Electromagnetic induction in subsurface metal targets: Clusteranalysis using local point-pattern spatial statistics

T. S. de Smet1, M. E. Everett2, C. J. Pierce2, D. L. Pertermann1, and D. B. Dickson1

ABSTRACT

The detection and localization of statistically significantspatial clustering of buried metal artifacts for applications,including archaeological, environmental site assessment,and civil infrastructure mapping, can be performed reliably,inexpensively, and noninvasively using transient electro-magnetic (EM) geophysics. The local Gi

�ðdÞ statistic basedon a weighted spatial autocorrelation were used to detect andlocalize statistically significant clustering of buried metalobjects from gridded electromagnetic responses acquiredat a seeded control site and at an active historical archaeo-logical site in Paint Rock, Texas. This statistic compares thelocal EM millivolt response values about point i radially tothe global mean and variance to calculate the Gi

� statistic asa standard variate at various length scales, which cantherefore be assessed for significance. Because the localGi

�ðdÞ statistic compares local to global averages, it spa-tially compacts the amplitude response signal of the EMdata. The resulting spatial cluster maps conformed well tothe known distribution of metal targets buried at the controlsite, and enabled a successful excavation strategy with asignificant reduction in false positives encountered at the ar-chaeological site, when compared with more traditionalmethods.

INTRODUCTION

Clustering of subsurface metal targets is important in near-sur-face geophysical application areas such as unexploded ordnance(UXO) remediation, mineral exploration, environmental or geotech-nical site assessment, and historical or industrial archeology. Thespatial distribution of metallic targets can reveal information aboutthe natural or anthropogenic spatiotemporal processes that led to the

emplacement of objects that are now of historical, cultural, envir-onmental, economic, geotechnical, or archaeological significance.Electromagnetic geophysical measurements offer a powerful non-invasive probe of subsurface metal distribution. The data, carefullyanalyzed, can be used to test and discriminate hypotheses about theunderlying site formation processes. Spatial cluster analysis is re-levant to archaeological reconstructions or site assessments becauseartifacts that are associated with a past event such as a battle, or pastindustrial use such as a foundry or railyard, tend to be found in closeproximity (Schwarz and Mount, 2006). At brownfield sites sched-uled for reclamation or redevelopment, due to past land-use patternsthere often develops clustering of targets of interest, such as under-ground pipes, drums, storage tanks, or the buried remnants of re-inforced concrete foundations.A wide variety of methods are available to discern patterns in

spatial data (Perry et al., 2002), including self-organizing maps(Benavides et al., 2009), various clustering algorithms (Paascheand Eberle, 2009, 2011), and numerous global and local point-pattern analysis (PPA) techniques (Getis and Ord, 1996). GlobalPPA of geophysical responses discriminated UXO from clutter ata practice bombing range in which the UXO was deposited accord-ing to known aircraft flight patterns while the clutter was randomlydistributed (MacDonald and Small, 2009).In the context of mineral exploration, Paasche and Eberle (2009,

2011) discuss and use numerous clustering algorithms like k-means,fuzzy c-means, and the Gustafson-Kessel method. One major draw-back of these techniques is that the number of clusters must be cho-sen prior to analysis, regardless of whether clustering is actuallypresent in the data set. As such, the usefulness of these clusters mustbe verified against external criteria. With local statistical measuresof spatial autocorrelation, as used in this study, no a priori assump-tions are made about the number of clusters.The preferred geophysical technique for detecting subsurface

metal items is transient electromagnetic induction (EMI). TheEMI data analyzed in this study were collected with a GeonicsEM-63 metal detector (www.geonics.com). The EM-63 records a

Manuscript received by the Editor 5 October 2011; revised manuscript received 28 February 2012; published online 9 July 2012.1Texas A&MUniversity, Department of Anthropology, College Station, Texas, USA. E-mail: tdesmet@neo.tamu.edu; jael73@tamu.edu; dickson@tamu.edu.2Texas A&M University, Department of Geology and Geophysics, College Station, Texas, USA. E-mail: everett@geo.tamu.edu; cpierce@geo.tamu.edu.

