Ž .Journal of Applied Geophysics 43 2000 281–295www.elsevier.nlrlocaterjappgeo

Multidimensional GPR array processing usingKirchhoff migration

Mark L. Moran a,), Roy J. Greenfield b, Steven A. Arcone a, Allan J. Delaney a

a US Army Cold Regions Research and Engineering Lab, HanoÕer, NH 03755-1290, USAb Department of Geosciences, Penn State UniÕersity, UniÕersity Park, PA 16802, USA

Received 8 October 1998; received in revised form 25 February 1999; accepted 15 March 1999

Abstract

Ž .We compare the ability of several practical ground-penetrating radar GPR array processing methods to improveŽ .signal-to-noise ratio SNR , increase depth of signal penetration, and suppress out-of-plane arrivals for data with SNR of

Ž . Ž .roughly 1. The methods include two-dimensional 2-D monostatic, three-dimensional 3-D monostatic, and 3-D bistaticKirchhoff migration. The migration algorithm is modified to include the radiation pattern for interfacial dipoles. Results arediscussed for synthetic and field data. The synthetic data model includes spatially coherent noise sources that yieldnonstationary signal statistics like those observed in high noise GPR settings. Array results from the model data clearlyindicate that resolution and noise suppression performance increases as array dimensionality increases. Using 50-MHz array

Ž .data collected on a temperate glacier Gulkana Glacier, AK , we compare 2-D and 3-D monostatic migration results. Thedata have low SNR and contain reflections from a complex, steeply dipping bed. We demonstrate that the glacier bed can

Žonly be accurately localized with the 3-D array. In addition, we show that the 3-D array increases SNR relative to a 2-D.array by a factor of three. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Ground-penetrating radar; Signal-to-noise ratio; Kirchhoff migration

1. Introduction

Ž .Two-dimensional 2-D seismic data sets areroutinely migrated using a variety of methodsŽ .Yilmaz, 1987 . The need for higher spatialresolution, greater target localization accuracy,

Ž .and increased signal-to-noise ratio SNR hasdriven the petroleum exploration community to

Ž .develop elaborate three-dimensional 3-D sur-vey and migration processing methods. Some

) Corresponding author. Tel.: q1-603-646-4274; fax:q1-603-646-4397; e-mail: mmoran@crrel.usace.army.mil

Ž .ground-penetrating radar GPR applicationshave similar requirements. Application ofpetroleum exploration data acquisition and pro-cessing methods have been demonstrated to im-

Ž .prove GPR results Fisher et al., 1992, 1994 .However, differences in the scale of costs anddata characteristics require modification of theseismic methods for practical implementation inGPR contexts.

We seek to develop methods to improveŽ .GPR performance in the areas of target detec-tion, spatial localization, signal penetration, andnoise suppression. For example, signal penetra-

0926-9851r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-9851 99 00065-8

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295282

tion is often limited by scattering losses. This isparticularly true for GPR surveys of temperate

Ž .glaciers e.g., Watts and England, 1976 . In thisapplication, the depth of investigation is limitedby signal levels which are low relative to noisescattered from inclusions in the ice.

There are different antenna configurations fortaking GPR data. Normally, data are collectedalong a single traverse with essentially collo-

Ž . Ž .cated transmitter Tx and receiver Rx anten-nas. This is denoted as a 2-D monostatic tra-verse. Grouping a series of parallel GPR tra-verses gives a 3-D monostatic survey array.Bistatic data are taken when each Tx position isrecorded by a number of offset Rx positions.The survey configuration offering the maximumSNR gain would be a large number of Tx andRx positions in a 3-D bistatic configuration. Atpractical spatial scales, bistatic configurationsrequire a much greater data collection effort andprocessing capability than do monostatic sur-veys. For most GPR applications, bistatic datacollection and processing are prohibitively ex-pensive.

