3D Seismic Refraction


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3D Seismic Refraction

  1. 1. 3D seismic refraction traveltime tomography at a groundwater contamination site Colin A. Zelt1 , Aron Azaria2 , and Alan Levander1 ABSTRACT We have applied traveltime tomography to 3D seismic re- fraction data collected at Hill Air Force Base, Utah, in an ap- proximately 95 ϫ 40-m area over a shallow ͑Ͻ 20 m͒ groundwater contamination site. The purpose of this study is to test the ability of 3D first-arrival-time data to characterize the shallow environment and aid remediation efforts. The aquifer is bounded below by a clay aquiclude, into which a paleochannel has been incised and acts as a trap for dense nonaqueous phase liquid ͑DNAPL͒ contaminants.Aregular- ized nonlinear tomographic approach was applied to 187,877 first-arrival traveltimes to obtain the smoothest minimum- structure 3D velocity model. The resulting velocity model contains a velocity increase from less than 300 to 1500 m/s in the upper 15 m. The model also contains a north-south- trendinglow-velocityfeatureinterpretedtobethepaleochan- nel, based on more than 100 wells in the area. Checkerboard tests show 7.5–10 m lateral resolution throughout most of the model. The preferred final model was chosen after a systematic test 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 migration and 2D waveform inversion of coincident reflection data. While the long-wavelength features of the model reveal the primary target of the survey, the paleochannel, the velocity model is likely a very smooth characterization of the true ve- locity structure, particularly in the vertical direction, given the size of the first Fresnel zone for these data. INTRODUCTION More than 20% of the earth’s freshwater is beneath the land sur- face ͑Dunne and Leopold, 1978͒, and much of the world’s popula- tion relies on groundwater reservoirs for drinking water and agricul- tural production. As populations increase and economies grow, the potential for groundwater contamination rises, with the result that groundwater contamination has emerged as a major environmental problem in many countries. In the United States, this situation has led to expensive groundwater cleanup, groundwater protection laws, and environmental protection programs ͑Moore and Jones, 1987͒. The U. S. Environmental Protection Agency ͑EPA͒ has identified morethan1200contaminatedareasthatqualifyforSuperfundclean- up funding ͑Moore et al., 1995͒. In 1987, the EPAlisted HillAir Force Base ͑HAFB͒, Utah ͑Figure 1͒, as a Superfund site and targeted 11 areas on the site for remedia- tion ͑Environmental ProtectionAgency, 2002͒. Much of the contam- ination consists of chlorinated solvents used to clean industrial prod- ucts, such as jet engines. At Operable Unit 2 ͑OU2͒ ͑Figure 1͒, the solvents — dense nonaqueous phase liquids ͑DNAPLs͒ — descend- ed into a shallow aquifer comprised mostly of unconsolidated sand and gravel. The aquifer is bounded below by an impermeable, pre- dominantly clay formation that prevents the solvents from moving deeper underground. The remediation at OU2 has been ongoing for more than 10 years and has consisted mainly of surfactant/foam pro- cesses to extract both the contaminants and the contaminated water ͑Hirasaki et al., 1997; Meinardus et al., 2002͒. More than 200 wells have been drilled as part of the remediation process.These wells pro- vide point control on the depth to the impermeable clay formation that bounds the aquifer from below. In August 2000, personnel from the Department of Earth Science at Rice University conducted a series of seismic surveys over the contaminated aquifer at OU2, funded by the U. S. Department of En- ergy ͑Dana et al., 2001; Gao et al., 2004; Gao et al., 2006͒. The seis- mic experiment that is the subject of this paper is a 3D refraction sur- vey covering an area roughly 95ϫ40 m. The application of 3D seismic methods to the shallow environ- ment is a relatively new field. Examples of near-surface 2D refrac- tion tomography studies include Lanz et al. ͑1998͒ and Morey and Schuster ͑1999͒. We derive a 3D P-wave velocity model to about Manuscript received by the Editor October 16, 2005; revised manuscript received February 28, 2006; published online September 5, 2006. 1 Rice University, Department of Earth Science, 6100 Main St., Houston,Texas 77251. E-mail: czelt@rice.edu; alan@rice.edu. 2 Formerly Rice University, Department of Earth Science, Houston, Texas; presently Compagnie Generale de Geophysique ͑CGG͒, Houston, Texas. E-mail: aronazaria@yahoo.com. © 2006 Society of Exploration Geophysicists.All rights reserved. GEOPHYSICS,VOL. 71, NO. 5 ͑SEPTEMBER-OCTOBER 2006͒; P. H67–H78, 14 FIGS. 10.1190/1.2258094 H67