© 2012 Society of Exploration Geophysicists. All rights reserved.

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time-decaying voltage at the receiver (RX) coil after a suddenswitch-off in the magnetic field generated by the transmitter(TX) coil. The RX voltage decay is due to the dissipation of eddycurrents that are induced in the host geology along with any subsur-face metal targets of sufficient inductance (Everett, 2005) that areburied within several meters of the surface. The RX voltage is di-gitized at 26 time gates, or channels, that are logarithmically spacedfrom t0 ¼ 180 μs to t1 ¼ 25 ms after TX switch-off.The EM-63 normally detects targets whose characteristic size a,

magnetic permeability μ, and electrical conductivity σ are such thatthe eddy-current diffusion time satisfies τ > t0, where τ ∼ μσa2

(Pasion, 2007; Benavides et al., 2009). The shape of the RX voltagewaveform is indicative of target characteristics. The amplitude ofthe early time RX voltage response, for instance, reads higher thanbackground geologic noise levels for all detectable metal artifactswhether small or large, shallow or deeply buried. The late-timeRX voltage response remains high, however, only for the larger ob-jects for which τ ≫ t0. An important diagnostic of such large ob-jects, therefore, is the lengthy time that is required for the inducededdy currents, and hence, the RX voltage, to decay to the instrumentnoise level. As the amplitude response is measured at 26 time gates,the initial response and shape of the decay curve could be used toroughly classify the depth, orientation, and size of specific anomalies.In this paper we consider two features of the EM-63 response:

(1) the magnitude of the early time RX voltage response (mV)(hereinafter called the channel-1 response); and (2) the timegate at which the RX voltage decays to the instrument noiselevel (hereinafter called the decay time). The channel-1 response

reads high for all detectable metal targets, and a lengthy decay timecan be used to preferentially select the larger ones.Local PPA is used herein to detect and locate target clustering.

The precise identification and location of target clusters helps sta-keholders to better comprehend site formation processes and to de-velop an efficient excavation strategy. We weight points accordingto their EM-63 channel-1 response and decay time. The location ofthe most interesting clusters is identified using the local Gi

� statistic(Getis and Ord, 1992, 1996; Ord and Getis, 1995).The plan of the paper is as follows. First, we suggest an EM-63

acquisition technique that ensures a high-quality data set. We thenreview elements of the point-pattern statistical methodology. EM-63 data are presented from a controlled test site seeded with a knownspatial distribution of common metal artifacts, and from a historicalarchaeological site, the Robert E. Lee camp at Paint Rock, Texas. Thelatter site, centrally located between Fort Mason and Fort Chadbourne,circa 1851–1874 was utilized by the U.S. Second Cavalry and manyother troops, most notably then Colonel Robert E. Lee in 1856 (Free-man, 1934). At both sites, we show how point-pattern spatial statisticscan be used to describe and locate the clustering of subsurface metaltargets identified by EM-63 responses. Excavation results from PaintRock are analyzed. The results demonstrate the utility of the approachfor archaeological site formation hypothesis testing.

METHODS

EMI data were acquired with the Geonics EM-63 at a controlledtest site and an active archaeological site in Texas (Figure 1). TheTran experimental site is located in College Station, Brazos County,

about 7 km east of Texas A&M University. TheRobert E. Lee campsite (U.S. registered archae-ological site no. 41CC295) is located in the townof Paint Rock in Concho County on a terrace ofthe Concho River near a series of natural fords.Both sites are flat grassy pastures characterizedby floodplain deposits of clays, silts, and clayeysands.The Geonics EM-63 is a transient controlled-

source electromagnetic induction instrument ar-rayed in the central-loop configuration. Thetransmitted current, which generates a primarymagnetic field, is suddenly switched off, indu-cing a secondary magnetic field which decaysslowly in subsurface ferrous and nonferrous me-tal targets. After the primary field is switched off,the secondary magnetic field is recorded at 26logarithmically spaced time gates. The eddy cur-rents induced in metal objects of different size,shape, strike, and orientation decay at character-istic rates, thus enabling a rudimentary targetclassification prior to excavation. The transientEM response amplitude, measured in millivolts,and its time rate of decay, measured inmV∕s, cangenerally be used to predict the size and depth ofsubsurface anomalies. For instance, a small chan-nel-1 response exhibiting a slow decay time ty-pically indicates a large metal object at depth,whereas a higher channel-1 response accompa-nied by a brief decay time suggests a shallowerburial.

