Rapid optical method for logging dust concentrationversus depth in glacial ice

Predrag Miocinovic, P. Buford Price, and Ryan C. Bay

We describe the design and simulated response of a dust logger consisting of a downward-pointingphototube, ;2 m below side-directed light-emitting diodes ~LEDs!, attached to a cable that can lower thedevice down a 3-in. ~7.5-cm! borehole filled with butyl acetate. LED photons that enter the ice arescattered or absorbed by dust grains, and those that reach the phototube provide a measure of dust orvolcanic ash concentration at a given depth. An increased dust concentration associated with an ancientcolder climate will usually result in an increase in collected light, but may decrease collected light if airbubbles are present. Centimeter-thick volcanic ash bands can also be detected. The concept is basedon six years of experience with pulsed light sources used to measure optical properties of deep Antarcticice. © 2001 Optical Society of America

OCIS codes: 290.5850, 280.1100, 230.0040, 120.5820, 010.1100.

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1. Introduction

The dust logger described in this paper exploits somefeatures of two modern optical techniques—the oceantransmissometer1 and the Antarctic muon and neu-trino detecting array ~AMANDA! collaboration’smethod for mapping optical properties of deep glacialice.2–5

To study depth dependence of the mass concentra-tion of particles ~usually mainly microorganisms! inthe ocean, oceanographers use a transmissometer,consisting of a 660-nm light-emitting diode ~LED!viewed by a detector with an acceptance of ;1 deg ata distance of 25 cm on the axis of a cylinder throughwhich water can freely flow. The transmission iscorrected to standard conditions when salinity, tem-perature, and density are recorded simultaneously.The contribution of yellowish dissolved organic mat-ter is negligible at a wavelength of 660 nm. Beamattenuation that is due to pure seawater is taken tobe constant and is calibrated at the factory. Thusthe concentration of small particles, mostly micro-bial, is determined by subtraction of the contributionof pure seawater to the attenuation by particles.6

The AMANDA collaboration recently completed a

The authors are with the Department of Physics, University ofCalifornia, Berkeley, Berkeley, California 94720-0001.

Received 3 July 2000; revised manuscript received 22 January2001.

0003-6935y01y152515-07$15.00y0© 2001 Optical Society of America

large observatory, buried in deep glacial ice, for track-ing high-energy neutrinos from astronomical sourc-es.7,8 They used an optical method to determine atwhat depths the ice near the South Pole is sufficientlytransparent to enable them to use the Cherenkovlight from charged particles to determine the direc-tion of the particles. Using a hot-water drilling tech-nique, they melted cylindrical holes down to depths of;2000 m in which were submerged strings of photo-multiplier tubes ~PMTs! and pulsed light sources,round which the water was allowed to refreeze.he PMTs served both to measure ice clarity as a

unction of depth and to record arrival times of Cher-nkov light from relativistic charged particles. Theight sources consisted of nitrogen lasers ~337 nm!nd LEDs ~370 and 470 nm! at various depths in thece and of light pulses transmitted from the surfaceown optical fibers to diffuser balls at various depths.istances in solid ice between emitters and receiversere 10–120 m. From analyses of the distributionf arrival times of photons traveling between themitters and the receivers, they were able to deter-ine the wavelength dependence and depth depen-

ence of both the scattering coefficient and thebsorption coefficient for light as a function of depthn ice.

The AMANDA collaboration found that air bubblesominated the light scattering at shallow depths, buthat this contribution decreased with depth becausef compression of the bubbles and because of theirransformation into nearly invisible air–hydraterystals. At ;1400 m the transformation was com-

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plete. Below 1400 m the propagation of light wasconstrained only by the presence of dust particlesdeposited onto the snow by aerosols and later com-pacted into ice. The dust concentration inferredfrom the timing distributions and from application ofMie theory varied with the depth of the ice. Be-tween 1400 and 2200 m near the South Pole thedepth dependence matched the pattern measured inthe Vostok ice core at depths from ;400 to ;930 mwhen properly scaled for differences in snow accumu-lation rate. The scaling was used to calibrate theage versus the depth at the South Pole9 by use of theage versus the depth that had been determined bychemical and physical studies of the dust as a func-tion of depth in the Vostok core.10