  2. 2. 15 m depth by inverting first-arrival traveltimes using the regular- ized inversion algorithm of Zelt and Barton ͑1998͒. This algorithm typically has been applied to crustal-scale 3D data sets ͑e.g., Schlindwein et al., 2003; Ramachandran et al., 2004͒, although Deen and Gohl ͑2002͒ have used it in a mining application to ap- proximately 100 m depth. This is the first time the Zelt and Barton ͑1998͒ algorithm has been applied in three dimensions to the near- surface ͑Ͻ20 m͒ environment. Dana et al. ͑1999͒ have applied the Zelt and Barton algorithm to 2D data from a pilot survey at OU2 and imaged the known geology and a channel feature important to reme- diation efforts. The areal dimensions of the 3D study area are nearly 1000 times smaller than a typical crustal survey study area, but the center fre- quency is only about 10 times higher; the typical center frequency for crustal data is approximately 5 Hz. Therefore, a wave traveling the length of the model ͑100 m͒ consists of only 5–10 wavelengths at the center frequency. The relative change in velocity over a short distance is also very different from a crustal survey. From the 2D pi- lot study, we know that velocity increases by at least a factor of five in the upper 15 m ͑Dana et al., 1999͒ or a velocity gradient of ϳ80 s−1 , compared with a typical crustal velocity gradient of ϳ0.1 s−1 . Our study serves as a test of the 3D refraction method to characterize the shallow environment accurately and thereby to aid remediation efforts. The resulting 3D velocity model is compared to the known structure of the subsurface from well data and the results of other seismic surveys at the site. GEOLOGIC SETTING AND SITE CHARACTERIZATION HillAir Force Base is located 60 km north of Salt Lake City, Utah, west of the Wasatch Mountains and east of the Great Salt Lake ͑Fig- ure 1͒. The Great Salt Lake is a remnant of the ancient glacial Lake Bonneville, a large terminal lake that existed roughly 32,000– 14,000 years ago.TheWeber River delta, which supplied Lake Bon- neville, is between the Wasatch Mountains and the Great Salt Lake. It was formed during the Pleistocene epoch by the Weber River as it flowed into the eastern edge of Lake Bonneville ͑Curry, 1980͒. HAFB is built on a plateau west of the Weber River Valley and rests on deltaic sediments of the Provo Formation, composed prima- rily of sand and gravel.The Provo Formation was deposited as sheet- flood lobes, braided channels, sieve deposits, and debris flow on a wave-reworked lacustrine fan delta ͑Curry, 1980͒. The Weber delta changed locations many times, leading to the deposition of laterally heterogeneous sands and gravels ͑Feth, 1955͒. Beneath the Provo Formation, which ranges in thickness from 2–15 m, lies the Alpine Formation, composed primarily of clay and silt and also a product of Weber delta deposition during the Pleistocene. The Alpine Forma- tion 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 1͒. For about 20 years, liquid degreasing solvents and jet fuel were deposited as waste into the ground at various sites located at the outer edges of the base. These sites include landfills, disposal pits, and spill areas. HAFB began investigating releases in 1976 when a civilian reported an orange discharge from a spring on his property near the base boundary ͑Environmental ProtectionAgency, 2002͒.As a result, theAir Force, Utah Department of Environmental Quality, and EPA began investigating and cleaning up the contami- nation. The EPA placed HAFB on the Superfund National Priorities list on July 22, 1987. Site OU2 is located on the northeastern boundary of HAFB and was used from 1967 to 1975 to dispose unknown quantities of sol- vents into at least two unlined disposal trenches. The disposal pro- cess resulted in groundwater contamination from trichloroethene ͑TCE͒, trichloroethane ͑TCA͒, and tetrachloroethylene ͑PCE͒ ͑Ool- man et al., 1995͒. These solvents are DNAPLs because they are im- miscible with water and have a higher density than water. During vertical migration, DNAPLs may be captured by capillary forces in the aquifer’s pore space, but most of the substance will sink until it comes in contact with a low-permeability surface, resulting in the formation of DNAPL pools at the bottom of the aquifer. More than 200 monitoring wells drilled