recorder (Fig. 4) andthe radar measurements were made. After the new on a magnetic tape recorder for later analysis on asnow accumulation was taken into comsideration, frequency analyzer. The two-way flight time wasthe agreement between the radar- and borehole- measured from where the transmit wavelet firstdetermined depths was typically within 2%. These crossed the zero voltage line to where the relectedresults indicate that, for the shelf firn layer, where wavelet of interest first crossed the zero line as de-the most significant depth variation in density oc- picted in Figure 5.curs, the dual-antenna radar sounding method pro- Two-way travel time measurements were madevided a satisfactory means for determining e. and at six sites in 1978 where cores were obtained for de-Ve as well as the depths to internal layers, which termining the depth to the brine layer and thewere dearly revealed in the radar records (Fig. 3 depth-density profile. The measured distance fromand 4). the edge of the McMurdo Ice Shelf, brine layer

While Kovacs et aL (1982) showed good agree- depth, average firn density and the two-way travelment between their radar-determined depth to the time are listed in Table 1 as are the calculated e' andbrine layer and the drill-hole-measured depth and Ve values for each radar sounding site. Also given isgave estimates of ce and Ve, they did not provide in- the location and the two-way travel time to the bot-formation for an assessment of the Robin equation. tom of the ice shelf at station 307, which was locatedNor did they attempt "to resolve the question of the immediately beyond the 1978 brine infiltration limitpossible discrepancy between laboratory and field (Figs. 2 and 3). The depth of the ice shelf at stationdielectric constant measurements" for firn and ice as 24, located just 40 m before station 307, was esti-did Jezek and Roeloffs (1983). In this report, data ob- mated by Kovacs et al. (1982). Using the 1977 dual-tained from the vertical two-way impulse radar antenna radar sounding data, they first determinedsounding measurements on the McMurdo Ice Shelf the depth to the brine layer at station 24. The two-are presented. The findings are discussed in relation way flight time from the brine layer to the bottom ofto the Robin equation and other field, Laboratory, the ice shelf was then used, along with an assumedand theoretical determinations of the dielectric con- value of ce = Z95 for this depth interval. The thick-stant of an air-ice mixture. ness of the ice shelf was then estimated (using eq 2

Table 1.1978 McMurdo Ice Shelf station data along traverse from shelf edge to ice shelf move-ment marker 307.

Distance Brine Average Wavelet Effctive bulk EffectiveStation inland depth* spec traud time t dielecric velocity V.

no. (M) (in) gwavity p (ns) constant (n¢ns)

A 5 2.5 0395 22 1.74 0.227B 770 8.85 0.509 83 1.98 0.213

lob 2900 13.5 0.540 130 2.08 0.208C 3590 9.45 0.56 190 2.15 0.204D 7370 33.8 0.624 344 2.33 0.196E 9560 50.4 0.686 529 2.48 0.190

307 9700 - - 1263 - -

°Drillhole measurements

5

INTERNAL LAYER

ts1

BEDROCK • ".

, -.

Figure 4. Graphic record of 300-MHz radar sounding data showing internal layers in the snowfield below Castle Rock(Fig. 1). The dotted line mnarks the site where a 20-rn firn core was obtained. Core analysi, reveadN the internal layerswere summner stratigraphy horizons.

6

Transmitted Brine LayerImpulse Ref lect ion

4

2- Figure 5. E=ple of receiw radio echo* Internal Layers Uumlet. In the graphic record many horwn

or internal •lyers uei observed in the ie shf-4_ __ I Ji. These__ __ o uld be tracAzdir many

0 20 40 60 80 100 120 140 klomee. Their voltae ampitu signatureTime (ns) is Amon aboveOwn zKovacs et al. 1982).

and 3) to be 113 m. This thickness Table 2. McMurdo Ice Shelf depth increment data.estimate will be compared withthe estimated thickness for sta- station increment ave t diEectric bulk ff tVtion 307 as determined from the increment (md gravity p (Ns) cstant e, (M/ns)1978 radar two-way travel timedata obtained at this site. A-B 6.35 0.504 61 2.08 0.20

The brine layer depths and B-C 10.6 0.633 107 2.29 0.199C-D 14.35 0.726 154 2.59 0.186

two-way travel time differences D-E 16.6 0.808 185 2.79 0.180between stations A-B, B-C, C-Dand D-E are listed in Table 2along with the average firn densities for the depth rather than perpendicular to the crystal c-axis. Smi-increments. Also listed are the calculated e' and Ve larly, Fujita et al. (1992) have shown experimentallyvalues for the depth intervals. A plot of the e vs.p that the change could be as much as 0.04 at 9.7 GHz.values given in Tables 1 and 2 is shown in Figure 2. Thin-section studies of the crystalline structure of

Numerous investigators have determined that, at the cores obtained from the McMurdo Ice Shelf re-- -10*C and a p of 0.917, the dielectric constant of vealed that the ice grains had a random c-axis fabricpure polycrystalline ice, at the frequencies of inter- that existed from the surface to the bottom of our 50-est, is well represented by a value of 3.15 (e.g., m-deep drill hole near station 307 (Fig. 2). This ran-Cummings 1952, Evans 1965, Ulaby et al. 1986, Koh dom fabric orientation therefore eliminates ice crys-1992). Koh (1992) also reaffirmed that er is high-fre- tal anisotropy effects as a contributing factor in ourquency-independent. Fujita et al. (1992) reconfirmed radar measurements.that er for polycrystalline ice is also insensitive to Three curves are also shown in Figure 6. Onetemperature, varying at about 0.0009/CO. Therefore, curve represents Robin's equation (eq 5). Another isin the subsequent discussion and equations, an Cr a refraction type curve statistically fitted through thevalue of 3.15 will be used for pure bubble-free ice at data. The equation for this curve,a specific gravity of 0.917. The intercept of these val-ues is shown by a cross in Figure 6 and in subse- ( =(0.992 + 0.848p)

