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GEOPHYSICS, VOL. 71, NO. 5 �SEPTEMBER-OCTOBER 2006�; P. H67–H78, 14 FIGS.10.1190/1.2258094

D seismic refraction traveltime tomographyt a groundwater contamination site

olin A. Zelt1, Aron Azaria2, and Alan Levander1

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ABSTRACT

We have applied traveltime tomography to 3D seismic re-fraction data collected at Hill Air Force Base, Utah, in an ap-proximately 95 � 40-m area over a shallow �� 20 m�groundwater contamination site. The purpose of this study isto test the ability of 3D first-arrival-time data to characterizethe shallow environment and aid remediation efforts. Theaquifer is bounded below by a clay aquiclude, into which apaleochannel has been incised and acts as a trap for densenonaqueous phase liquid �DNAPL� contaminants. A regular-ized nonlinear tomographic approach was applied to 187,877first-arrival traveltimes to obtain the smoothest minimum-structure 3D velocity model. The resulting velocity modelcontains a velocity increase from less than 300 to 1500 m/sin the upper 15 m. The model also contains a north-south-trending low-velocity feature interpreted to be the paleochan-nel, based on more than 100 wells in the area. Checkerboardtests show 7.5–10 m lateral resolution throughout most of themodel.

The preferred final model was chosen after a systematictest of the free parameters involved in the tomographic ap-proach, including the starting model. The final velocity mod-el compares favorably with a 3D poststack depth migrationand 2D waveform inversion of coincident reflection data.While the long-wavelength features of the model reveal theprimary target of the survey, the paleochannel, the velocitymodel is likely a very smooth characterization of the true ve-locity structure, particularly in the vertical direction, giventhe size of the first Fresnel zone for these data.

INTRODUCTION

More than 20% of the earth’s freshwater is beneath the land sur-ace �Dunne and Leopold, 1978�, and much of the world’s popula-

Manuscript received by the Editor October 16, 2005; revised manuscript re1Rice University, Department of Earth Science, 6100 Main St., Houston, T2Formerly Rice University, Department of Earth Science, Houston, Texas

ronazaria@yahoo.com.2006 Society of Exploration Geophysicists.All rights reserved.

H67

ion relies on groundwater reservoirs for drinking water and agricul-ural production. As populations increase and economies grow, theotential for groundwater contamination rises, with the result thatroundwater contamination has emerged as a major environmentalroblem in many countries. In the United States, this situation hased to expensive groundwater cleanup, groundwater protection laws,nd environmental protection programs �Moore and Jones, 1987�.he U. S. Environmental Protection Agency �EPA� has identifiedore than 1200 contaminated areas that qualify for Superfund clean-

p funding �Moore et al., 1995�.In 1987, the EPAlisted HillAir Force Base �HAFB�, Utah �Figure

�, as a Superfund site and targeted 11 areas on the site for remedia-ion �Environmental ProtectionAgency, 2002�. Much of the contam-nation consists of chlorinated solvents used to clean industrial prod-cts, such as jet engines. At Operable Unit 2 �OU2� �Figure 1�, theolvents — dense nonaqueous phase liquids �DNAPLs� — descend-d into a shallow aquifer comprised mostly of unconsolidated sandnd gravel. The aquifer is bounded below by an impermeable, pre-ominantly clay formation that prevents the solvents from movingeeper underground. The remediation at OU2 has been ongoing forore than 10 years and has consisted mainly of surfactant/foam pro-

esses to extract both the contaminants and the contaminated waterHirasaki et al., 1997; Meinardus et al., 2002�. More than 200 wellsave been drilled as part of the remediation process. These wells pro-ide point control on the depth to the impermeable clay formationhat bounds the aquifer from below.

In August 2000, personnel from the Department of Earth Sciencet Rice University conducted a series of seismic surveys over theontaminated aquifer at OU2, funded by the U. S. Department of En-rgy �Dana et al., 2001; Gao et al., 2004; Gao et al., 2006�. The seis-ic experiment that is the subject of this paper is a 3D refraction sur-

ey covering an area roughly 95�40 m.The application of 3D seismic methods to the shallow environ-ent is a relatively new field. Examples of near-surface 2D refrac-

ion tomography studies include Lanz et al. �1998� and Morey andchuster �1999�. We derive a 3D P-wave velocity model to about

February 28, 2006; published online September 5, 2006.251. E-mail: czelt@rice.edu; alan@rice.edu.tly Compagnie Generale de Geophysique �CGG�, Houston, Texas. E-mail:

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5 m depth by inverting first-arrival traveltimes using the regular-zed inversion algorithm of Zelt and Barton �1998�. This algorithmypically has been applied to crustal-scale 3D data sets �e.g.,chlindwein et al., 2003; Ramachandran et al., 2004�, althougheen and Gohl �2002� have used it in a mining application to ap-roximately 100 m depth. This is the first time the Zelt and Barton1998� algorithm has been applied in three dimensions to the near-urface ��20 m� environment. Dana et al. �1999� have applied theelt and Barton algorithm to 2D data from a pilot survey at OU2 and

maged the known geology and a channel feature important to reme-iation efforts.