as part of the remediation efforts at OU2 have shown that pools of DNAPL lie at the base of the Provo Formation at depths of 10–15 m ͑Hirasaki et al., 1997͒.The underly- ing Alpine Formation functions as an impermeable boundary to the DNAPLand the shallowest water table at approximately 9–10 m be- low the surface. Accurate characterization of the top of theAlpine Formation is in- tegral for remediation efforts because the DNAPL tends to pond in the topographic lows at the top of the clay surface. The depth to the clay surface was recorded at 267 monitoring wells at OU2, of which 141 are within the 95ϫ40 m area of the 3D refraction survey.The to- pography of the clay surface determined from the well data led to the discovery of a paleochannel incised into the clay, trending roughly north to south ͑Figure 2͒.At OU1, 1.3 km southeast of OU2, Young and Sun ͑1996, 1998͒ used ground penetrating radar ͑GPR͒ to image the top of the clay, although the presence of clay strongly attenuated the GPR signal. Nevertheless, their results clearly demonstrate the strong heterogeneity of the local geology. 3D EXPERIMENT AND DATA In 2000, a team of about 20 people led by personnel from the De- partment of Earth Science at Rice University conducted a series of seismic experiments at OU2, including a 3D refraction survey, 3D reflection survey ͑Dana et al., 2001; Gao et al., 2004͒, and combined dual vertical seismic profile/surface experiment ͑Gao et al., 2006͒. The 3D refraction and reflection experiments both occupied an area of roughly 95ϫ40 m, centered over a portion of the buried pale- Figure 1. Aerial photo of Hill Air Force Base. The study area is in Operable Unit 2 in the northeast section of the base near the Weber Canal. Dashed line marks the boundary of the base. Inset shows lo- cation of base in northeastern Utah between the Wasatch Range and the Great Salt Lake. H68 Zelt et al.
  3. 3. ochannel ͑Figure 2͒.The seismic experiments were surveyed using a Topcon Total Station unit, providing location accuracy of better than 10 cm. The ground surface is fairly smooth, with a gradual increase in elevation to the south and a total relief of about 2.5 m.The average elevation is nearly 1 m above the survey datum, which corresponds to 1430 m above sea level; this datum is zero in our models. The 3D refraction survey geometry consists of a single deploy- ment of 601 receivers in a stationary grid, each receiver consisting of a single-channel RefTek 125 Texan recorder attached to a 40-Hz Mark Products vertical geophone ͑Figure 2͒. There are 45 east-west lines consisting of alternating rows of 13 and 14 geophones with an inline receiver interval of 2.8 m. The crossline spacing is 2.1 m, with each line staggered by 1.4 m relative to the adjacent line. To- ward the southern end of the survey, the lines sys- tematically shift to the east, ending roughly 7 m east of the lines in the north ͑Figure 2͒. The shot locations are 0.3 m east of each receiver station. A single shot from a .223-caliber rifle was fired into a 6-cm-deep hole drilled into the ground be- side each receiver. Because of onsite obstacles such as propane tanks and trailers, 48 shot or re- ceiver stations deviate slightly from the standard geometry and seven stations have no shots or re- ceivers, while no shots were fired at an additional five stations. There were 596 shots, yielding about 360,000 traces and a maximum source-re- ceiver offset of 102 m. To our knowledge, this is the most dense 3D refraction experiment in terms of the number of shots and receivers ͑ϳ600 each͒. The data were recorded using a 1-ms sample rate and contain frequencies ranging from about 40–250 Hz ͑Figure 3͒. The dominant frequency varies from 40 to 80 Hz. The data were pro- cessed minimally using only a 40–80–240–400 -Hz band-pass filter and notch filters of 60 and 120 Hz to remove ground roll, low-frequency cultural noise, and noise from onsite electrical equipment.After filtering, the dominant frequen- cy of the data is near 75 Hz ͑Figures 3 and 4͒. The airwave obscures refracted energy at offsets less than about 12 m because the seismic velocity of air ͑ϳ330 m/s͒ is faster than the seismic velocity of the near surface ͑Dana et al., 1999͒. Despite filtering, the data contain significant noise from U. S.Air Force jets and remediation activities, in- cluding pumps in monitoring, injection, and ex- traction wells. A 3D reflection experiment was carried out over the same area as the refraction experiment using the same east-west recording lines and rifle