In this paper we show that AMANDA’s opticalmethod of measuring dust concentration in glacial icecan be adapted to fit into a vertical cylinder slenderenough to be lowered into a 3-in. ~7.5-cm! access holefilled with butyl acetate, a standard drilling fluid.From simulations of the response of this device, weconclude that one can rapidly read out the dust con-centration at depths down to bedrock, measure scat-tering by air bubbles, measure dust in the presence ofair bubbles, and detect volcanic ash layers with atypical thickness of ;1 cm. Advantages of this dustlogger include speed, economy, and the ability tomeasure both insoluble and soluble dust in situ atambient pressure. In contrast to the ocean trans-missometer, which measures a sample of ocean waterthat passes inside the instrument, our dust loggersamples the optical properties of a large volume of iceseveral meters in radius, which avoids contaminationthat might be introduced into the hole during drilling.

2. Motivation for Dust Logging

Dust serves as a proxy for climate: It correlates wellwith dO18, the oxygen isotopic composition. ThedO18 in glacial ice and in planktonic foraminifera insea sediments reflects the amount of the Earth’s wa-ter frozen in ice. It is thus a measure of long-termvariations of Earth’s temperature and of great inter-est to paleoclimatologists.10 In sea sediments thedO18 has traced a rough sawtooth curve with a peri-odicity of close to 100,000 years for eight cycles, show-ing that major ice ages recur every 100,000 years.11

For still earlier times the periodicity was approxi-mately 41,000 years.12 In both cases the periodicityis sufficiently precise that it must be controlled byastronomical phenomena. Some researchers believein Milankovitch’s explanation of the 105-year cycle interms of changes in the eccentricity of the Earth’sorbit,11,12 whereas others argue that the gradualchange in the Earth’s orbital inclination, which alsohas a period of 100,000 years, somehow causes themajor ice ages.13,14 The cause of the rather abrupthange from 41,000 to 100,000 years is unknown ands a subject of interest and speculation.

The paleoclimatic record in ice cores is not as ex-ensive as in sea sediments. The analysis of theust and dO18 in the oldest known ice core—at Vostok

Station—shows that the deepest ice, at ;3500 m, has

516 APPLIED OPTICS y Vol. 40, No. 15 y 20 May 2001

an age of ;420,000 years and that four cycles of iceages are preserved,10 in accordance with the corre-sponding record in sea sediments. To make furtherprogress in understanding the causes of ice ages, itwould be highly desirable to have a portable dustlogger that could search for major peaks in dust con-centration as a function of depth in regions of Ant-arctica suspected of having ice much older than420,000 years at its base.

A second motivation for a dust logger is in glaciol-ogy, especially in the study of the flow of cold ice.For a complete understanding of how ice flows, oneneeds to measure not only the stress and strain as afunction of depth and position for ice flowing down anincline, but at the same time to determine the tem-perature, crystal fabric, chemical composition of im-purities, and dust distribution in the same ice whoseflow is being studied.

A third motivation is in volcanology and the possi-ble role of volcanic ash in triggering worldwidecooling.15–17

3. Design of a Compact Dust Logger

Figure 1 shows the design of a logger whose per-formance we simulated. A high-speed mechanicalaccess drill18 would be used to drill a 3-in. ~7.5-cm!-

Fig. 1. Schematic design of the dust logger, immersed in a holefilled with transparent butyl acetate. Photons from side-directedLEDs scatter from dust or bubbles; some are absorbed by dust.Absorption by ice itself at a wavelength of 370 nm is negligible ona scale of tens of meters. A small fraction reaches the downward-directed phototube and provides a measure of dust or bubble con-centration. Electronics are at the surface.

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diameter hole, to be filled with butyl acetate drillingfluid, extending from the surface down to bedrock.After removal of the drill, the logger would be loweredon a cable kept taut by means of a weight, and read-ings would be taken either continuously or at prede-termined depth increments. The cable ~a standardfour-connector logging cable! would provide power forthe LEDs and for a 1-in. ~2.54-cm! downward-facingPMT and would return signals from the PMT to thesurface.