2 (6)

quent figures.It has been found that when glacial ice is under fits the data with an r2 = 0.989 and a standard error

stress, as in a flow regime, an anisotropy develops in of 0.035. The third curve shown was determined aswhich the c-axes of the ice crystals become aligned. follows. The four-parameter volume fraction typeJohari and Chasette (1975) found that in the infrared equationregion a dielectric constant change on the order of0.004 could arise if the electric field was parallel 4 vaNFEa + iVri )2(

7

Si'i 0r Eq. 513.0- 6 8

2.0Figure 6. Field-determined in-situ effective"dielectric constant e; vs. the bulk specific

1.5 gravity ofMcMurdo Ice Shelfirn. The curvespassing through the fiLd data * uere drvedfrom the indicated equations which are described

0. 0.2 0.4 0.6 0.8 1.0 in this report. The + represents the dilctric con-p, Spwfc Gmvfty stant (3.15) of pure ice (p = 0.917).

whereeis the dielectric constant ofair (= 1) andCriis E, (1 + 0.508p)3 (10)the dielectric constant of pure ice, va and vi, the vol-ume fractions of air and ice, respectively, were used Equation 9 can also be well represented by a refrac-to calculate the dielectric constant of fim and ice tion type equation, with an r2 = 0.999, asover the specific gravity range from 0 to 0.917 in in-crements of 0.5. A refraction type expression was = (0.988 + 0.845p)

2 (11)

then statistically fitted through this data. From thisprocedure it was found that eq 7 is well represented, whicheisnvery nearagreement withaeq 8.at a cross-correlation of r2 = 1.000, by the expression Wiener (1910) presented a two-phase mixing for-

mula containing an empircal structure factor callede =(l + 0.845p)2. (8) the Formzahl WL This function varies with the shape

and orientation of the inclusions. In fim and ice theIt is apparent from Figure 6 that both Robin's em- Formzahl may vary if the medium is nonisotropic.

pirical equation (eq 5) and the simplified volume The form of the equation for an air-ice mixture isfraction expression (eq 8) fit the McMurdo Ice Shelfdielectric constant vs. specific gravity field data very •_1 vi -1well. e + i Elri

Numerous other empirical and theoretical ex-pressions have been used to describe the dielectric (constant of an air-ice mixture. A number of these ex- + (1 - vi) j a -1 (12)pressions will be compared with the McMurdo Ice (Ca + AL /Shelf data and, where statistically permissible, theexpressions will be simplified to a refraction equa- Since wa is one, the second term on the right is zero. Ittion, following the procedure used to obtain eq 8. was found through statistical regression that 12

Looyenga (1965) proposed a mixing formula fits the McMurdo Ice Shelf fim dielectric constant vs.based on spherical inclusions specific gravity data best when gL = 5.5. This value is

in good agreement with the values of 5 given in' ,/+ 1/)vi ,/3 (9) Bogorodsky et al. (1985) and 75 given in Ambach

ari + .j and Denoth (1972) for vertically propagating elec-

and because %a = I then tromagnetic waves in firn and ice. But it is not inagreement with Shabtaie and Bentley (1982), who

S- v+]3 found that g = 0 provided the best fit for their com-S= [Er -1) Vi + 1mon reflection point measurements at Dome C, Ant-

arctica.This equation was simplified by Stiles and Ulaby The results from this measurement technique(1981) to read have caused the most concern regarding the validity

8

3.5

I 112.5-E.1 10

2.0 -

1.5- Figure 7. Field-determined in-situ efOfctive di-electric constant 4e vs. the bulk spefic gravity

1.C of McMurdo Ice Shelf firn. The curves passing0 0.2 0.4 0.6 0.8 1.0 through the field data were deved fom the inds-

p. specifc Gravity cated equatons which are described in this report.

of the Robin equation. It is generally expected that =Va = -_I Ea + (- II- +' I polar firn and ice g should be above 2 (e.g., Evans 3)• •a + 2r i+1965). A Formzahlin the range of - 5-7 suggests thatthe horizontal layering in polar fin has a weak ef-fect on F4. Equation 12 can be simplified to Since E = 1, the first term on the right side is zer,and the equation for an air-ice mixture becomes

r' = (1 + 0.840p)2 (13)

which cross-correlates extremely well with the 3 = V ri 2(16)3E'r E' j + 2E'Wiener equation, when IL = 5.5, at r2 = 1.000.