source as the refraction survey ͑Dana et al., 2001; Gao et al., 2004͒. The survey took 16 days to complete, compared to two days for the refraction survey, and produced a nominal fold of 52. The reflection survey took more time because it in- volved many more shots and a rolling geophone array, as compared to a static array for the refrac- tion survey.Acomparison of the 3D refraction ve- locity model with a 3D depth-migrated common- midpoint ͑CMP͒ stack, and the results of 2D waveform inversion of the reflection data are presented later. Traveltime picking and uncertainties A semiautomated interactive picking program was used to pick the first arrivals of the 360,000 traces. A total of 187,877 picks from 349 shots were made; the remaining 40% of the shots were not pick- able because of noise ͑Figure 2͒. Traveltimes were picked from shot gathers plotted versus offset in 12° azimuth bins ͑Figure 4͒. The bin aperture is a compromise between minimizing the variability in first-arrival time at different azimuths as a result of 3D structure and maximizing the number of traces. About every tenth trace was Figure 2. Experimental geometry of 3D refraction survey superimposed on the depth to clay from well data. White xs are shot locations. Green circles indicate shots for which traveltimes were picked. Black dots are receiver stations. Pink dots are well locations. There is some clipping of the depths to emphasize the paleochannel structure. 3D seismic refraction tomography H69
  4. 4. picked manually, and an automatic picker was applied to the inter- vening traces using the crosscorrelation between the unpicked traces and the two adjacent picked traces. The uniform areal distribution of shots and receivers over the sur- vey area has the advantage of providing uniform illumination of the subsurface but the disadvantage of spatial aliasing in both the inline and crossline direction. Results from a 2D pilot survey at OU2 using a 0.35-m receiver spacing clearly show that the near-offset ͑Ͻ12 m͒ refracted P-wave is slower than the airwave ͑Dana et al., 1999͒. However, it generally is impossible to distinguish the refract- ed arrival from the airwave in the 3D data because of the coarser re- ceiver spacing ͑2.8 m inline and 2.1 m crossline͒. Therefore, the first-arriving energy, interpreted to be an amalgamation of the air- wave and refracted wave, was picked and regarded as a body wave. The effect this has on the final model is addressed later. Only about 10% of the picks are in this near-offset region ͑Ͻ12 m; Figure 5a͒ The target of the survey, the paleochannel, is up to 15 m below the surface ͑Figure 2͒. For refracted waves to sample to this depth, a minimum offset of 25 m is required, based on the results of the 2D pilot survey ͑Dana et al., 1999͒.About 67% of the picks have an off- set greater than 25 m, providing confidence that the paleochannel is sampled adequately by the data. The dominant frequency of the filtered data is roughly 75 Hz, cor- responding to a quarter-period of 3.3 ms.Arule of thumb for picking accuracy is that an arrival can be identified at best to within one- quarter of the dominant period because if two waves arrive within this interval, they will add constructively and cannot be distin- guished from one another. Picking accuracy is further degraded by the presence of noise. To estimate the total pick uncertainty, the time difference of the picks from reciprocal source-receiver pairs was ex- amined ͑Figure 5b͒. About 56% of the reciprocal pairs are within 5 ms, and 86% are within 10 ms. Considering the frequency content of the data and the reciprocal differences, picks were assigned an un- certainty of 5 ms for traveltime inversion. Figure 3. Frequency spectrum for a typical raw ͑dashed͒ and filtered ͑solid͒ shot gather using a filter with notches at 60 and 120 Hz and a 40-80-240-400-Hz band-pass. The spectra have been normalized to the same peak value. Figure 4. Data examples.The traces for three shot gathers are plotted versus source-receiver offset within a 12° azimuth bin. Plot of the survey geometry to the right of each gather shows the shot location ͑large dot͒ and the trace aperture window. The data are shown trace normalized and filtered as described in Figure 3. First-arrival picks are indicated by horizontal marks on each trace. Figure 5. ͑a͒ Histogram of number of traveltime picks versus source- receiver offset in 2.1-m bins. ͑b͒ Histogram of number of shot-re- ceiver pairs versus reciprocal time difference in 1-ms bins. H70 Zelt et al.