Figure 1. Location of the controlled test site at College Station and Robert E. LeeCampsite archaeological site at Paint Rock. The major rivers of Texas and some largecities are included to aid orientation.

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Data acquisition

An improved data acquisition protocol was developed to provideaccurate sensor navigation, as required by the spatial statistics meth-ods used in this study. Slight irregularities in the terrain cause loss ofcontrol of the EM-63 when it is deployed in the conventional cart-mounted configuration. The EM-63 was mounted on a sled andpulled along the survey lines. Data on an accurate rectilinear gridare straightforward to acquire in this fashion, with consistent posi-tional accuracy to within a few centimeters using manual data trig-gering. Data acquisition times using the cart and sled systems aresimilar.

Tran experimental site

The improved acquisition protocol was used to evaluate the per-formance of the EM-63 for spatial cluster analysis at a controlledtest site seeded with metal artifacts. For this purpose, a clean site onprivate land was selected. The landowner Mr. S. Tran stated that thesite is used for agricultural purposes and that subsurface metal ob-jects are not expected. The site was seeded by 50 common metalitems in the spatial pattern shown in Figure 2. To test the ability ofthe statistics to discriminate between clustering and random spatialpatterning, we purposely buried 32 of these items in four clusters(these are called “artifacts”) and another 18 at randomly chosen lo-cations (these are called “clutter”). A background EM-63 data setwas acquired prior to the seeding (Figure 3a), in which minor andwidely scattered EM-63 signals are observed. The line spacing andthe station spacing are both 0.5 m for the 20 × 20-m surveyarea, for a total of 1681 data points. A second EM-63 dataset was then acquired after seeding. The resulting EM-63 chan-nel-1 response of the seeded site (Figure 3b) clearly reflects thespatial distribution of the shallow buried items.A third data set was acquired at the site using the Geometrics

G-858 cesium-vapor magnetometer (www.geometrics.com) to com-pare the capabilities of EMI and magnetometry for target clusteranalysis (Figure 4). Magnetometry is widely used in archaeologicalprospection (Kvamme, 2006; Perttula et al., 2008; Conyers andLeckebusch, 2010) and UXO mapping and detection (Beard etal., 2008; Doll et al., 2008), sometimes in conjunction with EMI(Beard et al., 2008; Pétronille et al., 2010). The G-858 magnet-ometer is a passive device that measures the intensity of the sumof the background geomagnetic field and the much smaller mag-netic field due to any nearby ferrous objects.The G-858 and EM-63 instruments have complementary capabil-

ities. The EM-63 responds to all conductive metal objects, whereasthe G-858 detects only ferrous targets. A G-858 data set does in-dicate, however, the background spatial variation of magnetic soilsand sediments. The G-858 yields a spatially distributed pattern ofdipole anomalies, rather than a discrete point set, because the mag-netic signature of a buried target is dipolar and often merges withneighboring signatures. Spatial filtering by methods, such as reduc-tion-to-pole, analytic signal, or regional subtraction, are required tobetter isolate the magnetic signatures, whereas virtually no proces-sing is necessary with EM data. For this reason, the G-858 data setis not as amenable as the EM-63 data set to target cluster analysisusing point-pattern spatial statistics. A qualitative visual inspectionof Figures 3 and 4 demonstrates that EM-63 anomalies are morecompact than their G-858 counterparts — note especially the iso-lated rebar at coordinates (2, 9) and (8, 13).

Figure 3. EM-63 channel-1 data acquired at the Tran test site:(a) before and (b) after seeding with artifacts.