There are a variety of GPR processing meth-ods that improve SNR. For monostatic data,combining reflections from a common point onthe surface can improve SNR. Delayed sum-ming of traces can be used to reject signal-gen-erated noise from directions away from theregions of interest. For bistatic multicoveragedata, common midpoint stacking has been shown

Ž .to improve SNR Fisher et al., 1992 . Onlylimited bistatic 3-D data have been obtained and

Ž .processed on glaciers Walford et al., 1986 .In this study, we discuss processing methods

that we have developed and applied to syntheticand field data which contain GPR reflections

Ž .from targets of interest signal as well as en-ergy scattered from other objects not of interestŽ .noise . We apply 2-D and 3-D methods to datacollected or generated using both monostaticand bistatic arrays. Time domain Kirchhoff mi-gration methods are applied to these array datasets to compare SNR improvement, target local-ization, and target resolution. The time domain

Ž .Kirchhoff method Schneider, 1978 is selectedbecause its spatial sampling criteria is less strin-

Žgent than frequency domain wave number Stolt,.1978 and time domain finite difference

Ž .Claerbout, 1985 migration methods. The timedomain Kirchhoff approach allows larger aper-ture arrays with lower sensor populations to be

Žused large apertures maintain array SNR im-.provements for deep targets . These less strin-

gent spatial sampling criteria are critical forkeeping data acquisition and processing costswithin manageable bounds.

We generate synthetic data to allow differentconfigurations to be examined without the costof collecting the data. It also allows array re-sults to be directly compared with the knowntarget signal. And importantly, synthetic arrayresults aid in the interpretation of processedfield data. The improvements seen in the syn-thetic results are supported by applying ourarray processing methods to 50-MHz data col-lected on a small temperate valley glacierŽ .Gulkana Glacier, AK . Like many temperateglacier GPR surveys, this data set has low SNRand complex bottom reflections.

2. Methods

2.1. 2-D and 3-D monostatic array processing

Relative to depths of interest, GPR data aretypically collected by nearly coincident Tx andRx antennas. Thus, each time series trace in aGPR survey can be considered as resulting froma single monostatic antenna. In a seismic con-text, common midpoint stacks may be consid-ered as improved monostatic data. Applicationof 2-D and 3-D Kirchhoff migration to commonmidpoint seismic and monostatic GPR data has

Žbeen widely reported e.g., Berryhill, 1979;.Robinson, 1983; Fisher et al., 1992 . A modifi-

cation made here is the inclusion of a half-spaceŽinterfacial dipole radiation pattern Smith, 1984;

.Arcone, 1995 in the Kirchhoff integral of

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295 283

Ž .Schneider 1978 . Our modified GPR formula-tion is given by

1 Ea u ,f ,´ EU rX ,tŽ . Ž .r 0 0 XU r s daŽ . H 0bX2p R Õ Etz s0

1Ž .where U is the migration depth image, andŽ X .U r ,t is the surface wavefield observation.0 0

Ž X X X.Primed parameters z , r , and a give spatialdimensions relative to an array’s coordinate ori-gin, R is the subsurface diffraction point rela-tive to a surface observation, r is the integralevaluation point relative to the array’s coordi-nate origin, Õ is the propagation speed in ice

Ž .and E u ,f,´ is the range normalized electricr

field dipole radiation pattern. The exponents a

and b are treated as processing parameters tobe determined by systematic trial-and-error vari-ation. This approach was taken becausepresently, there is no theory that includes effectsof transmitter and receiver radiation patterns orconsiders radiation pattern distortions due totime range gain. In the synthetic data, as2and bs1. In the glacier data, as2 and bs1.5. The interfacial radiation pattern is stronglyinfluenced by the relative dielectric constantŽ .´ . In 3-D problems, the dipole radiation pat-r

tern must be included under the integral since itŽ .is a function of both azimuth u and declina-

Ž .tion f . These direction parameters vary sig-nificantly between antenna locations. The dipole

Ž .radiation pattern is squared as2 to accountfor antenna directivity upon transmission andreception. Use of the half-space dipole formula-tion is appropriate for GPR settings in which theupper region of the material being probed isrelatively homogeneous.

The modified migration integral is applied toŽ .single 2-D GPR survey lines or multiple paral-

Ž .lel 3-D survey lines. The antenna positionswithin the survey lines are grouped into subar-rays. Using the recorded GPR time series in

Ž .each subarray, Eq. 1 is evaluated at a series ofevenly spaced nodes to yield a depth image in asubsurface focal plane. For large groups of longparallel survey lines, subarray divisions can be

made in both x and y directions. Furthermore,subarrays may be overlapped in both x and ydirections. This approach is similar to the syn-thetic aperture array processing done in high

Žaltitude radar imaging of the ground Curlander.and McDonough, 1991 . The subarray overlap

reduces edge effects in the migration results andprovides increased continuity of migrated ampli-tudes.