We carried out simulations for LEDs ~Nichia Cor-poration! with peak emission at 370 6 10 nm; LEDsthat emit at 470 nm would work just as well. ~Theabsorption coefficient measured in situ in the highlypure South Pole ice is less than 1022 m21 at both

avelengths.! An isotropic distribution of emittedhotons was tracked from the light source into iceontaining dust, bubbles, and volcanic ash, withinhich a small fraction of the photons scattered

nough to impinge in an upward direction on a thinylindrical disk of ice representing the PMT window.MT and other electronic efficiencies were not simu-

ated because we only wanted to find out relativehanges in the PMT signal as a function of dust orubble concentration in a local region of the ice. Theffective scattering coefficient be and the absorption

coefficient a were recalculated each time a photonpassed into an ice layer ~assumed to be horizontal!

ith a different dust or bubble concentration. Topeed up the simulation, instead of a photon beingbsorbed, it was given a weight from 0 to 1, depend-ng on the path traveled and the type of ice traversed.t the detection volume, these weights were summedp as a probability of a given photon reaching that

ocation in an upward direction. Because of the cy-indrical symmetry of the problem, we summed overll azimuth directions for photon emission and detec-ion. Results were compared for photons emitted inhree equal solid-angle bins, from 60° to 90° ~relativeo upward direction!, from 90° to 120°, and from 120°o 180°, simulating different LED emission configu-ations.

Because of the similarity of refractive index of bu-yl acetate ~n 5 1.390! to that of ice ~n 5 1.322!, we

ignored refraction at the wall of the hole and treatedbutyl acetate as being equivalent to ice. Owing tothe small volume of butyl acetate relative to the vol-ume of ice sampled by each photon, the resultingerror is small. Measurements with a laboratoryspectrophotometer showed that butyl acetate is quitetransparent to light throughout the visible and UVdown to a wavelength of approximately 260 nm.

The 1–3-m spacing between the emitters and thedetectors and the downward orientation of the PMTwere chosen to prevent photons from scattering fromthe wall of the hole or from the drill fluid and fromentering the PMT without sampling the bulk ice.

4. Dust Modeling

Based on measurements by the AMANDA collabora-tion,3,4 an optical model of high-purity glacial ice con-aining traces of dust was developed. Absorption is

treated by a three-component model that combineslaboratory measurements of absorption of infraredand UV light with in situ measurements in South

ole glacial ice in the 310–650-nm range. At wave-engths l , 210 nm and l . 500 nm, absorption is

dominated by the properties of ice itself, whereas inthe intermediate range absorption is dominated byimpurities. A simple but accurate expression of thedependence of absorption on wavelength3 is given by

a~l! 5 A exp~20.48175 l! 1 B exp~ 2 6700yl!

1 C Mdustl2k, (1)

where l is in nanometers and Mdust is the experimen-tally determined mass concentration of impuritiescontributing to light absorption. The first exponen-tial term is the Urbach tail, which dominates at l ,210 nm; the second exponential describes the rise ofabsorption in the red and infrared; and the thirdterm, proportional to dust concentration, dominatesin the range 210 , l , 500 nm. The values Mdustand k are determined from fits to AMANDA data inSouth Pole ice. The best-fit proportionality con-stants are given by3 A 5 8 3 1039 and B 5 8100,

hereas C is absorbed into Mdust during fitting ofexperimental data. The best fit19 to the exponent kyields 1.1. Because it is difficult to make an accu-rate measurement of the angular distribution of scat-tered light in the deep glacial ice, the AMANDAcollaboration used the approximation in which theeffective scattering coefficient be is given by be~l! 5b~l!@1 2 g~l!#, where b~l! is the depth-dependentmean coefficient for geometric scattering, g~l! 5 ^cosu&, and u is the scattering angle. The value ^cos u& 50.8 6 0.1 was found to be a good estimate for all icedepths.5

The best-studied wavelength in the AMANDA dataset is 532 nm ~green light of frequency-doubled YAGaser! and is our reference point. From the relation5

be~l! 5 ~ly532!2abe~532!, (2)

we can calculate be for any given wavelength. Byuse of the Mie-scattering theory, with concentrationsof four dust components ~mineral dust, acid droplets,salt grains, and soot! determined from measurementsin ice cores and with size distributions taken fromTable 4.2 of Ref. 20, a is calculated to be 0.84 for thedeep South Pole ice ~1.4–2.3 km!.5 Finally, C Mdustis an empirically determined value related to the im-purity concentration and can be well approximatedby C Mdust 5 158 be~532! 2 0.634.18 In our simula-tions, we used be~532! 5 0.026 m21 as a baseline,which corresponds to the cleanest South Pole icefound at depths below 2.1 km.