Figure 2. Distribution of seeded artifacts, symbol-coded by type, atthe Tran test site: (a) bolt, (b) washer, (c) cylinder, (d) bottle cap,(e) coke can, (f) bullet, (g) license plate, (h) rebar, (i) musket ball.Plot dimensions in meters.

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Archaeological case study at Paint Rock

An EM-63 data set was acquired at the Robert E. Lee campsite(Figure 5) over a 20 × 20-m grid with 0.5-m line and station spa-cing, for a total of 1681 measurements. The site was previouslyscanned with hand-held metal detectors by the local avocational ar-chaeological society (Ashmore, 2010) to identify subareas mostlikely to yield historic metal artifacts. This is standard archaeolo-gical practice (Connor and Scott, 1998; Bevan, 2006). TheEM-63 data sets were analyzed using point-pattern statistical

methods, which are described in the next section of this paper. ThePPA program (Aldstadt et al., 2002) is a statistical toolbox de-signed for spatial analysis applications, including cluster analysis.

Point pattern analysis statistics

Geostatistics has long been used by geoscientists to study con-tinuous natural or anthropogenic spatiotemporal processes and isbased on interpolating observations made at several discrete loca-tions and times. Geostatistics was developed originally (Krige,

1951; Matheron, 1963) within the mining indus-try as a method for determining the grade of re-coverable ore. The most important geostatisticaltechnique is kriging, which estimates an un-known process over a continuous region by inter-polating between its measured values at discretelocations, taking into account spatial correlationswithin the observations. Geostatistical and re-lated spatial techniques are best reserved for geo-physical applications in which the target ofinterest, such as a zone of groundwater contam-ination or oil and gas accumulation, is distributedmore or less continuously throughout the sub-surface.PPA differs from geostatistics in that the key

analyzed variable is the location of a specifiedevent, rather than the size or the probability ofan event as a continuous function of its location.PPA is broadly applicable to UXO remediation,archaeological prospection, brownfields rehabili-tation, or civil infrastructure assessment becauseordnance items, metal artifacts, and buried engi-neered structures are typically found or concen-trated at discrete locations in the subsurface(Ostrouchov et al, 2003).A local analysis of the autocorrelation struc-

ture of a spatial variable (Anselin, 1995) canbe used to detect clustering. A spatial clusteris characterized by the occurrence of a largernumber of points within a specified distance of

a given reference location than the number that would be expectedunder complete spatial randomness (CSR) (Diggle, 2003). A“point” is defined as a location at which the EM-63 responds sig-nificantly above the instrument noise level, indicating the presenceof an underlying metal target. Points may take binary (0/1, or hit/miss) values or they may be weighted (Getis, 1984) based on thevalue of the channel-1 response (in mV) or decay time (inmV∕s). Inaddition to detecting the presence of clustering by analyzing binaryor weighted-point distributions, we can also pinpoint the location ofclusters using the techniques originally described by Getis andOrd (1992).The standard K-function statistic (Ripley, 1977, 1981; Schwarz

and Mount, 2006) detects spatial clustering of events with respect tosome length scale d. An illustration of spatial clustering, with re-spect to a random distribution for which the expected number ofevents increases by one for each unit increase in radius around aspecified event, is given in Figure 6. A K-function tests the ob-served distribution of event locations against the null hypothesisof CSR. A set of events scattered randomly throughout astudied region is statistically equivalent to a homogeneous Poisson

Figure 5. EM-63 channel-1 data acquired at Robert E. Lee camp-site.

Figure 4. G-858 magnetometer total field data set from the Tran site.