Fig. 1 shows a series of survey lines runningparallel to the x-axis. We refer to all antennapositions in this group of survey lines as theGPR array. The figure indicates that the array isbroken into a series of overlapping subarrays.Directly below the center line of the array is asingle vertically oriented image plane. Whenusing 3-D surveys, our implementation allowsthe migration integral to be evaluated in a seriesof multiple parallel image planes with regularoffsets. Each discrete antenna position in thearray has an x and y coordinate on the earth’ssurface. Within any given subarray, the inter-element sensor position should be specified to aprecision of less than 0.25 of an in situ wave-length. These spatial accuracy requirements be-come easier to achieve in field surveys as GPRfrequency decreases; for example, at 50 MHz inice, a quarter wavelength is approximately 1 m.Fortunately, the accuracy requirements forinter-element sensor locations need only be en-forced for distances slightly larger than the sub-array dimensions.

The number of elements in a subarray, theinter-element separations, and the spatial dimen-

Ž .sions aperture of the subarray are chosen byconsiderations of the in situ GPR signal wave-length, the depths of interest, and the character-istics of the targets being investigated. In ourwork with GPR data, we find it is acceptable tohave roughly 0.1 of a wavelength samplingalong a survey line and roughly one to threewavelength separations between survey lines. Ingeneral, deeper targets and steeply dipping beds

Ž .require larger subarray apertures Yilmaz, 1987 .Trial-and-error processing was used in this studyto determine appropriate subarray dimensions.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295284

Ž .Fig. 1. An example of an array of monostatic GPR antenna locations small black triangles . In this illustration, each dipolehas the E field oriented parallel to the x-axis. The array is broken into four subarrays. the center of each subarray is labeled

Ž .S1 through S4. Each subarray overlaps the other by 50%. The modified migration integral of Schneider 1978 is evaluatedin the image area.

To demonstrate proper implementation of thealgorithm, we show the migration result for an

Ž .impulse response Fig. 2 in data space for thearray in Fig. 1. The procedure follows YilmazŽ . Ž .1987 p. 258 . To generate the impulse re-sponse, every array element’s time series iszeroed except the center element, which con-tains an impulse. The array data are then subdi-

Ž .vided into subarrays as shown in Fig. 1 . Thesubarray data are used in the migration integral,which is evaluated in the focal plane to producea depth image. For a properly functioning mi-gration algorithm, a point in time should mi-

Ž Ž ..grate Eq. 1 to a semicircle depth image, withthe amplitude varying according to the obliquity

Žcharacteristics in our case, the interfacial dipole.radiation pattern of the Kirchhoff integral. Fig.

2 shows the E and H field impulse responsesfor a homogeneous earth with ´ s8. The im-r

pulse was placed at a depth of 2.5 m. To obtainthe E plane result, each antenna is oriented withthe E field parallel to the x-axis. To obtain the

H plane response, each antenna’s E field isoriented parallel to the y-axis. Four subarraysare used. Each subarray overlaps the precedingsubarray by 50%. The plots show that the dipolearrays preferentially enhance backscatter fromnonvertically positioned targets. The off-centerH field maximum is 6 dB larger than the verti-cal. The off-center E-field maximum is reducedfrom the vertical by 3 dB. However, there aredeep spectral nulls between the vertical andsidelobe maximum. In standard implementa-tions of the Kirchhoff method, the array impulse

Ž .response has a cos u directivity with themaximum amplitude vertically downward.

2.2. Synthetic data generation

For the simulated data, we apply a pseudo-scalar wave equation for point target diffractorsin a homogeneous host material. The modifica-tion includes the directivity of the target diffrac-tors resulting from each diffractor–antenna pair-

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295 285

Fig. 2. Modified Kirchhoff migration applied to a point impulse. The plots indicate that dipole arrays enhance backscatterfrom off-axis targets. The off-center H-field maximum is 6 dB larger than the vertical. The off-center E-field maximum isreduced from the vertical by 3 dB. The sensor geometry is indicated in Fig. 1 with ´ s8.r

ing. In this formulation, the target’s scatteredfield polarization is controlled by the incidentelectric field characteristics. For a given an-tenna–diffractor pairing, the incident electricfield is controlled by the interfacial dipole radia-

Ž .tion pattern Smith, 1984 . This approximationfor the polarization holds when scattering ob-jects are small compared with a wavelengthŽ .van de Hulst, 1981 . A more advanced treat-ment would consider the full Mie solutionsŽ .e.g., Stratton, 1941 for scattering from smallspheres. Distributions in model space of manyuncoupled smaller amplitude point inclusionsallow background noise levels to be variedagainst a fixed target with a relatively largerscattering amplitude. Arrival times are deter-mined using straight ray travel paths for eachtarget or noise inclusion in the model spacevolume.