The areal dimensions of the 3D study area are nearly 1000 timesmaller than a typical crustal survey study area, but the center fre-uency is only about 10 times higher; the typical center frequencyor crustal data is approximately 5 Hz. Therefore, a wave travelinghe length of the model �100 m� consists of only 5–10 wavelengthst the center frequency. The relative change in velocity over a shortistance is also very different from a crustal survey. From the 2D pi-ot study, we know that velocity increases by at least a factor of fiven the upper 15 m �Dana et al., 1999� or a velocity gradient of

80 s−1, compared with a typical crustal velocity gradient of0.1 s−1. Our study serves as a test of the 3D refraction method to

haracterize the shallow environment accurately and thereby to aidemediation efforts. The resulting 3D velocity model is compared tohe known structure of the subsurface from well data and the resultsf other seismic surveys at the site.

GEOLOGIC SETTING AND SITECHARACTERIZATION

HillAir Force Base is located 60 km north of Salt Lake City, Utah,est of the Wasatch Mountains and east of the Great Salt Lake �Fig-re 1�. The Great Salt Lake is a remnant of the ancient glacial Lakeonneville, a large terminal lake that existed roughly 32,000–4,000 years ago. The Weber River delta, which supplied Lake Bon-eville, is between the Wasatch Mountains and the Great Salt Lake.t was formed during the Pleistocene epoch by the Weber River as itowed into the eastern edge of Lake Bonneville �Curry, 1980�.HAFB is built on a plateau west of the Weber River Valley and

igure 1. Aerial photo of Hill Air Force Base. The study area is inperable Unit 2 in the northeast section of the base near the Weberanal. Dashed line marks the boundary of the base. Inset shows lo-ation of base in northeastern Utah between the Wasatch Range andhe Great Salt Lake.

ests on deltaic sediments of the Provo Formation, composed prima-ily of sand and gravel. The Provo Formation was deposited as sheet-ood lobes, braided channels, sieve deposits, and debris flow on aave-reworked lacustrine fan delta �Curry, 1980�. The Weber delta

hanged locations many times, leading to the deposition of laterallyeterogeneous sands and gravels �Feth, 1955�. Beneath the Provoormation, which ranges in thickness from 2–15 m, lies the Alpineormation, composed primarily of clay and silt and also a product ofeber delta deposition during the Pleistocene. The Alpine Forma-

ion is at least 17 m thick, and Cambrian basement lies beneath it.HAFB has been active since the early 1940s and covers 27 km2

Figure 1�. For about 20 years, liquid degreasing solvents and jetuel were deposited as waste into the ground at various sites locatedt the outer edges of the base. These sites include landfills, disposalits, and spill areas. HAFB began investigating releases in 1976hen a civilian reported an orange discharge from a spring on hisroperty near the base boundary �Environmental ProtectionAgency,002�.As a result, theAir Force, Utah Department of Environmentaluality, and EPA began investigating and cleaning up the contami-ation. The EPA placed HAFB on the Superfund National Prioritiesist on July 22, 1987.

Site OU2 is located on the northeastern boundary of HAFB andas used from 1967 to 1975 to dispose unknown quantities of sol-ents into at least two unlined disposal trenches. The disposal pro-ess resulted in groundwater contamination from trichloroetheneTCE�, trichloroethane �TCA�, and tetrachloroethylene �PCE� �Ool-an et al., 1995�. These solvents are DNAPLs because they are im-iscible with water and have a higher density than water. During

ertical migration, DNAPLs may be captured by capillary forces inhe aquifer’s pore space, but most of the substance will sink until itomes in contact with a low-permeability surface, resulting in theormation of DNAPL pools at the bottom of the aquifer. More than00 monitoring wells drilled as part of the remediation efforts atU2 have shown that pools of DNAPL lie at the base of the Provoormation at depths of 10–15 m �Hirasaki et al., 1997�. The underly-

ng Alpine Formation functions as an impermeable boundary to theNAPLand the shallowest water table at approximately 9–10 m be-

ow the surface.Accurate characterization of the top of theAlpine Formation is in-

egral for remediation efforts because the DNAPL tends to pond inhe topographic lows at the top of the clay surface. The depth to thelay surface was recorded at 267 monitoring wells at OU2, of which41 are within the 95�40 m area of the 3D refraction survey. The to-ography of the clay surface determined from the well data led to theiscovery of a paleochannel incised into the clay, trending roughlyorth to south �Figure 2�. At OU1, 1.3 km southeast of OU2, Youngnd Sun �1996, 1998� used ground penetrating radar �GPR� to imagehe top of the clay, although the presence of clay strongly attenuatedhe GPR signal. Nevertheless, their results clearly demonstrate thetrong heterogeneity of the local geology.

3D EXPERIMENT AND DATA

In 2000, a team of about 20 people led by personnel from the De-artment of Earth Science at Rice University conducted a series ofeismic experiments at OU2, including a 3D refraction survey, 3Deflection survey �Dana et al., 2001; Gao et al., 2004�, and combinedual vertical seismic profile/surface experiment �Gao et al., 2006�.he 3D refraction and reflection experiments both occupied an areaf roughly 95�40 m, centered over a portion of the buried pale-

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channel �Figure 2�. The seismic experiments were surveyed using aopcon Total Station unit, providing location accuracy of better than0 cm. The ground surface is fairly smooth, with a gradual increasen elevation to the south and a total relief of about 2.5 m. The averagelevation is nearly 1 m above the survey datum, which correspondso 1430 m above sea level; this datum is zero in our models.