The model described here applies to dust in SouthPole ice at all depths. However, because the dustcomposition in glacial ice at other locations ~e.g., nearthe coast or near volcanic regions! may be somewhat

ifferent, we simulated the response of the dust log-er to ice containing dust with a wide range of valuesf the ratio of effective scattering to absorption at 370

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nm, D [ be~370!ya~370!. For deep South Pole ice,our model yields D 5 5.87.

5. Results of Simulations

A. Dust Bands without Air Bubbles

Inside a disklike band of enhanced dust concentra-tion, the simulated PMT signal as a function of timein response to a pulse of light from the LEDs showeda rapid rise to a peak value, typically occurring at atime ;5 ns after a hypothetical direct trajectory, fol-lowed by an approximately exponential decrease intime. The peak value of returned light, the inte-grated value for 1–22.5 ns, the integrated value for1–50 ns, and the integrated value for 1–100 ns trackthe shape of the excess dust in the band, and all ofthem scale faster than linearly with dust concentra-tion.

Figures 2–4 show examples of dust logger responsecharacteristics and spatial resolution in bubble-freeice for various vertical profiles, with dust concentra-tion rising to a maximum of a factor of 6 above back-ground. The factor of 6 increase is conservative inthat dust concentration increases as much as a factorof 30 above background at glacial maxima, for exam-ple, from the Holocene to the Last Glacial Maxi-mum.21 In Fig. 2 the thick solid curve shows atriangular dust profile, with the background valuenormalized to unity. The three broken curves showthe simulated PMT response integrated for 22.5, 50,and 100 ns for photons emitted at 60–90° zenith an-gles. For each of the three integration times thesignal sharply tracks the dust concentration, with adepth resolution of ;1 m. The ratio of response inand out of the dusty region is 7.5 times as high as the

Fig. 2. Response of 2-m dust logger to a triangular distribution ofdust in a 40-m thickness of bubble-free ice, for signal integrationtimes of 22.5, 50, and 100 ns, and for LEDs emitting at 60°–90°zenith angles.

518 APPLIED OPTICS y Vol. 40, No. 15 y 20 May 2001

ratio of dust concentration for an integration time of22.5 ns and five times as high for 50- and 100-nsintegration times.

With the integration time fixed at 50 ns, Fig. 3compares the responses to a 4-m-deep region of en-hanced dust concentration as a function of zenithangle of emission of the LEDs. For downward-directed light ~open squares!, the pattern of detectedsignal peaks ;3 m above the dust layer. For lightemitted at 60–90° ~crosses!, the signal peaks ;1 m

Fig. 3. Response to a 4-m-thick dust band ~thick solid curve witha triangular shape! for LEDs emitting in three different angularntervals into bubble-free ice for the 2-m logger.

Fig. 4. Response to two thin dust bands each 2 m thick and 10 mapart in bubble-free ice, with distances between the LEDs and thePMT of 1, 2, and 3 m.

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above the dust layer. The full width at half-maximum for the response of the logger is of the orderof the thickness of the dust band.

Figure 4 shows that the logger easily resolves two2-m-thick dust bands with a vertical separation of10 m. Shortening the LED to PMT separation im-proves the ability to separate the two dust bands.

In their optical study of dust at depths of 1200–2300 m in South Pole ice, the AMANDA collabora-tion19 detected bands of enhanced dust concentrationtypically at least 100 m thick and a factor of 2–4above minimum dust levels. Our simulations showthat, because of its compact size, our dust loggershould be able to detect a factor of 2 increase in dustconcentration in a band only a few meters thick.