The curves for eq 10,11 and 13 and the McMurdoIce Shelf 4E vs. p data are shown in Figure 7. Here which in turn is well represented at a ciss-correla-again the curves for the simplified equations are tion of r2 = 0.999 by

seen to fit the field data very well.A mixing formula by deLoor (1956), when ap- Er = (0.988 + 0.850p)

2. (17)plied to an air-ice medium containing spherical in-clusions, is For disk-shaped particles the Polder and van

Santen (1946) equation isF'= [3(l - 0) (Ei- 1) - E

( i (14) Er = 3ri + 24,ri (,ri - 1) (1 -*)

Cri - (4;r - 1) (1 -+ 2 ±1 V[3(1 - 0l) (E•,i - 1) - Er'i + 2]12 + 81•i]4 Whc a b ipif:L!t

+2± [31~)(I..1~4+22+4i/4 which can be simplified to

where 0 is the porosity. This equation, when simpli- ' ,+ (1.006 + 0.839p)2 (18)fled to a refraction type expression, becomes with a crosscorrelation of r2 = 1.000.

E' = (0.983 + 0.858 p)2 (15) The Tmga et aL (1973) mixing formula for an air-ice medium containing spherical inclusions is

with a cross-correlation of r2 = 0.999.The B6ttcher (1933) and Polder and van Santen 3vi (3Fri - 1)

(1946) mixing formula for a medium composed of Er = 1 + -r (19)spherical inclusions is ( +i

9

3.0

2.5-

2.0- Eq.1 2

1.5-17 Figure 8. Field-determined in-situ effective di-electric constant m vs. the bulk specific gravity of

1.0 McMurdo Ice Shelf fim. The curves passing0 0.2 0.4 0.6 0.8 1.0 through the field data were derived from the indi-

p, Specific Gravity cated equations which are described in this report.

which when simplified becomes which can be simplified to

r= (1 + 0.910p)/(1 - 0.455p) (20) e' = 0.367 + 3.035 p (24)

with a cross-correlation of r2 = 1.000. Equation 19 with a cross-correlation of r2 = 1.000.does not cross-correlate very well with a refraction The linear model proposed by Hufford (1991) fortype expression. an air-ice mixture is

The curves respresenting eq 15, 17 and 20 areshown in Figure 8, along with the e' vs. p data fromthe McMurdo Ice Shelf. Here we see that the curves Er = 1 + 3vi ri (25)representing eq 15 and 17 pass nicely through the rifield data but the curve representing eq 20 does not.From Figure 8 it appears that the Tmga et al. equa- which can be reduced totion should not be used. Sihvola et al. (1985) alsofound that the Tmga et al. expressbn (eq 19) is not Fr = 1 + 1.366 p (26)appropriate for determining Fr for an air-ice mix-ture. with a cross-correlation of r2 = 1.000.

There are other expressions that also do not fit the Equations 22,24 and 26 are graphically shown inMcMurdo Ice Shelf field data well. Three of these Figure 9, along with eq 6 and the McMurdo Ice Shelfequations are given below. The first is a volume av- ce vs. p field data. Clearly, eq 22 does not trackerage expression (Lang 1983): through the field results and should not be used.

Equations 24 and 26 appear to have a limited rangeEr = 4) La + (1 - 4)) Fr (21) of use; however, they are not considered acceptablein light of how well, for example, eq 6 fits the data.

which can be further simplified to Other expressions for determining the dielectricconstant of an air-ice mixture vs. specific gravity are

=1 + 2.345 p (22) listed in Appendix A.r To further show that a simple refraction typewith a cross-correlation of r2 = 1.000. equation can well represent the dielectric constant of

Ackley and Keliher (1979) proposed the use of a a mixture of air and ice, the 10 McMurdo Ice Shelfmixture formula by van Beek to determine er for po- dielectric constant vs. specific gravity data fromlar ice containing spherical inclusions: Tables 1 and 2 were combined with 15 laboratory

determinations of Cummings (1952) at 9.4 GHz, 17+ ' /- field measurements made at 20 MHz on "old" al-

Lr=E'riI1+ 3E-rE ri. (23) pine snow by Denoth (1978) and 47 laboratory mea-E'ri + aJ surements by Nyfors (1982) made at UHF and SHF

10

3.05 1 1

2*5

12.0- q 2 2

S1.5 - Figure 9. Field-determined in-situ effective di-electric constant 'e;vs. the bulk speci*i gravity

. 1of McMurdo Ice Shelffirn. The curves passing0 0.2 0.4 0.6 0.8 1.0 through thefield data rwr derie•flvm the mda-

p. Specific Gravity cated equations which are escribe in this report.

3.5I I I I

g 3.0-

Eq. 27

2.0--

1.5- Figure 10. Field and laboratoSdeinedvalues of the dielectric constant offirn vs. spe-

10 _ __ gravity. The regression curve passing0.2 0.4 0.6 0.8 1.0 through the data is represented by equation 27 as

p, Specific Gravity discussed in this report.

frequencies on a variety of snow types (e.g., fine- stant test data at the higher specific gravities. With-and coarse-grained snow). A plot of these data out the weighted point, the regression equationalong with a weighted point of Cri =3.15 at p = 0.917 would read eri = (1.002 + 0.836 p)2 with an r2 of 0.994is given in Figure 10. The resulting regression curve and a standard error of 0.035. This equation gives anpassing through the data is derived from c' of 3.13 at a p of 0.917, the same value obtained by

using eq 6.E' = (1.000 + 0.845p)2 (27) It was previously stated that Jezek and Roeloffs(1983) made radar sounding measurements, in