  5. 5. 3D REFRACTION TOMOGRAPHY We use the 3D first-arrival regularized tomographic method of Zelt and Barton ͑1998͒ in which the simplest model is sought that predicts the picked traveltimes to within an accuracy consistent with their assigned uncertainties. This algorithm is designed to yield a model with the minimum amount of structure required by the data. Traveltime inversion is a nonlinear problem because the raypaths are dependent on the velocity model. Therefore, a linearized iterative approach is applied using a Taylor series expansion in which a start- ing model is required and the model and raypaths are updated over a series of iterations until the normalized misfit ␹2 between the ob- served and predicted data ideally reaches one ͑Bevington, 1969͒: ␹2 = 1 N ͚i=1 N ͫti o − ti p ␴i ͬ2 , ͑1͒ where N is the number of data points, ti o and ti p are the ith observed and predicted traveltime, and ␴i is the assigned picking uncertainty. At each iteration, an objective function ⌽, which measures a com- bination of the data misfit and the structure of the model, is mini- mized in the least-squares sense ͑Menke 1989͒: ⌽͑s͒ = ␦ tT Cd −1 ␦ t + ␭͓␣͑sT Wh T Whs + sz sT Wv T Wv s͒ + ͑1 − ␣͒␦ sT Wp T Wp␦ s͔, ͑2͒ where ␦ t is the traveltime misfit vector, s is the model slowness vec- tor, ␦ s is the perturbed model vector equal to s − so, so is the starting model vector, Cd is the data covariance matrix that contains the esti- mated pick uncertainties, Wp is the perturbation weighting matrix, and Wh and Wv are the horizontal and vertical roughness matrices, respectively. The perturbation weighting matrix is a diagonal matrix containing the reciprocal of the starting slowness values; it measures the relative perturbation of the current model from the starting mod- el. The roughness matrices are second-order spatial finite-difference operators that measure the roughness of the model in the horizontal and vertical directions. These operators are normalized also by the starting slowness value at the center of the operator ͑Zelt and Barton, 1998͒. The parameters ␭, ␣, and sz control the weight of the terms in the objective function. The parameter ␭ determines the overall amount of regularization and is not strictly free, in that it is reduced systemat- ically by the algorithm from a free-parameter starting value ␭o. The systematic reduction of ␭ with each iteration by a factor ␭r stabilizes the inversion by constraining the long-wavelength model structure in the initial iterations and by allowing finer model structure in later iterations.The parameter ␣ determines the relative weight of the sec- ond derivative and perturbation regularization; perturbation regular- ization is not part of the original Zelt and Barton ͑1998͒ algorithm, equivalent to using an ␣ value of one. The value sz governs the rela- tive weight of the vertical and horizontal smoothing regularization. The final free parameter is the number of iterations of the conjugate gradient algorithm Nlsq, used to solve the large sparse system of lin- ear equations at each iteration ͑Zelt and Barton, 1998͒. The free-pa- rameter values were varied to facilitate a systematic exploration of the model space to determine the simplest and most geologically rea- sonable model that fits the data. The model parameterization for the forward calculation of travel- times and raypaths is a uniform 1-m node spacing.The 3D finite-dif- ference eikonal solver of Vidale ͑1990͒, with modifications for large velocity gradients by Hole and Zelt ͑1995͒, is used. For the inverse step, the model is divided into cells of constant slowness. The cell size is chosen to balance the trade-off between increased resolution using smaller cells and increased constraint on the slowness values using larger cells. In practice, the largest cell size is used that allows the data to be fit within their uncertainties according to equation 1.A cell size of 2ϫ2ϫ1 m in the x-, y-, and z-directions, respectively, is used. The model dimensions are 60 ϫ 110 ϫ 28 m, resulting in 46,200 cells. Starting model The study area consists of two sedimentary formations. The sur- face layer, the Provo Formation, is comprised primarily of sand and gravel, while the buried Alpine Formation is primarily clay. From the well data, we know the clay top