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distribution (Cressie, 1993). The model of CSR is always approx-imate because it rests on a largely untenable assumption that theinvestigated site contains a distribution of targets that is statisticallyequivalent to that of surrounding areas. Generally however, an ar-chaeological, environmental, or UXO site is expected to contain astatistically distinct target distribution compared with the surround-ing areas that have not been subject to the same set of naturalprocesses and past land uses.A global K-function analysis uses simulations to determine the

statistical significance of clustering. For instance, M ¼ 95 permu-tations tests the null hypothesis of CSR at the α ¼ 0.05 level, suchthat values of LðdÞ outside the confidence envelope are interpretedto be significant, thereby rejecting the null hypothesis of CSR. Pre-vious geophysical research utilizing the K-function to detect sub-surface metal target clusters was carried out on airborne helicoptermagnetometer data acquired over two former precision bombingranges (MacDonald and Small, 2009). Spatial clustering of the mag-netic anomalies caused by buried UXO and clutter could not bedetermined by visual inspection. PPA was required to distinguishstatistically significant clustering patterns from apparent clusteringof randomly distributed targets.The K-function is a global statistic that detects the presence or

absence of significant clustering and dispersal at a given lengthscale. The Gi

� function (Getis and Ord, 1992; Ord and Getis,1995), on the other hand, is a local statistic that can characterizeand pinpoint individual clusters. We use the K-function to deter-mine whether a data set is significantly clustered, or completely spa-tially random, or significantly dispersed. Then we apply the localGi

� statistic to determine the locations and length scales of indivi-dual clusters.

Local Gi�ðdÞ statistic: Hot spot analysis

The purpose of the Gi�ðdÞ statistic is to identify “hot spots,” or

locations that are surrounded by a cluster of events carrying anom-alous weight. Positive values Gi

�ðdÞ >0 indicate spatial clusteringof events with large weight, whereas negative values Gi

�ðdÞ < 0

correspond to clustering of low-weighted events. The formula is

Gi�ðdÞ ¼

Pjkijðxj − x̄Þ

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNP

j≠ik2ij−ð

PjkijÞ2

N−1

r ; (1)

where x̄ is the mean of the weights, s is the variance of the weights,N is the total number of events (or sample size), and kij is the num-ber of events within distance d of point i. The variables x̄ and s arethe same for all distance scales d as they represent the global meanand variance.The nullGi

�ðdÞ hypothesis is that there is no association betweenthe weight xi at point i and the weights of its neighbors xj that liewithin radius d. Therefore, the null hypothesis can be restated as thesum of the weights of the j points (including point i) that lie withinradius d of point i is not more than the sum that would be expectedby chance for a population of mean x̄ and variance s (Getis and Ord,1996). In this paper, the distance d is taken to be a multiple of 0.5 m.It is important to note that the expected number of neighbors forshort distance scales is small (Table 1). Accordingly, the Gi

�ðdÞstatistic may be biased at short-distance scales by the weight xiat point i itself and by the small number of neighbors.

It can be shown that the Gi�ðdÞ statistic is asymptotically nor-

mally distributed as d increases. Thus, under the null hypothesis,the expected value of the Gi

�ðdÞ statistic is zero and its varianceis one. As such, the Gi

�ðdÞ statistic is a standard variate, and itsvalue is equivalent to a z-score at each point. The z-scores canbe used to assess significance of clustering at various length scalesabout point i. However, the weights xj of the neighbors j aroundpoint i are often correlated, in violation of assumptions of indepen-dence. Because of this dependence, a Bonnferroni-type correctioncan be used to control for a false positive, or Type I error (Ord andGetis, 1995; Getis and Ord, 1996). To determine significance values(Table 2), we prefer instead to use the Šidàk correction (Šidàk,1967) because it is more powerful against a false negative, or TypeII error (Abidi, 2007).The local Gi

� statistic is an improvement over a global statisticsuch as the K-function insofar as it indicates the locations of indi-vidual clusters. For the case in which the observed events areweighted by the EM-63 decay time, for example, a high value

Figure 6. Illustration of spatial clustering. Circles with integer ra-dius are drawn about three specified events: black circle, gray circle,and gray square. There is clustering around the black circle event atradii 1 < d < 2. The same clustering is recorded at 3 < d < 4 aroundthe gray circle event. The gray circle event, like the gray squareevent, shows no clustering at small radii 1 < d < 3.

Table 1. Number of neighbors calculated by the local Gi � �d�statistic.