Target backscatter responses can be gener-ated for point diffractors, line diffractors at arbi-trary azimuths, and arbitrarily dipping planarreflectors. Material properties of the target scat-

tering are emulated via specification of scatter-ing amplitude and amplitude polarity. Noise inthe synthetic data is produced by several cate-gories of spatially organized point diffractors.These include randomly distributed volumetricscatterers, regionally localized scatterers, andangularly confined scatterers. This gives a sta-tistically nonstationary noise field. We believethis accurately represents GPR signal-generatednoise. Stationary random system noise can alsobe included. The level of noise in a data set iscontrolled by specifying the number, ampli-tudes, and polarizations of the scattering inclu-sions. For each object in the model space, smallrandom perturbations in frequency content, andarrival time are added.

3. Results

Array results are given for monostatic 2-D,3-D, and 3-D bistatic GPR arrays using synthet-ically generated data. The synthetic results are

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295286

followed by 2-D and 3-D array results fromfield data collected on a temperate glacier. Thespatial scales of the synthetic results differ fromthose of the glacier data set. Using syntheticdata for simple array geometries, we establishperformance improvements for SNR, target lo-calization, and target resolution from pointdiffractors. The results from glacier data usemore complex GPR arrays to show similar arrayprocessing improvements for reflections fromdeep, steeply dipping bed topography under lowSNR conditions. The combination of these re-sults spans a wide range of typically encoun-tered GPR survey scales and target types.

3.1. Monostatic 2-D Õs. monostatic 3-D: syn-thetic data

Using the analytical model, a 4-m-long, 21-Ž .position monostatic GPR survey line is simu-

lated. The offset between antenna positions is0.2 m. The model contains six point diffractorslocated 3 m below the ground surface. The halfspace has an ´ s5.7 and is nonconductive. Wer

keep these electrical properties constant for allsimulations discussed. Fig. 3B shows the targetlocations in the x–y plane at a depth of 3 m.The targets are grouped in pairs along the y-axis.Within a pair, the target separation is 0.25 m.

Ž .The polarities sign of the scattering coeffi-cients are reversed within each pair. The magni-

tude of the reflection coefficients are equal forall six diffractors. The x positions of each pairare y0.75, 0, and 0.5 m.

In the simulated data, a 3rd derivative of theGaussian function is used as a source wavelet.For all simulations, the center frequency of thesource wavelet is 700 MHz. This gives an insitu wavelength of roughly 0.18 m. Fig. 4Ashows the source wavelet with a small amountof added noise. Fig. 4B gives the synthetic datatime series for the array. Signal amplitudes indi-cate that the SNRs for the data are approxi-mately 100. All SNR quantities discussed in thispaper are determined by amplitude compar-isons. Fig. 4C gives the 2-D monostatic Kirch-hoff migration result in the vertical y–z planepassing through xs0 m. The depth imageclearly resolves the targets around the x–y ori-

Žgin. However, the out-of-plane diffractors at.xs0.5 and y0.75 show large energy leakage

into the migration plane.We demonstrate the performance improve-

ment for a 3-D monostatic GPR array relative tothe 2-D result given above. In this example, weuse the same center frequency, SNR, and targetmodel parameters as those given for the 2-Dcase. The 3-D array is composed of five parallelsurvey lines with an aperture of 2=4 m2. The

Žoffset between each line is 0.5 m 2.7 wave-.lengths . Within a survey line, the monostatic

antenna positions are separated by 0.2 m. Fig.