Figure 5 shows the effect of variations in the opticalproperties of dusty ice from D 5 0.1 ~strongly absorb-ing, e.g., hematite! to 10 ~highly transparent, e.g.,quartz!. For D 5 0.1 the presence of dust leads to atrong decrease in signal; for D 5 10 the dust isransparent and more strongly scattering than theure ice, and thus leads to a strong increase in signal.Instead of a single-scattering albedo, we used a and

be, which provide more physical insight when repre-senting multiple scattering of light through dustyice.!

B. Detectability of Dust Bands in Regions of High BubbleConcentration

At a site where the accumulation rate is large, therecord of the Holocene ~the warm period from thepresent back to the end of the last ice age, ;17,000years ago! extends well below 1000 m, and the recordof the Last Glacial Maximum ~;22,000 years ago!peaks at a still greater depth, where all bubbles haveundergone a phase transformation into solid air–

Fig. 5. Responses to dust bands with values of D ~[beya! from 0.1~highly absorbing! to 10 ~highly scattering! in 20 m of bubble-freeice. Note the semilogarithmic scale.

hydrate crystals. However, at a site such as Vostokor Dome C, the snow accumulation rate is so low thatthe Last Glacial Maximum record is at a depth of onlya few hundred meters. At such a shallow depth, airbubbles contribute far more to light scattering thandoes dust, but they contribute nothing to absorption.We now show that the dust logger can detect in-creases in dust concentration even at depths wherebubbles dominate light scattering. In regions ofstrong scattering, a photon undergoes a random walkfrom the emitter to the receiver, and an analytic ap-proximation is valid22:

u~d, t! 5 @3be~ z!y4pvg t#3y2 exp@23d2be~ z!y4vg t

2 a~ z!vg t#. (3)

ere u~d, t! is the density of photons at a distance drom the source at time t ~normalized to unity at t 5!; be [ bbub 1 bdust is the sum of scattering coeffi-

cients for bubbles and dust; vg [ cy1.322 is the groupvelocity of 370-nm photons in ice; d is the distancefrom the emitter to the receiver; and a~z! is the ab-sorption coefficient of light ~with dust but not bubblescontributing! at depth z. Equation ~3!, which isalid in the limit of many scatters ~d .. be

21!, ismuch quicker to evaluate than running numericalsimulations. The effective scattering coefficient forbubbles is given by

bbub 5 ~1 2 ^cos u&!nbubprbub2, (4)

where the first factor, with ^cos u& ' 0.8, takes intoccount the forward peaking in the scattering. Forypical bubble concentrations and radii at depths of aew hundred meters ~nbub ' 500 cm23 and rbub ' 100m!, bbub ' 3 m21. For an ;2-m dust logger, the

nequality d .. be21 is thus satisfied, even though

bdust ,, bbub.Figure 6 shows the results of an application of Eq.

~3! to air bubbles plus dust at a site with a low accu-mulation rate. For bbub we used Eq. ~4! with nbuband rbub taken from microscopic measurements ofVostok ice core samples,23 with values shown as solidcircles. For bdust representative of a warm period wechose a constant value of 0.025 m21, and for dustrepresentative of a cold period we chose a trapezoidalshape, ramping up linearly at depths from 300 to400 m to a plateau value of 0.325 m21 and decreasingback to 0.025 m21 at depths from 475 to 500 m. Thevalues used in our calculations are shown as solidtriangles. To illustrate the effect of the presence ofbubbles on the dust signal, it does not matter that weignored the subpeaks and valleys in the measureddust concentration in a cold period.20

The solid curves show the calculated signals in thedust logger for a 250-ns integration time for threedifferent dust types ~D 5 1, 4, and 8!. Note that, byvirtue of their large scattering coefficient, the bubblescause an amplified negative image of the dust band.In the absence of dust ~dashed curve!, the signal thatis due to the bubbles would track the decline of bbubwith depth; in the absence of bubbles, the signal that

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is due to the dust would increase, tracking the trap-ezoidal dust concentration ~see Figs. 2–4 for triangu-ar and square-wave patterns!. When both bubbles

and dust are present, the bubbles confine most of thephotons to the dusty region until they are absorbed,thus leading to the negative image of the dust ~solidcurves!.