Distance (m)Number of neighbors

calculated

0.5 5

1 13

1.5 29

2 49

2.5 81

3 113

3.5 149

4 197

4.5 253

5 317

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of Gi�ðdÞ implies that large buried metal targets are clustered about

the specified point i. On the other hand, a low value of Gi�ðdÞ in-

dicates that such targets are relatively dispersed about point i. Forthe case of the channel-1 response, the value of Gi

�ðdÞ indicates therelative concentration or dispersal of all detectable metal targets.Because different EM-63 response features could be used asweights, the Gi

�ðdÞ statistic enables the geophysicist to examinethe spatial distribution of targets with specific attributes. In thisway, the Gi

�ðdÞ statistic provides a powerful method of testing hy-potheses about site formation processes based on geophysical data.

RESULTS

Tran control site

The Gi�ðdÞ local statistic was analyzed at specific coordinate

points to explore clustering about those points. The coordinates(3.5, 6.5) and (3.5, 11.5) were selected because both correspondto high-amplitude EM-63 responses; one is a member of a clusterand the other is a clutter item, respectively. The former is an auto-mobile license plate with a 675 mV channel-1 response, which wasthe largest in the survey area, and the latter is a piece of rebar with a272 mV channel-1 response. We first explored the effect of samplesize on the Gi

�ðdÞ statistic. The effect of decreasing the sample sizeby counting only events with channel-1 response values greater thanthresholds of 5 mV (n ¼ 159) and 50 mV (n ¼ 52) is to decreasesignificance, even after adjusting the z-scores. There are two rea-sons for this: (1) A larger sample size implies many more neighborswithin radius d of a point i, most of which are below the thresholdlevels. (2) The mean and variance increase as the sample size isdecreased. These factors both contribute to lower the Gi

�ðdÞ statis-tic, as shown in Figure 7a, 7b. We therefore use the entire data set(n ¼ 1681) to maintain the highest possible significance.The EM-63 channel-1 target responses from the license plate and

the rebar are both statistically significantly clustered at the 1-m dis-tance scale (Figure 7c). The rebar EM-63 response shifts to nonclus-tered at greater distance, reflecting the fact that the rebar waspurposely seeded as isolated clutter. However, the license plateEM-63 response is significantly clustered to a distance of 7 mbecause the license plate belongs to a purposely seeded cluster,which at large ranges merges with other clusters.

Table 2. Significance Values of the local Gi��d� statistic at

the 90, 95, 99, and 99.9th percentiles for various sample sizes(α � 0.10, 0.05, 0.01, and 0.001, respectively).

n90th

percentile95th

percentile99th

percentile99.9th

percentile

1 1.282 1.645 2.326 3.09

10 2.309 2.568 3.089 3.719

25 2.635 2.870 3.351 3.944

50 2.862 3.083 3.539 4.107

100 3.075 3.283 3.718 4.265

1000 3.706 3.884 4.264 4.753

1500 3.807 3.982 4.353 4.834

1681 3.835 4.009 4.378 4.856

Figure 7. The Gi�ðdÞ statistic for stratified data sets at Tran site:

(a) Clustered’ license plate at (3.5, 6.5); (b) clutter rebar at (3.5,11.5); (c) comparison of (a and b) for the entire data set.

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Maps of the Gi�ðdÞ statistic at the Tran site are shown in Figure 8

for various distances d ¼ 1–4 m. The maps are formed by calculat-ing the Gi

�ðdÞ statistic at each grid coordinate, and plotting the re-sults. It is apparent that the EM-63 responses of the artifactsmaintain significant clustering at greater distances than the clutterresponses. Of the latter, only the previously analyzed rebar showsany significant clustering. It is also apparent that only three of thefour artifact clusters are identified. The cluster of small artifacts atthe lower right corner of the Tran site (Figure 2) is missed by theGi