This curve fits the data with a correlation of r2 = Greenland and Antarctica, for the purpose of evalu-0.999 and a standard error of ± 0.031. It should be ating the validity of the Robin equation. In thesenoted that eq 27 is also the simplified form of the measurements, a metal target was lowered down avolume fraction expression (eq 8). borehole and the travel time of a transmitted wave

The justification for adding a weighted dielectric from the surface to the target and back was re-constant of 3.15 at a specific gravity of 0.917 to the corded. Using the known depth to the target and thedata in Figure 7 is based on our earlier determina- density of the fim and ice above the target, they cal-tion that this dielectric constant is a representative culated the effective radar wave velocity in the me-value for pure ice. In addition, the weighted value dium for different target depths. The average Vewas added because of the paucity of dielectric con- data for each depth at the Dye 3 Greenland site are

11

V,. Eft"h V4od0y (m'f ) to note that the form of this refraction expression16 170 175 ISO may also be used to describe the dielectric constant0I I of soil vs. its moisture content, as shown in Appen-

dix B.

V,. =-168.3W0 DISCUSSIONr a 0.848 Il,2oo)- StdiErr. 1.24 / ,y"sid 1.24 df The borehole-measured depths to the brine layer

S/ in the McMurdo e Shelf were plotted vs. the radar- 7wavelet two-way flight time measurements in Fig-

"/ ,/ ure 12. The two-way flight time measured to the bot-.tom of the ice shelf in 1978 at station 307 was 1263 ns

400 * (Table 1). From the regression equation given in Fig-

d ure 12, this time would represent a depth of 116 m._ .As previously stated, Kovacs et al. (1982) gave an

va. = 1sa + 1775s estimated thickness of 113 m for the shelf at stationvi $ e • Ro•'. q. 24 in 1977. Since station 307 was 40 m east of station

600 - . 307, one could assume that the ice is - 0.3 m thicker

Vs, = 169 + 1782/D at station 307 than at station 24 because the ice shelfvia sq. 27 increases in thickness to the east of this station (Fig.

2) at about 8 m/km. In any event, the depth differ-2- ff-- s ence between the two determinations (113 m and

82 1 I I 116 m) is about a 21/2% variance. Clearly the twoassessments of ice shelf thickness are in close agree-

Figure 11. Effective radar velocity vs. depth at DYE-3 ment, given the snow accumulation (0.9 m betweenGreenland. The data points are lezek and Roeloffs' average surveys), bottom melting and shelf movement dy-values, the Robin curve is from their analysis and the right namics, which can cause short- as well as long-termcurve is based on eq 17 in this report. ice shelf thickness variations at a location that is not

fixed in space. In addition, the 1982 estimate wasbased on an assumed bulk ice density for the shelfbelow the brine layer depth, a density that now ap-

shown in Figure 11. Also shown is the Ve vs. depth pears to be a bit high.curve they calculated using Robin's equation, the Another interesting plot is that of the dielectricdepth--density profile data for the site and eq 3. The constant values vs. depth, as shown in Figure 13.regression curve we fitted to their velocity data was From the regression equation for the curve in Figureselected because it paralleled the calculated curve 13, ee for the -116-m-thick ice shelf at station 307 canusing Robin's equation. be estimated to be - 2.74. Jericek and Bentley (1971)

As indicated in Figure 11, the regression curve gave an e' of 3.01±0.03 for the 510-m-thick Ross Icethrough Jezek and Roeloffs' data gives an apparent Shelf near Roosevelt Island, and Jezek et al. (1978)2 m/pis slower velocity gradient than the velocity estimated an E value of 2.99 for the 480-m-thickvs. depth curve calculated with use of Robin's equa- Ross Ice Shelf at station N19. The equation in Figuretion. 13 gives an a of 3.02 and 3.01 for these two ice shelf

The third curve shown in Figure 11 was calcu- thicknesses, respectively. The dose agreement be-lated with the use of eq 27, the site depth-density tween the field and calculated values are surprisingdata and eq3. As one would expect, this curve gives when one considers that the depth-density profilea slightly higher velocity vs. depth profile. Never- of the fim layer can be expected to vary with icetheless, the agreement between the three curves is shelf locations. Nevertheless, this variation may notconsidered to be very good. be enough to significantly influence the bulk dielec-

We believe that the dose simlarity between eq 5 tric constant of the fir layer and in tum that of theand eq 6 and 27 reaffirms that the empirical assess- ice shelf. If so, then the results from the McMurdoment of Robin et al. (1%9) and Robin (1975) for de- Ice Shelf, a lobe of the Ross Ice Shelf, may be appli-scribing the dielectric constant of polar fin and ice cable to other areas of the Ross Ice Shelf. In any

vs. their specific gravity is valid. It may be of interest event, Figure 12 may be used for estimating the

12

0 2000 t, T0(no)4I ! I I I WO

40-- #00 0AT

d d201 200!

0D --0.117 + 0.007t + 0.197i - 6E-7t2-

rFigure 12. Horizon depth within the Mc-0I I o 0 Murdo Ice Shelf vs. radar wavelet two-Uwy02 t. "M (,) 400flight time.