The 3D refraction survey geometry consists of a single deploy-ent of 601 receivers in a stationary grid, each receiver consisting ofsingle-channel RefTek 125 Texan recorder attached to a 40-Hzark Products vertical geophone �Figure 2�. There are 45 east-west

ines consisting of alternating rows of 13 and 14 geophones with annline receiver interval of 2.8 m. The crossline spacing is 2.1 m,ith each line staggered by 1.4 m relative to the adjacent line. To-ard the southern end of the survey, the lines sys-

ematically shift to the east, ending roughly 7 mast of the lines in the north �Figure 2�. The shotocations are 0.3 m east of each receiver station.

single shot from a .223-caliber rifle was firednto a 6-cm-deep hole drilled into the ground be-ide each receiver. Because of onsite obstaclesuch as propane tanks and trailers, 48 shot or re-eiver stations deviate slightly from the standardeometry and seven stations have no shots or re-eivers, while no shots were fired at an additionalve stations. There were 596 shots, yieldingbout 360,000 traces and a maximum source-re-eiver offset of 102 m. To our knowledge, this ishe most dense 3D refraction experiment in termsf the number of shots and receivers ��600ach�.

The data were recorded using a 1-ms sampleate and contain frequencies ranging from about0–250 Hz �Figure 3�. The dominant frequencyaries from 40 to 80 Hz. The data were pro-essed minimally using only a 40–80–240–400Hz band-pass filter and notch filters of 60 and20 Hz to remove ground roll, low-frequencyultural noise, and noise from onsite electricalquipment. After filtering, the dominant frequen-y of the data is near 75 Hz �Figures 3 and 4�. Theirwave obscures refracted energy at offsets lesshan about 12 m because the seismic velocity ofir ��330 m/s� is faster than the seismic velocityf the near surface �Dana et al., 1999�. Despiteltering, the data contain significant noise from. S.Air Force jets and remediation activities, in-

luding pumps in monitoring, injection, and ex-raction wells.

A 3D reflection experiment was carried outver the same area as the refraction experimentsing the same east-west recording lines and rifleource as the refraction survey �Dana et al., 2001;ao et al., 2004�. The survey took 16 days to

omplete, compared to two days for the refractionurvey, and produced a nominal fold of 52. Theeflection survey took more time because it in-olved many more shots and a rolling geophonerray, as compared to a static array for the refrac-ion survey.Acomparison of the 3D refraction ve-ocity model with a 3D depth-migrated common-

Figure 2. Expclay from weltraveltimes wThere is some

idpoint �CMP� stack, and the results of 2D waveform inversion ofhe reflection data are presented later.

raveltime picking and uncertainties

A semiautomated interactive picking program was used to pickhe first arrivals of the 360,000 traces. A total of 187,877 picks from49 shots were made; the remaining 40% of the shots were not pick-ble because of noise �Figure 2�. Traveltimes were picked from shotathers plotted versus offset in 12° azimuth bins �Figure 4�. The binperture is a compromise between minimizing the variability inrst-arrival time at different azimuths as a result of 3D structure andaximizing the number of traces. About every tenth trace was

tal geometry of 3D refraction survey superimposed on the depth toWhite xs are shot locations. Green circles indicate shots for whichked. Black dots are receiver stations. Pink dots are well locations.g of the depths to emphasize the paleochannel structure.

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icked manually, and an automatic picker was applied to the inter-ening traces using the crosscorrelation between the unpicked tracesnd the two adjacent picked traces.

igure 3. Frequency spectrum for a typical raw �dashed� and filteredsolid� shot gather using a filter with notches at 60 and 120 Hz and a0-80-240-400-Hz band-pass. The spectra have been normalized tohe same peak value.

igure 4. Data examples. The traces for three shot gathers are plottedersus source-receiver offset within a 12° azimuth bin. Plot of theurvey geometry to the right of each gather shows the shot locationlarge dot� and the trace aperture window. The data are shown traceormalized and filtered as described in Figure 3. First-arrival picksre indicated by horizontal marks on each trace.

The uniform areal distribution of shots and receivers over the sur-ey area has the advantage of providing uniform illumination of theubsurface but the disadvantage of spatial aliasing in both the inlinend crossline direction. Results from a 2D pilot survey at OU2 using

0.35-m receiver spacing clearly show that the near-offset�12 m� refracted P-wave is slower than the airwave �Dana et al.,999�. However, it generally is impossible to distinguish the refract-d arrival from the airwave in the 3D data because of the coarser re-eiver spacing �2.8 m inline and 2.1 m crossline�. Therefore, therst-arriving energy, interpreted to be an amalgamation of the air-ave and refracted wave, was picked and regarded as a body wave.he effect this has on the final model is addressed later. Only about0% of the picks are in this near-offset region ��12 m; Figure 5a�he target of the survey, the paleochannel, is up to 15 m below theurface �Figure 2�. For refracted waves to sample to this depth, ainimum offset of 25 m is required, based on the results of the 2D

ilot survey �Dana et al., 1999�. About 67% of the picks have an off-et greater than 25 m, providing confidence that the paleochannel isampled adequately by the data.