C. Volcanic Ash

We modeled a volcanic ash band 1 cm thick and witha concentration and size distribution of ash chosen tomimic a typical ash band reported by Gow and Wil-liamson.15 D was taken to be 5.87, the same as thatf the dust modeled in Figs. 2–4. The increasedignal that is due to the ash band was easily detect-ble. Although the resolution in depth would de-end on the logging speed and details of thelectronics, a resolution of ;1 m would appear feasi-le. If the ash consisted of dark, highly absorbingrains, the amount of light reaching the phototubeould decrease instead of increase ~as could be con-

luded from Fig. 5!, thus providing a crude measuref composition.

D. Volume of Ice Sampled

One way of seeing the effect of bubbles is to comparethe radius of the volume of ice outside the hole that issampled when bubbles are absent or present. Toestimate volume, we used Eq. ~3!. For integrationtimes of 22.5, 50, and 100 ns, 90% of the photonsscattered back into the PMT from bubble-free ice~bdust 5 0.035 m21! come from radial distances as farout as 3.5, 4.7, and 6.3 m, respectively, compared withmuch smaller radial distances for bubbly ice withbbub 5 2.5 m21: 0.41, 0.55, and 0.74 m, respectively.

Fig. 6. Response to bubbles plus dust for a 250-ns integrationtime. The scale on the left shows the values of be used as inputsto the calculations. Values for bubbles ~solid circles! were basedon microscopic measurements of bubble concentrations and radii inactual Vostok ice; values for dust concentration ~solid triangles!assumed a trapezoidal distribution above a constant low-background dust level. The solid curves ~arbitrary units! give theresponses to the combination of bubbles plus dust for three dusttypes; the dashed curve shows the response if no dust were present.The dust, by absorbing some of the light, depresses the signal.

520 APPLIED OPTICS y Vol. 40, No. 15 y 20 May 2001

In each case the presence of bubbles reduces the vol-ume sampled by a factor of approximately 600.

6. Conclusions

The principle on which the dust logger is based hasbeen demonstrated thoroughly by the AMANDA col-laboration, who used pulsed light emitters and pho-totube receivers separated by distances from 10 to120 m to map the vertical distribution of bubbles anddust. The same simulation techniques and diffusionequation used by AMANDA apply to our logger,which we plan to test in a 1-km-deep butyl-filled holeat Siple Dome, Antarctica.

The logger can detect both thin and thick dustbands in bubble-free ice. For dust with the ratiobeya $ 0.5, typical of most glacial ice, the PMT signalin the dust band is greater than background; for ahypothetical dust band with beya , 0.25, the signal isdepressed below background. The logger can alsolocate regions of large dust concentration even in thepresence of a strongly scattering bubble concentra-tion, but as a negative image, i.e., a decrease in signalsuperimposed on a high-background signal that isdue to bubbles alone. Volcanic ash bands ;1 cmthick can be detected, with a depth resolution of theorder of 1 m.

Because the refractive indices of the ice and of thebutyl acetate are similar, the results are insensitiveto the scale of roughness of the hole. The logger iseconomical to build, and readout is continuous andstraightforward. It has several other advantagesover methods such as laser light scattering and mi-croscopic or chemical analysis, which require thatthousands of sections of a several-kilometer-long corebe removed from the ice and transported to an ice-core laboratory for analysis: It can quickly read outdata for in situ ice at ambient pressure; it provides acontinuous record, unaffected by possible fractureand loss of portions of a core; and it averages over avolume several meters in radius in the ice surround-ing the hole, rather than a volume of a few centime-ters in radius inside the hole.

In the absence of bubbles, dust concentrations typ-ical for glacial maxima produce large signals, narrowdust bands only a few meters apart can clearly beresolved, and the signal tracks both triangular andsquare-wave dust distributions to within ;1 m.

We thank M. Solarz and J. de la Torre for measur-ing light absorption in butyl acetate as a function ofwavelength and J. Keasling for use of his spectropho-tometer. This research was supported in part byNational Science Foundation grant PHY-9971390.

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