Ž .Fig. 3. A Standard monostatic GPR survey with 21 sensor locations over 4 m line. Six point diffractors are located at aŽ .depth of 3 m. B x–y locations of these six diffractors. Each pair is separated by 0.25 m.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295 287

Ž . Ž .Fig. 4. A 700-MHz center frequency source wavelet used for all synthetic data. B Synthetic data for standard GPRŽ .survey. C 2-D Kirchhoff migration result. Targets near x–y origin are resolved and target polarity is distinguishable. Large

Ž .amplitudes in the vicinity of ysy0.5 and ys0.5 are due to out-of-plane targets at xsy0.75 m and xs0.5 m .

5A gives the array geometry and shows raypaths from each sensor to a diffractor. Fig. 5Bgives the 3-D Kirchhoff migration result in thevertical y–z plane at xs0 m. Diffractors areclearly resolved in the vicinity of the x–y originand the polarization reversals are distinct. Mostnotable is the suppression of out-of-plane en-ergy leakage from the diffractors located alongxs0.5 and y0.75 m. Equally good results areobtained when a vertical y–z focal plane passesthrough the xs0.5 and y0.75 m.

3.2. Monostatic 3-D Õs. 3-D bistatic: syntheticdata

For the 3-D bistatic data, we again utilize theŽ . Ž Ž ..modified integral of Schneider 1978 Eq. 1 .

For this demonstration, synthetic data are gener-ated for two oppositely polarized diffractors at adepth of 2 m. Both targets are in the xs0

plane and are offset by 0.125 m on either sideof ys0. This gives a separation of 0.25 m. Thehost half space has ´ s5.7. A large number ofr

small amplitude point scatters are distributedthroughout the model space to produce GPRdata with an SNR of approximately 1. Monos-tatic signals are calculated for a 2=2 m2 array

Žconsisting of 25 equally spaced elements 0.5.m . This array geometry is marginal for resolv-

ing the two targets. Bistatic synthetic reflectionsare calculated for the same array element posi-tions. However, in the bistatic case, when eachelement transmits a radar pulse, every elementrecords the resulting backscattered radar signal.This results in 650 time traces from a 25-ele-ment array. Fig. 6A shows the model spaceŽ .with target diffractors and noise inclusions andarray element locations. Fig. 6B shows themonostatic array time traces at each y positionat xs0 m. Target diffractor signals arrive inthe vicinity of 35 ns.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295288

Ž .Fig. 5. A 3-D monostatic GPR array using five parallel survey lines with 0.5 m separation between lines and 0.2 mseparation between sensor locations along each line. 105 elements total. Target and source model parameters are the same as

Ž .Fig. 3. B 3-D monostatic Kirchhoff migration result for the y–z plane at xs0. Targets near the x–y origin are clearlyseparated and polarizations are maintained. Most notable is the suppression of energy from targets outside the focal plane.

Fig. 7A gives the 3-D monostatic migration.The two targets are marginally resolved. How-ever, the target polarities are ambiguous, if notmisleading. This is caused by spatially coherentnoise in the vicinity of the target signal arrivals.Fig. 7B gives the bistatic migration result fordata with the same signal and noise statistics. Inthis case, the target diffractors are clearly sepa-rated in space and the target polarizations arecorrect. Also of importance is the substantiallysuppressed noise field. However, these improve-ments are very costly in terms of data acquisi-tion and computation times. Both the computa-tional burden and size of the data sets scale asthe square of the number of element positionsŽ 2.N .

Fig. 8 shows the amplitude variation vs. depthfrom the 3-D monostatic and bistatic results.This depth profile was taken at surface point

xs0, ysy0.125 m. In the vicinity of theŽ .target depth zsy2 m , the bistatic migration

shows a roughly 12 dB noise suppression im-provement relative to the monostatic migrationresult. In problems with incoherent randomnoise, the noise suppression should be enhanced

Žby 1r6N with N being the number of indepen-.dent samples of the process . If the noise in our

synthetic data was totally incoherent, the noisesuppression for the bistatic array should havebeen roughly 14 dB greater than the monostaticarray.

3.3. Results from temperate glacier data

The electrical characteristics of temperateglaciers present challenging processing prob-lems for time domain GPR operating above 10

ŽMHz Watts and England, 1976; Arcone et al.,

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Ž . 2 Ž .Fig. 6. A 2=2 m 25 position GPR array and model space. Coherent spatial noise is simulated by adding random pointŽ .diffraction scatters. Targets heavy circles are at depth of 2 m and are separated by 0.25 m around ys0, at xs0. Target

reflection coefficients have opposite signs. The array geometry provides minimal resolution capability for targets at thisŽ .depth and separation. These modelrarray parameters are used for both the monostatic and bistatic data synthesis. B

Monostatic synthetic waveforms are from the center line. SNR is roughly 1. Target reflections arrive between 35 and 40 ns.