The dominant frequency of the filtered data is roughly 75 Hz, cor-esponding to a quarter-period of 3.3 ms.Arule of thumb for pickingccuracy is that an arrival can be identified at best to within one-uarter of the dominant period because if two waves arrive withinhis interval, they will add constructively and cannot be distin-uished from one another. Picking accuracy is further degraded byhe presence of noise. To estimate the total pick uncertainty, the timeifference of the picks from reciprocal source-receiver pairs was ex-mined �Figure 5b�. About 56% of the reciprocal pairs are withinms, and 86% are within 10 ms. Considering the frequency content

f the data and the reciprocal differences, picks were assigned an un-ertainty of 5 ms for traveltime inversion.

igure 5. �a� Histogram of number of traveltime picks versus source-eceiver offset in 2.1-m bins. �b� Histogram of number of shot-re-eiver pairs versus reciprocal time difference in 1-ms bins.

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3D REFRACTION TOMOGRAPHY

We use the 3D first-arrival regularized tomographic method ofelt and Barton �1998� in which the simplest model is sought thatredicts the picked traveltimes to within an accuracy consistent withheir assigned uncertainties. This algorithm is designed to yield a

odel with the minimum amount of structure required by the data.raveltime inversion is a nonlinear problem because the raypaths areependent on the velocity model. Therefore, a linearized iterativepproach is applied using a Taylor series expansion in which a start-ng model is required and the model and raypaths are updated over aeries of iterations until the normalized misfit �2 between the ob-erved and predicted data ideally reaches one �Bevington, 1969�:

�2 =1

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p are the ith observednd predicted traveltime, and �i is the assigned picking uncertainty.

At each iteration, an objective function �, which measures a com-ination of the data misfit and the structure of the model, is mini-ized in the least-squares sense �Menke 1989�:

��s� = � tTCd−1� t + ����sTWh

TWhs + sz sTWvTWv s�

+ �1 − ��� sTWpTWp� s� , �2�

here � t is the traveltime misfit vector, s is the model slowness vec-or, � s is the perturbed model vector equal to s − so, so is the starting

odel vector, Cd is the data covariance matrix that contains the esti-ated pick uncertainties, Wp is the perturbation weighting matrix,

nd Wh and Wv are the horizontal and vertical roughness matrices,espectively. The perturbation weighting matrix is a diagonal matrixontaining the reciprocal of the starting slowness values; it measureshe relative perturbation of the current model from the starting mod-l. The roughness matrices are second-order spatial finite-differenceperators that measure the roughness of the model in the horizontalnd vertical directions. These operators are normalized also by thetarting slowness value at the center of the operator �Zelt and Barton,998�.

The parameters �, �, and sz control the weight of the terms in thebjective function. The parameter � determines the overall amountf regularization and is not strictly free, in that it is reduced systemat-cally by the algorithm from a free-parameter starting value �o. Theystematic reduction of � with each iteration by a factor �r stabilizeshe inversion by constraining the long-wavelength model structuren the initial iterations and by allowing finer model structure in laterterations. The parameter � determines the relative weight of the sec-nd derivative and perturbation regularization; perturbation regular-zation is not part of the original Zelt and Barton �1998� algorithm,quivalent to using an � value of one. The value sz governs the rela-ive weight of the vertical and horizontal smoothing regularization.he final free parameter is the number of iterations of the conjugateradient algorithm Nlsq, used to solve the large sparse system of lin-ar equations at each iteration �Zelt and Barton, 1998�. The free-pa-ameter values were varied to facilitate a systematic exploration ofhe model space to determine the simplest and most geologically rea-onable model that fits the data.

The model parameterization for the forward calculation of travel-imes and raypaths is a uniform 1-m node spacing. The 3D finite-dif-erence eikonal solver of Vidale �1990�, with modifications for large

elocity gradients by Hole and Zelt �1995�, is used. For the inversetep, the model is divided into cells of constant slowness. The cellize is chosen to balance the trade-off between increased resolutionsing smaller cells and increased constraint on the slowness valuessing larger cells. In practice, the largest cell size is used that allowshe data to be fit within their uncertainties according to equation 1.Aell size of 2�2�1 m in the x-, y-, and z-directions, respectively, issed. The model dimensions are 60 � 110 � 28 m, resulting in6,200 cells.

tarting model

The study area consists of two sedimentary formations. The sur-ace layer, the Provo Formation, is comprised primarily of sand andravel, while the buried Alpine Formation is primarily clay. Fromhe well data, we know the clay top is at 2–15 m depth and is incisedy a paleochannel �Figure 2�; the water table is at 9–10 m depth.wo wells separated by 1.8 m show a difference in clay depth of1.7 m. The true velocity field is therefore expected to be laterallynd vertically complex. The only prior information concerning 3Dtructure is the depth to clay from the well data, but this is what weant to determine using the seismic data. Therefore, we use 1D start-

ng models as a test of 3D refraction tomography in a complex near-urface environment.