is at 2–15 m depth and is incised by a paleochannel ͑Figure 2͒; the water table is at 9–10 m depth. Two wells separated by 1.8 m show a difference in clay depth of 11.7 m. The true velocity field is therefore expected to be laterally and vertically complex. The only prior information concerning 3D structure is the depth to clay from the well data, but this is what we want to determine using the seismic data.Therefore, we use 1D start- ing models as a test of 3D refraction tomography in a complex near- surface environment. Three different starting models were tested ͑Figure 6͒. Because the airwave obscures the refracted wave in the near-offset region, we know 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 ͑Dana et al. 1999͒, a surface velocity of about 200 m/s is used for each model ͑Figure 6͒. The velocity increases rapidly with depth in each model and approaches the seismic velocity of water to account for the water table at 9–10 m. Each starting model increases with differ- Figure 6. Three 1D starting models. ModelAis preferred. Model B is slower than the model A from 0–9 m. Model C is faster than the modelAfrom 0–13 m. 3D seismic refraction tomography H71
  6. 6. ent gradients in depth until about 12 m depth, where they converge at roughly 1400 m/s and then slowly increase to slightly more than 1600 m/s at 25 m depth. Starting modelAis constructed by laterally averaging the 3D final models from some preliminary inversions of the data. Starting models B and C are designed to test the sensitivity of the results using slower and faster models, respectively. RESULTS The preferred final model was determined after numerous inver- sions using the three starting models and a range of free-parameter values. In this way, model nonuniqueness was explored, in that dif- ferent models were obtained that fit the data similarly according to equation 1. The preferred final model was selected in accordance with Occam’s principle of minimum structure ͑e.g., Constable et al., 1987͒ to avoid overinterpreting the data. Starting modelA͑Figure 6͒ was used to produce the final preferred model. The starting rms trav- eltime misfit is 9.25 ms ͑␹2 = 3.42͒, and the misfit provided by the preferred final model after eight iterations is 5.39 ms ͑␹2 = 1.16͒ ͑Figure 7͒. We could not achieve ␹2 = 1, probably because of the number of reciprocal time differences greater than 5 ms ͑Figure 5b͒. The 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 preferred final model and the starting model.Acoherent low-veloci- ty anomaly that trends roughly north-south is evident in each slice. The anomaly curves slightly eastward in the north, where it reaches its largest value of around 250 m/s perturbation from the starting model and widens to cover almost the full width of the model. It dis- appears south of about y = 80 m. The anomaly increases in coher- ence and magnitude until 12 m depth; it loses coherence below this. It shows considerable lateral variation, notably in the x- direction, where it can change by more than 300 m/s in roughly 15 m. The shape of the low-velocity anomaly is generally consistent with the paleochannel from the well data. Figure 9 shows east-west cross sections through the preferred fi- nal model. There is considerable heterogeneity in the upper 4 m of the model. Below 4 m, the model is generally smoother without any sharp features, and the isovelocity contours take the form of a broad depression, with the center roughly in agreement with the center of the paleochannel from the well data; this is the prominent north- south low-velocity anomaly seen in the horizontal slices. Model assessment To assess the robustness of the preferred final model, we have ap- plied a number of tests and examined the ray coverage. Ray coverage Ray coverage is a rough indicator of how well the model is con- strained at a particular point ͑Figures 8b and 10͒. Ray coverage is a maximum between 8 and 12 m depth, with the deepest rays reaching nearly 21 m. Ray coverage is concentrated toward the eastern side of the model between x values of 0–15 m and y values of 20–90 m. Rays are concentrated on the east because of the velocity structure, i.e., avoiding the low-velocity paleochannel, and also because the survey geometry shifts to the east at the southern end of