D, Depth (m)0 100 200 300 400 SOO 600

3.5 1 1 I 1

U

2.5-

2.0

ILU

Se'= (1.688 + 0.083DY(1 + 0.027D - 7 x 10-7D2).• ~r2. 0.99

_.0_ 1_ 1_ 1_1_1____Figure 13. Effective dielectric constant of the

0 10 20 30 40 so 6 firn-ice in the McMurdo Ice Shelf vs. depth in-D. Depth (m) cremnent.

depth of these ice shelves from the two-way travel tained from the saline ice/seawater interface, thentimes obtained from vertical radar sounding mea- the two-way travel time measured in this saline icesurements. layer may be used to estimate the layer thickness T

However, a note of caution is in order. For ex- fromample, the Ross Ice Shelf at Site J-9 is known to havea -6-m-thick layer of saline ice accreted to the bot- T=-0.708+0.088t (28)tom (Zotikov 1979, Zotikov et al. 1980, Morey and and the layer effective dielectric constant fromKovacs 1982). Because this ice attenuates electro-magnetic energy at the frequencies often used in ra- e' = 5.983 exp(-0.477T) + 3.172 (29)dar sounding (as does the brine-soaked fim), and e

given the spreading losses which occur with dis- Equations 28 and 29 are from the results of impulsetance, a reflection from the saline ice/seawater inter- radar two-way time of flight measurements made atface may not be obtained. Nevertheless, a reflection - 100 MHz on thick sea ice by Kovacs and Moreymay be received from the fresh ice/saline ice inter- (1990). For saline ice growth over 10 m thick on theface, and therefore the depth to this interface could bottom of an ice shelf, a value of 3.25 ± 0.05 for Febe estimated using a two-way travel time measure- may be reasonable for estimating T using eq 3ment and Figure 12. Should a reflection also be ob- wherein T is substituted for D.

13

It set rn-s that many distributions in nature tend to Bogorodsky, V.V., C.I. Bentley and RE. Gudmand-follow exponential-like trends. The above results for sen (1985) Radioglaciology Dordrecht, Holland: D.the variation in the dielectric constant of fire and ice Reidel Publishing Co.vs. specific gravity as well as the results for the di- Bbttcher, C.J.F. (1952) Theory of Electric Polarization.electric constant vs. the moisture content of soil Amsterdam: Elsevier, 1st ed., sec. 64, p. 415.(App. B) appear to represent two of them. Cummings, WA. (1952) The dielectric properties of

ice and snow at 3.2 centimeters. Journal of AppliedPhysics, 23: 768-773.

CONCLUSIONS deLoor, G.R (1956) Dielectric properties of heteroge-neous mixtures. Thesis, University of Leiden.

The findings of this report reaffirm that a simple Denoth, A. (1978) On the calculation of the dielectricrefraction type equation can be used to describe ex- constant of snow. Deuxieme Rencontre Internationaletremely well the dielectric constant vs. specific grav- sur la Neige et les Avalanches, Assocation nationaleity of fim and ice. It was further verified that the so- pour l'etude de la neige et des avalanches, p. 61- 70.called Robin expression [fr = (1 + 0.851 p) 2] is very Evans, S. (1965) Dielectric properties of ice andsuitable for determining the dielectric constant vs. snow-A review. Journal of Glaciology, 5(42):773-792.specific gravity of dry polar firn and ice, but that it Fujita, S., M. Shiraishi and S. Mae (1992) Measure-may be slightly improved by changing the constant ment on the microwave-dielectric constant of ice by0.851 in the equation to 0.845, especially if one ac- the standing wave method. In Physics and Chemistrycepts 3.15 for the dielectric constant of pure ice as of Ice (N. Maeno and T. Hondoh, Ed.) Sapporo: Uni-measured by Cummings (1952) again reaffirmed by versity Press, p. 415-421.Koh (1992). Why previous investigators' field data Hufford, G. (1991) A model for the complex permit-did not correlate well with the Robin equation is de- tivity of ice at frequencies below 1 THz. Internationalbatable. Jezek and Roeloffs' (1983) explanation of a Journal of Infrared and Millimeter Waves, 12(7): 677-timing error is plausible. However, wide-angle re- 682.flection measurements have been made with radar Hughes, D. (1985) V w/o T: Velocity without tears.sounding systems other than the ones they state to Geophysica: The Leading Edge, 4(2)have the timing error and still a discrepancy exists in Jericek, G.R. and C.R. Bentley (1971) Velocity ofthe D and E' determinations. We suggest that electromagnetic waves in Antarctic ice. In Antarcticcurved ray path effects associated with Snell's law Snow and Ice Studies 11 (A.P. Crary, Ed.) Americanand the standard wide-angle reflection analysis us- Geophysical Union, Antarctic Research, Ser. 16: 199-ing a time2-distance 2 plot are a cause of the discrep- 208.ancy. Indeed, the findings of Hughes (1985) and Jezek, K.C., J.W. Clough, C.R. Bentley and S.Morey and Kovacs (1985) show that a standard Shabtaie (1978) Dielectric permittivity of glacier icewide-angle reflection measurement analysis gives measured in situ by radar wide-angle reflection.lower e' and higher D determinations than are ap- Journal of Glaciology, 21(85): 315-329.propriate. Jezek, K.C. and E.A. Roeloffs (1983) Measurements

of radar wave speeds in polar glaciers using adown-hole radar target technique. Cold Regions Sci-

LITERATURE CITED ence and Technology 8: 199-208.Johari, G.P and PA. Chasette (1975) The permittiv-