Three different starting models were tested �Figure 6�. Becausehe airwave obscures the refracted wave in the near-offset region, wenow the seismic velocity at the surface is less than the velocity of air

nearly 330 m/s. Based on the results of the 2D pilot survey �Danat al. 1999�, a surface velocity of about 200 m/s is used for eachodel �Figure 6�. The velocity increases rapidly with depth in eachodel and approaches the seismic velocity of water to account for

he water table at 9–10 m. Each starting model increases with differ-

igure 6. Three 1D starting models. ModelAis preferred. Model B islower than the model A from 0–9 m. Model C is faster than theodelAfrom 0–13 m.

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nt gradients in depth until about 12 m depth, where they converget roughly 1400 m/s and then slowly increase to slightly more than600 m/s at 25 m depth. Starting modelAis constructed by laterallyveraging the 3D final models from some preliminary inversions ofhe data. Starting models B and C are designed to test the sensitivityf the results using slower and faster models, respectively.

RESULTS

The preferred final model was determined after numerous inver-ions using the three starting models and a range of free-parameteralues. In this way, model nonuniqueness was explored, in that dif-erent models were obtained that fit the data similarly according toquation 1. The preferred final model was selected in accordanceith Occam’s principle of minimum structure �e.g., Constable et al.,987� to avoid overinterpreting the data. Starting modelA �Figure 6�as used to produce the final preferred model. The starting rms trav-

ltime misfit is 9.25 ms ��2 = 3.42�, and the misfit provided by thereferred final model after eight iterations is 5.39 ms ��2 = 1.16�Figure 7�. We could not achieve �2 = 1, probably because of theumber of reciprocal time differences greater than 5 ms �Figure 5b�.he preferred free-parameter values are �o = 5000, �r = 1.317, �1.0, sz = 0.4, and Nlsq = 250.Figure 8a shows horizontal slices of the difference between the

referred final model and the starting model. A coherent low-veloci-y anomaly that trends roughly north-south is evident in each slice.he anomaly curves slightly eastward in the north, where it reaches

ts largest value of around 250 m/s perturbation from the startingodel and widens to cover almost the full width of the model. It dis-

ppears south of about y = 80 m. The anomaly increases in coher-nce and magnitude until 12 m depth; it loses coherence belowhis. It shows considerable lateral variation, notably in the x-irection, where it can change by more than 300 m/s in roughly5 m. The shape of the low-velocity anomaly is generally consistentith the paleochannel from the well data.

igure 7. Traveltime residuals for the preferred starting model andreferred final model as a function of source-receiver offset. The rmsraveltime misfit for the starting and final models is 9.25 ms ��2

3.42� and 5.39 ms ��2 = 1.16�, respectively.

Figure 9 shows east-west cross sections through the preferred fi-al model. There is considerable heterogeneity in the upper 4 m ofhe model. Below 4 m, the model is generally smoother without anyharp features, and the isovelocity contours take the form of a broadepression, with the center roughly in agreement with the center ofhe paleochannel from the well data; this is the prominent north-outh low-velocity anomaly seen in the horizontal slices.

odel assessment

To assess the robustness of the preferred final model, we have ap-lied a number of tests and examined the ray coverage.

ay coverage

Ray coverage is a rough indicator of how well the model is con-trained at a particular point �Figures 8b and 10�. Ray coverage is aaximum between 8 and 12 m depth, with the deepest rays reaching

early 21 m. Ray coverage is concentrated toward the eastern side ofhe model between x values of 0–15 m and y values of 20–90 m.ays are concentrated on the east because of the velocity structure,

.e., avoiding the low-velocity paleochannel, and also because theurvey geometry shifts to the east at the southern end of the studyrea �Figure 1�.

lternative starting models

Figure 11 shows a slice at z = 10 m from the preferred final modeln comparison with eight alternative final models. The normalized

isfits for the final models obtained from starting models B and Cere both 1.17, essentially the same fit as the preferred final model

�2 = 1.16�. Both alternative final models show a north-south-trend-ng low-velocity anomaly similar to the preferred final model. Shal-ower depth slices through the models obtained using starting mod-ls B and C show consistently faster and slower perturbations, re-pectively, compared to the preferred final model at the same depth.his indicates starting model B is biased slow and starting model C

s biased fast. However, the absolute velocities in these alternativeodels are very similar to the preferred final model, illustrating the

obustness of the tomographic technique to biased starting models.

ree parameters

The alternative final models shown in Figure 11 are obtained byarying the free-parameter values to �o = 10,000, �r = 1.414, �0.95, sz = 0.3, and Nlsq = 325. For these runs, the preferred start-

ng modelAwas used and all free parameter values were the same asor the preferred final model, except for the one being varied. Theve final models provide normalized misfits of 1.06–1.19. Theseodels contain the north-south-trending low-velocity anomaly, al-

hough they are generally rougher than the preferred model. The ex-eption to this is the model obtained using sz = 0.3, which is smooth-r than the preferred final model in this horizontal slice but is roughern the vertical direction, as expected using a smaller value of sz thanhat used for the preferred final model. Increasing sz from 0.3 to 0.4dded little horizontal roughness but significantly decreased verticaloughness. Increasing sz from 0.4 to 0.5 did not substantially smoothhe model vertically but increased horizontal roughness, leading tohe preferred sz value of 0.4. All of the models obtained by varyinghe free parameters are viable because they similarly fit the data ac-ording to equation 1, but the preferred final model was the smooth-st.