the study area ͑Figure 1͒. Alternative starting models Figure 11 shows a slice at z = 10 m from the preferred final model in comparison with eight alternative final models. The normalized misfits for the final models obtained from starting models B and C were both 1.17, essentially the same fit as the preferred final model ͑␹2 = 1.16͒. Both alternative final models show a north-south-trend- ing low-velocity anomaly similar to the preferred final model. Shal- lower depth slices through the models obtained using starting mod- els B and C show consistently faster and slower perturbations, re- spectively, compared to the preferred final model at the same depth. This indicates starting model B is biased slow and starting model C is biased fast. However, the absolute velocities in these alternative models are very similar to the preferred final model, illustrating the robustness of the tomographic technique to biased starting models. Free parameters The alternative final models shown in Figure 11 are obtained by varying 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- ing modelAwas used and all free parameter values were the same as for the preferred final model, except for the one being varied. The five final models provide normalized misfits of 1.06–1.19. These models contain the north-south-trending low-velocity anomaly, al- though they are generally rougher than the preferred model. The ex- ception to this is the model obtained using sz = 0.3, which is smooth- er than the preferred final model in this horizontal slice but is rougher in the vertical direction, as expected using a smaller value of sz than that used for the preferred final model. Increasing sz from 0.3 to 0.4 added little horizontal roughness but significantly decreased vertical roughness. Increasing sz from 0.4 to 0.5 did not substantially smooth the model vertically but increased horizontal roughness, leading to the preferred sz value of 0.4. All of the models obtained by varying the free parameters are viable because they similarly fit the data ac- cording to equation 1, but the preferred final model was the smooth- est. Figure 7. Traveltime residuals for the preferred starting model and preferred final model as a function of source-receiver offset.The rms traveltime misfit for the starting and final models is 9.25 ms ͑␹2 = 3.42͒ and 5.39 ms ͑␹2 = 1.16͒, respectively. H72 Zelt et al.
  7. 7. Near-offset picks Because refracted body waves were not distinguished confidently from the airwave in the near-offset region and because the near-off- set picks predominantly influence the shallow part of the model, there is some question as to how the near-offset picks might affect the deeper structure of the model.An inversion was run in which ve- locities above 3 m were laterally homogeneous and fixed at the preferred starting model values; these values are based on the results of a 2D pilot survey in which refracted arrivals were identified in the near-offset region behind the airwave. The north-south-trending low-velocity anomaly is present in the final model ͑Figure 11i͒, although the magnitude of the variations are about 100 m/s greater than the preferred model at this depth and the model is rougher than the preferred final mod- el at all depths below 3 m. The normalized misfit of 1.21 for this model is the poorest of any of the alternative final models, although this is, in part, from the inability to fit the near-offset picks close- ly because the shallow portion of the model is fixed. Lateral resolution We have estimated the lateral resolution of the preferred final model using Zelt’s method ͑1998͒, which has been used in a number of 3D refraction studies ͑e.g., Day et al., 2001; Zelt et al., 2001; Morgan et al., 2002͒. The method consists of a se- ries of checkerboard tests using the source-re- ceiver geometry of the picked data. The preferred starting model and preferred free-parameter val- ues are used, and Gaussian noise is added to the synthetic data using a standard deviation equal to the assigned picking uncertainty, 5 ms. Five anomaly sizes were tested: 5, 7.5, 10, 15, and 20 m ͑Figure 12͒. Velocity anomalies of 35% en- sured the initial misfits were similar to the initial misfit of the real data for the preferred starting model. The semblance between the