Ž . 2Fig. 7. A 3-D monostatic Kirchhoff image from 2=2 m , 25 element array. Raw data SNR is 1.25. Targets at 2 m depthŽ . 2are barely resolved and the polarity is confused by the noise field. B 3-D bistatic Kirchhoff image from 2=2 m , 25

Ž .position array generates 650 time traces . Raw data SNR is roughly 1. Both targets are clearly resolved and the polaritydistinction is clear. The added performance is due to the N 2 increase in data coverage.

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Fig. 8. 3-D monostatic and bistatic migration amplitudeŽ .wiggle traces vs. depth from Fig. 7 . Each trace passes

through the target positioned at ysy0.125, xs0. Thetarget reflection in the bistatic trace shows noise suppres-sion greater than 12 dB relative to the monostatic trace.

.1995 . Temperate glaciers have thermal states ator slightly below 08C. Thus, there is typically asignificant fraction of liquid water present in theice. The large dielectric contrast between liquid

Ž .and frozen water ´ s81, ´ s3.17r-water r-ice

causes GPR signals to scatter strongly, produc-Ž .ing high clutter data low SNR . Crevasses and

rock inclusions also produce scattering losses.Multidimensional GPR arrays can mitigate theseproblems by rejecting energy scattered fromundesirable directions.

We have collected and processed GPR arrayŽ Xdata from the Gulkana Glacier, AK 1458 30

X .longitude, 638 15 latitude . The Gulkana is aŽ .small 8-km-long temperate valley glacier in

the Alaska Range of central Alaska. The arrayŽwas situated just below the firn line roughly

.1800 m elevation in the upper northeast end ofthe glacier. On temperate glaciers, the firn lineis defined as the boundary between snow and

Žice at the end of the melt season Patterson,.1994 . The array’s rectangular dimensions are

100-m-wide by 340-m-long. The western endŽ .ys0 m of the array was situated on the toeof a rock outcrop below a hut maintained by theUniversity of Alaska, Fairbanks. The grid isshown in Fig. 9. The 100-m-wide base of thegrid had a roughly north–south orientation thatparalleled the ice flow direction. The widthdirection is defined as the x-axis. The 340-mlength of the survey grid trended roughly westto east and is designated as the y-axis of thesurvey grid.

We used a laser theodolite to place surveyflags at 10-m intervals along the x-axis and at20-m intervals along the y-axis. Relative eleva-tion changes between flags were also obtainedfrom the theodolite. A snowmobile was used totow the antennas along the y direction at every2-m interval along the x-axis to yield 51 paral-lel survey lines. The center frequency of the16-bit array data was 50 MHz. Total trace dura-tion was 3400 ns with 1024 samples. All signals

Ž .Fig. 9. 50-MHz GPR survey grid located on the Gulkana Glacier, Alaska. Surveyed flags represented by large dots wereplaced every 20 m along y direction, and every 10 m along the x direction. There are a total of 51 survey lines.

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of interest were contained in the first 2000 ns ofthe GPR records. The raw data were justified togive 10 traces per meter. Elevation corrections,spatial justification, and Wiener spike deconvo-

Ž .lution Robinson and Treitel, 1980 were ap-plied prior to array processing. The deconvolu-tion operation substantially broadened the fre-quency content of raw GPR reflections andimproved the resolution of bottom reflectionsand ice inclusions.

Fig. 10 shows a data record from the surveyline located at xs71 m. The data have beenelevation-corrected and justified. The tails ofhyperbola resulting from diffraction scatteringfrom ice inclusions, can be used to estimate

Ž .GPR signal phase velocity or ´ . The steepestr

hyperbolae in our data at a variety of depthsconsistently indicated a value of ´ s3.17. Inr

Fig. 10, the ice bottom reflection is the steeplydipping reflector, sloping from the upper leftdown to the lower right. At y locations beyond125 m, the data are dominated by spatiallycoherent noise from scattering. The data arerelatively noise-free at y locations less than 100m. The apparent bed discontinuity in the vicin-ity of ys130 m is due to a local increase inbed dip. In addition to the bed’s y–z plane dip

component, there is also a strong x–z dip inand out of the plane of the figure. With suchsteep, complexly dipping bed characteristics, thedepth to the ice bottom cannot be determinedfrom the raw data. Migration must be applied toaccomplish this.