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ear-offset picks

Because refracted body waves were not distinguished confidentlyrom the airwave in the near-offset region and because the near-off-et picks predominantly influence the shallow part of the model,here is some question as to how the near-offset picks might affecthe deeper structure of the model. An inversion was run in which ve-ocities above 3 m were laterally homogeneousnd fixed at the preferred starting model values;hese values are based on the results of a 2D piloturvey in which refracted arrivals were identifiedn the near-offset region behind the airwave. Theorth-south-trending low-velocity anomaly isresent in the final model �Figure 11i�, althoughhe magnitude of the variations are about 100 m/sreater than the preferred model at this depth andhe model is rougher than the preferred final mod-l at all depths below 3 m. The normalized misfitf 1.21 for this model is the poorest of any of thelternative final models, although this is, in part,rom the inability to fit the near-offset picks close-y because the shallow portion of the model isxed.

ateral resolution

We have estimated the lateral resolution of thereferred final model using Zelt’s method �1998�,hich has been used in a number of 3D refraction

tudies �e.g., Day et al., 2001; Zelt et al., 2001;organ et al., 2002�. The method consists of a se-

ies of checkerboard tests using the source-re-eiver geometry of the picked data. The preferredtarting model and preferred free-parameter val-es are used, and Gaussian noise is added to theynthetic data using a standard deviation equal tohe assigned picking uncertainty, 5 ms. Fivenomaly sizes were tested: 5, 7.5, 10, 15, and0 m �Figure 12�. Velocity anomalies of 35% en-ured the initial misfits were similar to the initialisfit of the real data for the preferred startingodel. The semblance between the recovered

nomaly pattern and the true anomaly pattern wasalculated at each model node. A semblance val-e of 0.7 is the threshold for good resolution at theength scale of the anomaly size �Zelt, 1998�.

At z = 10 m, much of the central part of theodel has a lateral resolution of at least 7.5 m,

nd most of the model at this depth has a resolu-ion of at least 10 m �Figure 12�. Zelt’s method1998� determines the lateral resolution of theodel by estimating the anomaly size that would

ield a semblance of 0.7 at each model node �Fig-re 8c�. Resolution exceeds 7.5 m throughoutost of the model down to 10 m depth. Resolu-

ion at the 10-m length scale includes most of theodel to 12 m depth and the central part of theodel down to 14 m.

Figure 8. �a� Pstarting modethe well data100 m/s. Unsthrough each m200 rays. Unsthe depth slicegions have beare unsampled

DISCUSSION

The geology at OU2 consists of heterogeneous unconsolidatedediments above a predominantly clay formation with an incised pa-eochannel. Large changes in velocity occur over short distancesoth laterally and vertically, based on extensive well data and a 2Dilot study �Dana et al., 1999�. The final velocity model increasesapidly with depth, from approximately 200 m/s at the surface to500 m/s at 12–15 m depth �Figure 9�. The model is more heteroge-

d final model displayed as perturbations with respect to the preferredpths from 6–14 m as labeled. Depth to clay contours �in green� from11 m overlay the 8- and 10-m slices. Black contour interval isregions at the edges are white. �b� The number of rays that pass

ell corresponding to the depth slices in �a�. Black contour interval isregions are white. �c� Lateral velocity resolution corresponding to

�. The 7.5-m contour is white; the 10-m contour is black. Black re-n 5 m resolution; white regions have worse than 20 m resolution or

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eous in the upper 4 m, likely a reflection of the complexity of thenconsolidated near-surface sediments and consistent with higher-esolution waveform inversion results �Gao et al., 2006; Gao et al.,004�. The model becomes significantly smoother below 4 m, withhe isovelocity contours taking a generally concave-up shape andith the deepest point being 2–3 m lower than at the edges of theodel. The deepest points generally coincide with the incised pale-

channel as defined by the well data, although the channel in the re-raction model, is smoother than the well data indicate �Figure 9�.he vertical cross sections suggest the velocity, in a very smooth

igure 9. East-west cross sections through the preferred final modelt y-positions as labeled. The clay layer from the well data overlayshe model in white. Arrow indicates known water table at 9–10 m.ontour interval is 100 m/s; thick contour is 1000 m/s. Unsampled

egions are white.

ay, is consistent with the known geology and site conditions. Theow velocities of the sand-gravel Provo Formation overlie the high-r-velocity clay Alpine Formation, which has a nearly 10-m-deeporth-south-trending trough in its top, forming the paleochannel,nd a water table at 9–10 m depth.

The water table may reduce the velocity anomaly that would oth-rwise be associated with the paleochannel below 9–10 m and couldherefore, at least in part, explain the very smooth nature of the deeportion of our model. It is typical for the saturated zone to be shal-ower in clay than in sand because of capillary forces, and the transi-ion in clay occurs over a broader interval. Therefore, we would ex-ect the water table to follow the shape of the channel, although itill be smoothed laterally and to a lesser extent vertically. Also,

ince saturated clay is typically a bit slower than saturated sand, thease of the channel may correspond to a velocity decrease. In anyvent, the deep velocity structure is likely the result of a combinationf lithology and water saturation, which is greatly smoothed out inhe model from the resolution of the data.