Ackley, S.F. and T.E. Keliher (1979) Ice sheet inter- ity and attenuation in polycrystalline and single-nal radio-echo reflections and associated physical crystal ice I h at 35 and 60 MHz. Journal of Glaciology,property changes with depth. Journal of Geophysical 14(76):293-303.Research, 84(B10): 5675-5680. Koh, G. (1992) Dielectric constant of ice at 26.5-40Ambach, W. and A.D. Denoth (1972) Studies on the GHz. Journal of Applied Physics, 71(10): 5119-5122.dielectric properties of snow. Zeitschriftffir Gletsche- Kovacs, A. and A.J. Gow (1975) Brine infiltration inrkunde und Glazialgeologie, VIII(1-2): 113-123. the McMurdo Ice Shelf, McMurdo Sound, Antarc-Bentley, C.R. (1979) Ice studies: Visit to the radio tica. Journal of Geophysical Research, 80(15): 1957-physics laboratory of the Arctic and Antarctic Re- 1961.search Institute in Leningrad. EOS, Transactions of the Kovacs, A. and R.M. Morey (1979) Remote detec-American Geophysical Union, 60(10) tion of massive ice in permafrost along the Alyeska

14

pipeline and pump station feeder pipeline. In Pro- by means of borehole interferometric techniques.ceedings of American Society of Civil Engreers Pipeline Journal of Glaciology, 15(73): 151-160.Division Specialty Conference, Pipelines in Adverse Envi- Robin, G. deQ., S. Evans and J.T. Bailey (1969) In-ronments. New Orleans, Louisiana, vol. 1, p. 268-279. terpretation of radio echo sounding in polar iceKovacs, A., A.J. Gow and J.H. Cragin (1981) The sheets. Philosophical Transactions of the Royal Society ofbrine zone in the McMurdo Ice Shelf, Antarctica. In- London, Series A, 265(116): 437-505.ternational Glaciological Society, Annals of Glaciology, 3: Shabtaie, S. and C.R. Bentley (1987) Measurement166-171. of radio wave velocities in fim zones of polar iceKovacs, A., A.J. Gow, J.H. Cragin and R.M. Morey sheets. Annals of Glaciology, 3:342.(1982) The brine zone in the McMurdo Ice Shelf, Ant- Sihvola, A., E. Nyfors and M. liuri (1985) Mixingarctica. USA Cold Regions Research and Engineer- formulae and experimental results for the dielectricing Laboratory, CRREL Report 82-39. constant of snow. Journal of Glaciology, 31(108): 163-Kovacs, A. and R.M. Morey (1990) Sea ice thickness 170.versus impulse radar time-of-flight data. Cold Re- Steenson, B.O. (1951) Radar methods for the explo-gions Science and Technology, 18:91-98. ration of glaciers. PhD Thesis, California Institute ofLang, N. (1983) Reply by the author to J. Korringa Technology, Pasadena, California.and R.J.S. Brown. Geophysics, March: 367-375. Stiles, W.H. and F.T. Ulaby (1981) Dielectric proper-Looyenga, H. (1965) Dielectric constant of heteroge- ties of snow. In Proceedings of Workshop on the Proper-neous mixtures. Physica, 21:401-406. ties of Snow (R.L. Brown, S.C. Colbeck and R.N.Morey, R.M. and A. Kovacs (1985) Analysis of wide- Young, Ed.). USA Cold Regions Research and Engi-angle reflection and refraction measurements. In Pro- neering. Laboratory, Special Report 82-18.ceedings of Workshop on Permafrost Geophysics, Golden, Tinga, W.R., W.A.G. Voss and D.F. Blossey (1973)Colorado, 23-24 October 1984. USA Cold Regions Re- Generalized approach to multiphase dielectric mix-search and Engineering Laboratory, Special Report ture theory. Journal of Applied Physics, 44: 3892-3920.85-5, p. 53-60. Ulaby, ET., R.K. More and .K. Tung (1986) Micro-Morey, R.M. and A. Kovacs (1982) The effects of con- wave Remote Sensing: Active and Passive. Volume III,ductivity on high-resolution impulse radar sound- From Theory to Applications. Artech House, Inc.ing, Ross Ice Shelf, Antarctica. USA Cold Regions Wiener, 0. (1910) Theorie der Refractions konstan-Research and Engineering Laboratory, CRREL Re- ten. Ber. Vt rhandl. Koniglich Sachs. Ges. Wiss. Leip-port 82-42. zig, Math. Phys. K/., 63(5): 256-268.Nyfors, E. (1982) On the dielectric properties of dry Zotikov, I.A. (1979) Antifreeze-thermal drilling forsnow in the 800-MHz to 13-GHz range. Helsinki core through the central part of the Ross Ice ShelfUniversity of Technology Radio Laboratory Report (J-9 camp), Antarctica. USA Cold Regions ResearchS-125. and Engineering Laboratory, CRREL Report 79-24.Polder, D. and J.H. van Santen (1946) The effective Zotikov, LA., V.S. Zagoradnov and J.V. Raikovskypermeability of mixtures of solids. Physica, 12(5): (1980) Core drilling through the Ross Ice Shelf (Ant-257-271. arctica) confirmed basal freezing. Science, 207(4438):Robin, G. deQ. (1975) Velocity of radio waves in ice 1463-1465.

15

APPENDIX A. SUPPLEMENT EQUATIONS FOR DETERMININGTHE DIELECTRIC CONSTANT OF AN AIR-ICE MIxrURE.