Fig. 11 gives the 2-D monostatic migrationresult using the survey line located at xs71 m.The y subarray aperture was 60 m and con-tained 60 elements separated by 1 m. Eachsubarray overlapped the preceding subarray by50%. The figure contains a portion of the verti-cally oriented migration focal plane orientedperpendicular to the x-axis. It shows the mi-grated image between y values of 100 and 320m and depths between 80 and 160 m. In thisregion, the bed reflection is weak and the SNRis low. The bottom reflection is the vague dip-ping reflector starting at zsy100, ys100 mand trending downward to zsy138 m at ys230 m. The migration image plane was speci-fied to be vertically down, and perpendicular tothe x-axis. However, the result is misleadingsince a 2-D migration can incorrectly placeout-of-plane reflections in the image. This wouldbe the case for reflections from a bed with asignificant x–z dip. The lobate dipole directiv-

Fig. 10. A deconvolved 50-MHz Gulkana survey line from the array data set. The line is located at xs71 m in Fig. 9. Thesteeply dipping bed requires migration to accurately determine the true bed depth profile.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295292

Fig. 11. 2-D migration from Gulkana Glacier. The survey line was located at xs71 m. The bottom reflection is the dippingreflector starting at a depth zsy100, ys100 m and trending downward to zsy138 m at ys230 m. However, this 2-Darray has no out-of-plane control. Therefore, the normal reflection from a plane with a strong x–z dip will be resolved, butmay be mislocated.

ity aggravates this mislocation problem in stan-dard 2-D surveys by having the maximum in theradiation pattern occur at nonvertical azimuths.

For our 3-D monostatic migration result, weused a rectangular subarray with an x aperturewidth of 40 m, and a y aperture length of 60 m.The elements in each subarray are separated by1 m in the y direction and 2 m in the xdirection. Each subarray contained 1200 an-tenna positions. The survey line located at xs71 m defined the centerline of the 40-m x-aper-ture. As in the 2-D case, each subarray over-lapped the preceding subarray by 50%. Whenusing a 3-D array, we have both x and yresolution control, which allows the image focalplane to be substantially offset from the array.In this example, the focal plane was vertical andoriented perpendicular to the x-axis at xs35m. Fig. 12 shows this geometry in an x–z planecross-section. The xs35 m image plane loca-tion puts the array focal point in the vicinity ofa normal reflection for the x component of thebed dip. Fig. 13 shows the 3-D migration resultusing these processing parameters. The bed nowhas a high degree of continuity and the SNRalong the bed reflection shows a significant

Ž .increase relative to the 2-D result Fig. 11 .

The optimal xs35 m, y–z focal plane loca-tion was determined by calculating results formultiple parallel focal planes spaced betweenxs25 and 71 m. The xs35 m focal plane

Ž .location shown in Fig. 13 produced the largest

Fig. 12. 3-D Gulkana migration geometry in an x – z planecross-section. The 40=60 m2 subarrays are centered onthe xs71 m survey line. Individual antenna elements inthe array record the normal reflection from the dippingbed. To observe the maximum signal return from the bed’snormal reflection, the migration focal plane must be posi-tioned at xs35 m.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295 293

Fig. 13. 3-D Gulkana migration result. The rectangular array had an x dimension of 40 m, and a y dimension of 60 m. Thevertically oriented image plane was located at xs35 m. The image plane offset puts the array focal point in the vicinity ofnormal reflection for the x component of the bed dip. In addition to accurately positioning the bed, the 3-D migration hassubstantially increased the SNR of the bed reflection, when compared with the 2-D result.

amplitudes, and highest SNR in the vicinity ofthe bed reflection. To demonstrate this 3-Dlocalization capability, we give results for avertically oriented y–z focal plane at xs71 mŽ .Fig. 14 . This is directly below the centerline

Ž .of the array Fig. 12 . The image shows poorbed continuity. And in most places, it has lowerSNR in the vicinity of the bed reflection. Alsoof significance is the mislocated bed reflection