The horizontal slices of the velocity perturbations are dominatedy a north-south-trending low-velocity anomaly that curves slightlyo the northeast in the north �Figure 8a�. The anomaly increases inrea and velocity fluctuation with depth, peaking between 10 and2 m depth and then diminishing and losing continuity below this.he anomaly at 10–12-m depth ranges from the edge of the model in

he north to about y = 80 m in the south and roughly narrows inidth from about 30 m to 10 m over this distance.As discussed, the

nomaly is well resolved, with a lateral resolution at 10–12 m depthetter than 10 m throughout most of the model and better than 7.5 mhrough much of it �Figure 8c�. The outline of the low-velocity

igure 10. Raypaths through the preferred final model projected intohe x-y and y-z planes. For clarity, every 200th raypath is shown.

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nomaly is consistent with the general shape of the paleochannelrom the well data �Figure 8a�, suggesting the paleochannel incisednto the clay layer influences the long-wavelength velocity structure.t a given depth, the velocities are generally higher at the south endf the model than at the north �Figure 8a�, perhaps because the sur-

igure 11. The preferred final model and eight alternative final mod-ls at 10 m depth, displayed as perturbations with respect to the start-ng model. The reference velocity at this depth in the preferred start-ng model is 1150 m/s. The preferred final model is in the center; thether models are obtained using �a� starting model B, �b� startingodel C, �c, e� �o = 10 000, �d� �r = 1.4142, �f� � = 0.95, �g� sz

0.3, �h� Nlsq = 325, and �i� model above 3 m fixed at starting-mod-l values �see text for details�. The preferred starting model �e� isroduced using starting model A in Figure 6 and free-parameter val-es �o = 5000, �r = 1.3173, � = 1.00, sz = 0.4, and Nlsq = 250.lack contour interval is 100 m/s. Depth-to-clay contours �green�

rom the well data for 7–11 m overlay the models. White edges arensampled regions.

ace elevation is roughly 1 m higher in the south, resulting in greateronsolidation and higher velocities.

resnel zones

The size of the first Fresnel zone and the picking uncertainty pro-ide insight into the smoothness of the final model because they areelated to the spatial resolution. For first-arrival traveltime tomogra-hy, the Fresnel zone is the volume within which any scattered waveill arrive within one-quarter period of the dominant frequency of

he first arrival — roughly 3.3 ms for these data.As a result, any het-rogeneity within the Fresnel zone is averaged, although overlap-ing Fresnel zones from different source-receiver pairs makes it pos-ible for traveltimes to resolve details that are nearly 60% of theresnel zone’s dimensions �Pratt et al., 2002�. Ray-theoreticalresnel zones are calculated by summing the first-arrival-time fieldsrom the source and receiver points and by contouring the traveltimeorresponding to the first-arrival time between the two points, plusne-quarter of the dominant period. The volume within the contourorresponds to the first Fresnel zone because it represents all subsur-ace points from which scattered energy between the source and re-eiver will arrive within one-quarter period of the first arrival.

Consider four representative Fresnel zones for refracted raypathshrough the final model with offsets of 15, 30, 60, and 90 m that bot-om above, within, and beneath the paleochannel �Figure 13�. Thereater heterogeneity in the upper 4 m of the model �Figure 9� coulde a good representation of the true structure, given the more local-zed shape of the Fresnel zones in the upper 4 m, although contami-ation of the short-offset first arrivals by the airwave for this experi-ent must be factored in. The results of the checkerboard tests indi-

ate lateral resolution exceeds 5 m in the upper 5 m throughout mostf the model.

igure 12. Recovered checkerboard anomaly patterns �top row� andorresponding semblance values �bottom row� at z = 10 m for theve anomaly sizes: 5, 7.5, 10, 15, and 20 m. The boundaries of the

rue checkerboard pattern overlay the recovered perturbations. In theemblance plots, the contour interval is 0.1; the 0.7 contour is white.

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The Fresnel zones are thickest and broadest approximately half-ay between the source and receiver, where they are as much as5–20 m vertically and 15–30 m horizontally for raypaths that sam-le the paleochannel. Although large, the overlapping Fresnel zonest the target depth of about 10 m, arising from many different

igure 13. Comparison of first Fresnel zones in the final model for aenter frequency of 75 Hz and source-receiver offsets of 15, 30, 60,nd 90 m. �top� Vertical cross section through the Fresnel zones at x0 m. �bottom� Horizontal cross sections at 4, 10, and 16 m depth.

he 10-m depth-to-clay contour from the well data overlays the 10m cross section in gray.

igure 14. �a� Horizontal slice of the preferred velocity model per-urbations at 10 m depth. �b� Depth to the 800-m/s isovelocity sur-ace from 2D full waveform inversion of the 45 east-west 2D reflec-ions lines �Gao et al., 2004�. �c� Horizontal slice of the poststack 3Depth-migrated reflectivity from the reflection data at 10 m depthFradelizio et al., 2004�. The 7- and 10-m depth-to-clay contoursrom the well data are labeled. White edges are unsampled regions.