Additional formulations are presented in this section for determining the e, vs. p for fimand ice. All equations have been offered by the indicated authors as a means of determining therE of an air-ice mixture. Below each equation is a table giving example air-ice mixture specific

gravities and the calculated c' value as determined by eq 27 and by the new expressions pre-sented.

Turi et al. (1984) made measurenents in the 0.85-12.6 GHz range on snow. Their empiricalequation for Fr is

ri

Fr = 1 + 1.7 p + 0.7 p 2 (A)

which they state for practical purposes can be simplified to

r-= 1 + 2 p. (A2)

p &;(eq27) er (eqA1) e'(eqA2)

0.0 1.0 1.0 1.00.2 1.37 1.37 1.400.4 1.79 1.79 1.800.6 227 2.27 2200.8 2.81 2.81 2.600.917 3.15 3.15 2.83

Ambach and Denoth (1980) give the following empirical equation for their dry snowmeasurements at 20 MHz:

r =1 + 2.2 p. (A3)

p £r (eq 27) c'(eqA3)

0.0 1.0 1.00.2 1.37 1.440.4 1.79 1.880.6 227 2.320.8 2.81 2.760.917 3.15 3.02

Hallikainen et al. (1982) made measurements at 4-18 GHz on dry snow and found empiri-cally that

Er = 1.91p. (A4)

17

p e ,(eq 27) e (eqA4)

0.0 1.0 1.102 137 1.380.4 1.79 1.760.6 2.27 2.150.8 2.81 2.530.917 3.15 2.75

Burns et al. (1985) made measuremerns at 100 MHz on dry snow and found empirically that

er= 1.1 + 2.2p. (A5)

P E' ,(eq 27) Er (eq A5)

0.0 1.0 1.102 137 1.540.4 1.79 1.980.6 2.27 2.420.8 2.81 2.860.917 3.15 3.12

Fujita et al. (1992) made measurements at 9.7 GHz on polyaystalline ice and found fromtheir results that

= 3 .08p + 0.41. (A6)

P c,(eq27) E,(eqA6)

0.0 1.0 0.410.2 1.37 1.030.4 1.79 1.640.6 2.27 2260.8 2.81 2.870.917 3.15 3.23

Pearce and Walker (1967) proposed the following expression based on theoretical con-siderations:

Er = 3.16p + 0.41 (A7)

where 0.535•< p

p e;(eq 27) e4(eqA7)

0.6 2.27 2.310.7 2.53 2.620.8 2.81 2.940.917 3.15 3.31

Sihvola et al. (1985) proposed a mixing formula by Taylor (1965) for an air-xoe mixture withrandomly oriented disk-shaped inclusons of the form

0 •q(1-Z)

er 3 (A8)Ir =+ AL (I - 3eri) (S

which can be simplified to

er = (1.007 + 0.838p)2 (A9)

with aacross-orrelation of r2= 1.000. Sihvola et A showed that eqA8 fitted their data, obtainedat 0.8-13 GHz, better than another one by Taylor for spherical inclusions.

P e'r(eq27) Fr (eqA9)

0.0 1.00 1.0102 1.37 1.380.4 1.79 1.800.6 2.27 2.280.8 2.81 2.810.917 3.15 3.15

In an important paper on dielectric mixing formulas, Sihvola (1989) presents a self-consis-tent general mixing formula for determining the complex permittivity of a homogeneous ma-terial containing spherical inclusions. As applied to determining the dielectric constant of dryfirn and ice, his expression is

"b 2 + 4ac - b (A10)

where

b = e + 2 e. - 2 0ae -fi (e'ri - La) (1 + cy)

C=, a[Ci + (2- )Ea+f(2 m)(e'rje-)

19

and parameter a is a positive integer and parameterf is the ice density fraction.Sihvola showed the ,nterrelationship between his mixing formula and that of other authors.

His results indicated that when a = 3, eq A10 gave e; values for firn and ice in dose agreementwith eq Al. Equation A10, with a = 3, can be simplified to

E = (0.988 + 0.85 9p)2 (All)

with a cross-correlation of r2 = 1.000.

P e(eq27) c,(eqAll)

0.0 1.00 0.9802 137 1350.4 1.79 1.770.6 2.27 2.260.8 2.81 2.810.917 3.15 3.15

Sihvola also showed that an expression by Sen et al. (1981) for a medium containing spheri-cal inclusions:

• /, 1/3

E'*i - E

when applied to firn and ice gave e rvalues in good agreement with equation Al. When eq A12is simplified to a refraction type expression we obtain

Er = (0.995 + 0.848p) 2 (A13)

with a cross-correlation of r2 = 1.000.

Er (eq27) er(eqA13)

0.0 1.0 0.990.2 137 1.360.4 1.79 1.780.6 2.27 2260.8 2.81 2.800.917 3.15 3.14

The interested reader is directed to Sihvola's paper for additional mixing formulas that maybe applied to estimating the dielectric constant of fim and ice.

Of the above expressions, it appears that eqAl, A9, All and A13 correlate best with eq 27.

20

APPENDIX B: THE DIELECTRIC CONSTANT OF A SOIL-WATER MIXTURE.

The dielectric constant of dry soil e'r typically lies between 2 and 4, while the relativedielectric constant of water Frw is 81 at 20'C. This value will vary with temperature from about88 at 00C to lower values as the temperature climbs. The value for r ', is also frequency depen-dent. Since erw is such a large value it has a major influence on the relative dielectric constant ofthe soil-moisture mixture •r,. Here we show the variation of Erm vs. soil moisture content m,at a fixed frequency of 1.074 GHz and at room temperature. The soil moisture content is theratio of the weight of water per unit volume of soil.