�

analysis because these artifacts are too small and/or deeply buried tobe detected by the EM-63. These results are similar to those ofBeard et al. (2008) in that small buried objects were missed becausethey fall below the threshold of EM-63 detection. This clusterwas detected by the magnetometer, however, as a dipolar anomaly(Figure 4). There are four large dipolar anomalies in the magneto-metry data set and two single poles; two dipoles are due to artifactclusters while the other two are caused by isolated rebar. The iso-lated rebar, emplaced as clutter at (2, 9) and (8, 13), generate thelargest dipolar anomalies in the magnetic data set, but they appear asmuch more compact anomalies in the EM-63 maps. The two otherdipolar anomalies and two single poles in the magnetic data set,which correspond to clusters, are actually more compact than theisolated rebar. This is possibly because the magnetization directionsof the various artifacts within the clusters are not aligned. Althougha magnetic data set is always a useful complement to EM-63 data,magnetic anomalies are spatially extended relative to EM, asmentioned, and not as amenable to application of point-patternstatistics.The Tran site provided a useful test bed for localGi

�ðdÞ statisticalanalysis of EM-63 responses generated by subsurface metal distri-butions. The Gi

�ðdÞ significance value maps (Figure 8) provide va-luable graphical representations of clustering, which can be used toguide excavations and constrain archaeological site formation the-ories. Our attention now turns to the archaeological site.

Robert E. Lee campsite

In the summer of 2010 and spring of 2011, archaeological exca-vations at the Robert E. Lee campsite were undertaken according tostandard archaeological conventions. Thirty-three 1 × 1-m unitswere carefully excavated with hand troweling in precise 5-cm depthincrements, measured with respect to a Topcon RL-H3C laser levelcalibrated daily. The excavation strategy was informed by the re-sults of point-pattern statistical analysis of the EM-63 data set.We followed the same protocol as at the Tran site with Gi

�ðdÞ ana-lyses of the complete channel-1 response data set.Maps of the local Gi

�ðdÞ statistic at the Lee campsite are shownin Figure 9. There are three clusters of significant Gi

� values, basedon α ¼ 0.10 (Gi

� values > 3.835) as in Table 2, at scale d ¼ 1 m,two clusters at d ¼ 2 m, and only one at d ¼ 4 m. This suggeststhat the single cluster toward the bottom left of the maps (3, 7) cor-responds to an isolated target with a high channel-1 response, ana-logous to the aforementioned rebar at the Tran site. Subsequentexcavation confirmed that the target was in fact a large piece ofsaw-tooth barbed wire patented in the 1880s (Clifton, 1970). A sec-ond area of high Gi

� values in the upper left indicates clustering atthe 1-m distance scale, persisting through the 2-m scale, then fallingoff (2, 15). This suggests the presence of neighboring items withhigh response values in the vicinity. Excavations confirmed this be-cause a horse shoe was found in situ, while present in adjacent units

were a nail belonging to this horse shoe, fragmentary metal, and ashotgun shell. A third cluster in the bottom right (6, 15) is signifi-cantly clustered up to 2 m, but then falls off. Excavations revealedunidentifiable barbed wire along with nails and other fragmentarymetal suggestive of fence remnants.

Figure 8. The Gi�ðdÞ significance maps, Tran site: (a) d ¼ 1.0;

(b) 2.0; (c) 3.0; and (d) 4.0 m.

Figure 9. TheGi�ðdÞ significance maps, Lee campsite: (a) d ¼ 1.0;

(b) 2.0; (c) 3.0; and (d) 4.0 m.

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DISCUSSION

Reduction of false positives is important in UXO remediation(Butler, 2004) and archeology because both disciplines work withbudgetary and temporal constraints. The EM-63 performance at theLee campsite gives encouraging results in this direction. We exca-vated 10 units characterized by EM-63 “hits” along with 23 adja-cent EM “barren” units. Hits were defined as Gi

� (d ¼ 1 m) values>3.835 (n ¼ 26), which represents a p-value of 0.10, or a one in 10chance of Type I error, as can be seen in Table 2; and barren iseverything below this threshold.We report seven false negatives because we failed to predict the

presence of metal in seven of the 16 units that contained metal uponexcavation; although some units labeled “barren” were rather closeto the Gi

�ðdÞ values deemed significant because there are 18 Gi�

values between three and 3.835. Moreover, some of the metal inthese units was quite fragmentary. If we relax the significancethreshold of Gi