Ž .indicated with an arrow . In Fig. 14, the depthto the bed reflection is given as 125 m at

Žys140 m. In the properly focused result Fig..13 , the bed reflection has a depth of 115 m at

ys140 m.In Fig. 15, we compare the amplitude varia-

tion at ys180 m as a function of depth for thethree Gulkana migrations discussed. The uppertrace shows the result at xs71 m for the 3-D

Ž .Fig. 14. 3-D Gulkana migration result focus directly down xs71 m . The same array was used in Fig. 13. This imageplane no longer contains well-focused normal reflections from bed. And as expected, for a steeply dipping plane, very littleenergy is reflected back to the array at these angles of incidence. Thus, the image has very poor bed continuity and lowSNR.

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295294

Fig. 15.

array focused in the y–z plane; the middle traceis from the 3-D array with the y–z focal planeat xs35 m. The bottom trace is from the 2-D

Ž .array which resolves the normal reflection .The properly focused xs35 m trace has a SNRof roughly 3. It indicates a bed depth of 121 mŽ .at xs35 m, ys180 m . The 2-D result hasan SNR of roughly 1. The bed reflection has a

Ž .depth of 126 m at xs71 m, ys180 m . TheŽ .vertically focused xs71 m 3-D array has no

identifiable bed reflection at this location.

4. Conclusions

There are many circumstances in which GPRsurvey objectives require high precision targetlocalization, increased signal penetration depth,and noise suppression. We have presented costeffective array processing methods to addressthese requirements.

The Kirchhoff migration integral of Schnei-Ž .der 1978 was modified to include the radiation

pattern for an interfacial dipole and imple-mented for monostatic 2-D, 3-D, and bistatic3-D data. Utilization of time domain Kirchhoffmigration allows array elements to have separa-tions as large as two wavelengths. In 3-D sur-veys, this less stringent sampling requirementgreatly reduces the data collection and computa-

tional expenses. The presence of strong dipoleradiation patterns in GPR data tends to enhancesignal scattering from out-of-plane objects.Consideration of this effect in the migrationintegral coupled with greater spatial control froma multidimensional array allows increased accu-racy in target localization and noise suppres-sion.

Application of these array processing meth-ods to synthetic GPR data demonstrated thatsignificant improvements in target localizationand noise suppression can be achieved by 3-D

Žmonostatic GPR arrays compared to standard.2-D methods . Simulation results using 3-D

bistatic arrays shows a further increase in per-formance. However, dramatic increases in datacoverage and processing costs make it impracti-cal to conduct 3-D bistatic GPR surveys usingcommercially available GPR hardware.

2-D and 3-D monostatic array results for thefield data support the results observed in thesynthetic data processing. Our glacier resultsdemonstrate that 3-D monostatic arrays can im-prove SNR from bed reflections by a factor ofthree, that signal penetration is improved, bedreflection continuity is improved, and that thecomplexly dipping bed can be accurately local-ized. Lastly, the resolution improvements usinga 3-D array bring out bed reflection details notobserved in the raw data, or in the 2-D arrayprocessing.

Acknowledgements

Support for this research was provided by theŽUS National Science Foundation NSF grant

.OPP-9531800 and OOP-9531579 , by the USArmy Cold Regions Research and Engineering

Ž .Laboratory CRREL Project 4A161102AT24,work unit AT24-SS-E10, and the CRREL pro-ject 96-ILIR, titled ‘‘Signal Penetration Depthand Noise Suppression Improvement Using ATime Domain Radar Array’’. We wish to ex-press many thanks to Mr. Les Davis and Dr.Peter Annan of Sensors and Software, Missis-

( )M.L. Moran et al.rJournal of Applied Geophysics 43 2000 281–295 295

sauga, Ontario, for use of equipment and fieldassistance during data collection at Camp Bor-den. The Borden data were used extensively indeveloping the methods applied in this paper.Further thanks go to Mr. Gary Kuhen of AreteWilderness Guides, Sandy Bay TAS, AU, forhis professional support in providing glaciersafety, basecamp management, and technicalservices while collecting glacier radar data.Thanks go to the organizers and participants ofthe ‘‘12th Annual Arctic Man Ski and Sno-GoClassic’’, 1997, for their consideration duringour experiments.

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