Presented in Figure B1 are the results of 403 laboratory c'm vs. m, tests by Lundien (1971).His measurements were made on sand, silt, silt-loam and day soils using an L-band interfer-ometer. Also shown is a refraction equation which well describes £rw vs. m, for the com-mingled soils. The regression curve in Figure B1 fits the data with an r2 = 0.970 and a standarderror of ± 2.02. When the regression curve is forced through an Er£w for water of 81, the equationfor the curve becomes as shown in Figure B2. The data lying below the regression curve tendsto be those for day type soil while the data above the curve is that for the coarser grained soils.Representative regression curves passed through the sand and clay material and forcedthrough an ew of 81 at mv = 1 are shown in Figure B3.

The test results shown in Figure B1 will vary with temperature as previously mentioned.However, Lundien (1971) found that over a temperature range of 0' to 651C the change in Fr,appears to be uniform, varying at about 112% per *C.

40

•30° °

II-u). " •r 'n (1.658 + 7.72Mv,)2

r2 = 0.970Standard Error = 2.02

0 i . -. - . I , L . I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7MW, Moisture Content (MgWm

3)

Figure B). Dielectric constant of soil vs. moisture content.

21

100 ' I I I

-'nn = (1.57 + 8.47Mv - 1.04Mv2 )2

2 = 0.997S0 Std. Error =1.81

*60-

40

0 0.2 0.4 0.6 0.8 1.0Mv, Moisture Content (Mg/m

3)

Figure B2. Dielectric constant of soil vs. moisture content wherethe regression curve was forced through a dielectric constant forwater of 81.

II

- E'rmn(1.61 +9.55Mv -2.16Mv 2 )240 ~Sand /*40-.

20- - '.. (1.47 + 7.55Mv)2"-W Clay

0 0.2 0.4 0.6 0.8 1.0Mv, Moisture Content (Mg/m3 )

Figure B3. Representative curves for the dielectric constant ofsand and clay soil vs. moisture where the respective curves wereforced through a dielectric constant for water of 81.

22

REPORT DOCUMENTATION PAGE O ft. 0704-0-Put& rwta b~dn W bOW cobftc&n is mmain Is ebmatd to avaus 1 hWur pw mpmoa. fhkm*V fta tens Ire ;r ; ig smwru•,i. • aewý0 w" da a cmema. pmrwf aW-maimw lie dat eMedad. and cW onOlv and revewm ft coft•con of iniorman. Send cafnmv regangV tn bwrdan eaanata ot any ote aspa of #ia I , ",on 0lcim•aron.Vwki0 auggeou tfo reda• f bwdam. w WaMon Heaftsa Seiee. Dueo•tat r Inorkmatdo Op•Min and Reports, 1215 Jeftln Da•, Hiemy. Suas 1204. Arkow.VA 2222-4302. and to the Oftoficer0 ~agomneM and &udg. Paperwork Redacton Propa* (0704-01M61. Waahekgon DC M060.1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

I December 1993 -

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

A Reassessment of the In-Situ Dielectric Constant of Polar Firn NSF-DPP 74-23654

6. AUTHORS NSF-DPP 8004221

Austin Kovacs, Anthony J. Gow and Rexford M. Morey

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

U.S. Army Cold Regions Research and Engineering Laboratory72 Lyme Road CRREL Report 93-26Hanover, New Hampshire 03755-1290

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

Division of Polar ProgramsNational Science FoundationWashington, D.C. 20314

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT- 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161

13. ABSTRACT (Maximum 200 words)

The success in using VHF and UHF frequency systemsfor sounding polar ice sheets has been tempered by an uncer-tainty in the in-situ dielectric constant c', which controls the effective velocity Ve of an electromagnetic wave propa-gating in an air-ice mixture. An empirical equation for determining S' vs. density (specific gravity, p ) was proposedin 1968 by Robin et al. where e'= (1 + 0.851 p)2. However, this expression has met with uncertainty because wide-angle radar refraction sounding techniques have produced values of e' that are lower than Robin's equation pre-dicts. This report discusses radar soundings made on the McMurdo Ice Shelf, Antarctica, and compares the resultingt' values with Robin's equation, laboratory measurements on firn and ice and other expressions given in the litera-ture for determining e' vs. the specific gravity of dry firn and ice. Our findings indicate that the form of Robin's equa-tion is valid. However, our analysis also indicates the expression could be slightly improved to read c' = (1 + 0.845p)2. Reasons are suggested as to why previous wide-angle radar sounding studies did not reproduce Robin's find-ings.

14. SUBJECT TERMS Glaciology 15. NUMBER 9f PAGES

Antarctica Firn Ice shelves 16. PRICE CODEDielectric constant Glacial sounding Radio echo sounding

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

OF REPORT OF THIS PAGE OF ABSTRACT

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INFORMATION

ERRATACRREL REPORT 93-26

Throughout the report, E' should read e. and be defined as the effective (bulk) dielectric constant.

Inside cover

Abstract, line 5, "1968" should read "1969"

Cover caption, the words "traverse" and "Antarctica" were misspelled

p. 1, column 1, paragraph 2, last line: ">>" should read "