� values to include all those >3, we reduce theamount of false negatives to just three. This is expected becauseOrd and Getis (1995) believe the corrected p-values for multiplecomparisons is overly cautious against Type I error, therefore inflat-ing Type II error, or false negatives. By exploring the relationshipbetween these two sources of error we are able to examine morepatterns in the data. There was, however, only one false positive,which was near the detection threshold and probably the resultof an overlapping footprint from larger channel-1 responses in ad-jacent units. Interestingly, one false positive — or Type I error —is expected from the ten EM hits at the α ¼ 0.10 level.A Pearson’s chi-squared test of the 76% correct predictions

(ð9þ 16Þ∕ð9þ 7þ 1þ 16Þ) gives a p-value of 0.001652 (Table 3).

The odds of such a distribution occurring by chance are small(Drennan, 2010). When this is compared with a traditional ap-proach, in which EM channel-1 response values greater than onestandard deviation above the mean are considered (> 21 mV,n ¼ 51), the results are striking (Table 4). There are nearly identicalfalse negatives. The percentage of correct predictions drops to just55% (ð10þ 12Þ∕ð10þ 6þ 5þ 12Þ). The chi-squared value for thetraditional approach is not significant at the α ¼ 0.05 level, whereasthe statistical approach is significant at the α ¼ 0.01 level. Mostnoticeable, however, is the sharp increase in false positives, becausethe spatial extension of EM signals from large anomalies causesfalse positives in adjacent units. The Gi

�ðdÞ is better than the tradi-tional approach because it takes into account the large nearby chan-nel-1 responses and the smaller background signals from thesurrounding area, thereby increasing the Gi

� value and compactingthe EM anomalies, resulting in less false positives. It is clear that theGi

�ðdÞ analysis of the EM-63 data set acquired at the Lee campsiteproved very valuable as a guide to the archaeological excavations.

CONCLUSIONS

The application of PPA spatial statistics to EM-63 data can beused to detect significant clustering of subsurface metal objectsof historical, cultural, environmental, geotechnical, or archaeologi-cal significance. However, a high-quality data set is necessary be-fore global and local spatial statistical analyses are attempted. Werecommend the sled-mounted data acquisition protocol employedherein, although any acquisition method can be used if the naviga-tion is accurate. EM-63 responses include the initial amplitude andthe subsequent decay time. Both features can be used as weightingfactors. Our results at the Tran experimental site indicate that thelocal Gi

�ðdÞ statistic can be used to locate clusters of artifacts, evenwhen clutter is present. These results were confirmed at the Leecampsite, where local statistics were used to successfully guideour excavation strategy, greatly reducing false positives.Global and local PPA techniques provide valuable information

regarding the length scales of clustering and dispersal. Althoughuseful, global approaches like K-function analysis can be used onlyto determine the presence or absence of significant clustering ordispersal at a given length scale. The Gi

�ðdÞ statistical analysis,however, can be used to locate hot-spots in the data set. The useof multivariate significance values while analyzing the Gi

� valuesis necessary to guard against Type II error, or false negatives; thisprecaution is necessary to avoid missing significant clustering pat-terns that may be hidden in the data.

ACKNOWLEDGMENTS

We would like to thank the three anonymous reviewers for theirhelpful comments which greatly improved the quality of this paper.We would also like to thank Steve Tran and Fred and Kay Campbellfor the use of their property throughout this research. Wealso thank Michael Waters for loaning excavation equipment.This research was funded by the Texas A&M Program to EnhanceScholarly and Creative Activities.

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Table 3. Chi-squared test for the local Gi��d� statistical

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EM barren(n ¼ 23)

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Table 4. Chi-squared test for the predictions based upontraditional measures, herein defined as one standarddeviation above the mean (channel-1 responses >21 mV,n � 51), based upon excavations at Paint Rock; Χ2 � 3.6397,df � 1, p-value � 0.05642.

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EM barren(n ¼ 18)

6 (false negative) 12 (true negative) 18

Total 16 17 33

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