ource-receiver pairs, make it possible to resolve lateral variations inhe paleochannel on a length scale consistent with the resolution de-ived from the checkerboard tests �Figure 8c�. However, for verticalesolution at the target depth �approximately 10 m�, every Fresnelone with an offset of 25–40 m that bottoms near the target depthill average the structure over the entire depth range of interest.As a

esult, the traveltime data will only sense a very smooth vertical gra-ient. It is not possible to determine from the traveltime data whetherhe final model accurately describes a smooth velocity increase at thelay contact or the water table or whether a sharp velocity contrastxists but is smoothed out because of the size of the Fresnel zones.hus, it is prudent to refrain from viewing the velocity values in thenal model as localized point measurements. Regardless of the in-bility to determine the precise nature of the velocity increase result-ng from a change in lithology or the water table, the lateral geometryf the paleochannel is resolved within the final model at a lengthcale of 7.5–10 m. We estimate that a dominant frequency of ap-roximately 200 Hz and a picking error of about 2 ms would be re-uired to infer anything about the nature of the clay contact or theater table.

omparison with reflection data andaveform inversion

Figure 14 compares a slice at z = 10 m from the preferred finalodel with results from waveform inversion of the 2D reflection

ata along each east-west line and a migrated stack of the 3D reflec-ion data. The waveform result is presented in the form of depth tohe 800-m/s velocity contour, interpreted by �Gao et al., 2004� to behe clay top. The 3D reflection data are presented as a depth slice at0 m from a poststack 3D depth-migrated volume �Fradelizio et al.,004�. Although the waveform isovelocity surface shows artifactselated to contouring the results from independent 2D inversions ofhe 45 east-west lines, the paleochannel is clearly defined from–11 m depth, in good agreement with the well data. The 3D reflec-ion data show generally enhanced reflectivity within the channel asefined by the well data, although this reflectivity fades out betweenbout y = 30 and y = 40 m. In the north, all three images show thehannel curving to the east. This is where the strongest anomaly is inhe traveltime model, the deepest point is in the waveform surface,nd the largest patch of enhanced reflectivity is in the reflection im-ge. South of about y = 80 m, the results are inconsistent. The low-elocity anomaly disappears in the preferred traveltime model; thehannel defined by waveform inversion is generally consistent withhe well data, and the high reflectivity is shifted east of the channel asefined by the well data. South of y = 80 m is an area where the al-ernative models show considerable variation �see models 4 and 8,igure 11, d, i�. This is not surprising, given the relatively poor reso-

ution at the south end of the model �Figure 8c�.The generally favorable comparison of the 3D velocity model

ith the waveform and reflection results lends credibility to the in-erpretation of the north-south low-velocity anomaly being an ex-ression of the topography on the clay surface and the low-velocityediments within the paleochannel. The waveform and reflection re-ults have higher resolution than the traveltime result, as expected,ut all three methods image the channel structure in close agreementith the well data. We estimate that the amount of experiment, com-uter, and human time necessary to produce the refraction model is aactor of 5–10 less than the time to produce the other two results.

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CONCLUSIONS

The 3D seismic refraction experiment at HAFB and the applica-ion of 3D first-arrival-time tomography were a feasibility study forhallow seismic investigations at environmental remediation sites.maging the velocity structure of the near-surface environment pro-ides encouraging results, despite less-than-ideal seismic data re-ulting from airwave contamination, onsite noise from ongoing re-ediation activities, and a relatively low dominant frequency for

uch a shallow target.Regularized first-arrival-time tomography obtained a minimum-

tructure velocity model that outlines the shape of the low-velocityll in the paleochannel at the top of the clay formation. The north-outh low-velocity structure appears to mimic the paleochannel asetermined from over 100 wells, generally consistent with the re-ults of waveform inversion and 3D poststack depth migration of theeflection data. The low-velocity anomaly may represent the shapef the paleochannel accurately at length scales of about 10 m, ac-ording to checkerboard tests and considering the Fresnel zones.

The results suggest that first-arrival traveltime tomography canonstrain the long-wavelength features of a rapidly changing, near-urface heterogeneous environment. A higher center frequency inhe data would have meant smaller Fresnel zones and, along with aetter S/N ratio, a smaller picking error, which in turn would haveustified a closer fit to the data, increasing model resolution. In anyhallow seismic study, the center frequency is dictated by site condi-ions and the need to propagate energy to and from the target. In com-arison to the 3D seismic reflection method, the seismic refractionethod was relatively simple, quick, and inexpensive. In addition,

he analysis and interpretation of refraction data is potentially lessubjective than conventional reflection processing. There is minimalata processing and objective arrival picking, assuming low noise,nd solving for a minimum-structure model minimizes the subjec-ivity of the interpretation. Compared to waveform inversion, travel-ime inversion is robust, even in the presence of considerable noiser spatial aliasing. Finally, the velocity model obtained by first-ar-ival-time tomography can be used as a starting model for waveformnversion and as an independent check on the images obtained fromrocessing reflection data.

ACKNOWLEDGMENTS

Hans Meinardus of Duke Power acted as our liaison with HAFB,nd Jon Ginn at HAFB made possible our access to OU2. We thankhe volunteer field crew members from nine countries for their greateamwork. D. Dana and I. Morozov helped to prepare the data fornalysis. G. Fradelizio and F. Gao provided figures from their work.omments by the associate editor �J. Bradford� and five anonymous

eviewers were very helpful. GMT �Wessel and Smith, 1998� wassed to produce some of the figures. IRIS/PASSCAL provided theeismic recording instruments and field support. This research wasunded by DOE grant DE-FG07-97ER14827.

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