recovered anomaly pattern and the true anomaly pattern was calculated at each model node. A semblance val- ue of 0.7 is the threshold for good resolution at the length scale of the anomaly size ͑Zelt, 1998͒. At z = 10 m, much of the central part of the model has a lateral resolution of at least 7.5 m, and most of the model at this depth has a resolu- tion of at least 10 m ͑Figure 12͒. Zelt’s method ͑1998͒ determines the lateral resolution of the model by estimating the anomaly size that would yield a semblance of 0.7 at each model node ͑Fig- ure 8c͒. Resolution exceeds 7.5 m throughout most of the model down to 10 m depth. Resolu- tion at the 10-m length scale includes most of the model to 12 m depth and the central part of the model down to 14 m. DISCUSSION The geology at OU2 consists of heterogeneous unconsolidated sediments above a predominantly clay formation with an incised pa- leochannel. Large changes in velocity occur over short distances both laterally and vertically, based on extensive well data and a 2D pilot study ͑Dana et al., 1999͒. The final velocity model increases rapidly with depth, from approximately 200 m/s at the surface to 1500 m/s at 12–15 m depth ͑Figure 9͒.The model is more heteroge- Figure 8. ͑a͒ Preferred final model displayed as perturbations with respect to the preferred starting model for depths from 6–14 m as labeled. Depth to clay contours ͑in green͒ from the well data for 7–11 m overlay the 8- and 10-m slices. Black contour interval is 100 m/s. Unsampled regions at the edges are white. ͑b͒ The number of rays that pass through each model cell corresponding to the depth slices in ͑a͒. Black contour interval is 200 rays. Unsampled regions are white. ͑c͒ Lateral velocity resolution corresponding to the depth slices in ͑a͒. The 7.5-m contour is white; the 10-m contour is black. Black re- gions have better than 5 m resolution; white regions have worse than 20 m resolution or are unsampled. 3D seismic refraction tomography H73
  8. 8. neous in the upper 4 m, likely a reflection of the complexity of the unconsolidated near-surface sediments and consistent with higher- resolution waveform inversion results ͑Gao et al., 2006; Gao et al., 2004͒. The model becomes significantly smoother below 4 m, with the isovelocity contours taking a generally concave-up shape and with the deepest point being 2–3 m lower than at the edges of the model. The deepest points generally coincide with the incised pale- ochannel as defined by the well data, although the channel in the re- fraction model, is smoother than the well data indicate ͑Figure 9͒. The vertical cross sections suggest the velocity, in a very smooth way, is consistent with the known geology and site conditions. The low velocities of the sand-gravel Provo Formation overlie the high- er-velocity clay Alpine Formation, which has a nearly 10-m-deep north-south-trending trough in its top, forming the paleochannel, and a water table at 9–10 m depth. The water table may reduce the velocity anomaly that would oth- erwise be associated with the paleochannel below 9–10 m and could therefore, at least in part, explain the very smooth nature of the deep portion of our model. It is typical for the saturated zone to be shal- lower in clay than in sand because of capillary forces, and the transi- tion in clay occurs over a broader interval. Therefore, we would ex- pect the water table to follow the shape of the channel, although it will be smoothed laterally and to a lesser extent vertically. Also, since saturated clay is typically a bit slower than saturated sand, the base of the channel may correspond to a velocity decrease. In any event, the deep velocity structure is likely the result of a combination of lithology and water saturation, which is greatly smoothed out in the model from the resolution of the data. The horizontal slices of the velocity perturbations are dominated by a north-south-trending low-velocity anomaly that curves slightly to the northeast in the north ͑Figure 8a͒. The anomaly increases in area and velocity fluctuation with depth, peaking between 10 and 12 m depth and then diminishing and losing continuity below this. The anomaly at 10–12-m depth ranges from the edge of the model in the north to about y = 80 m in the south and roughly narrows in width from about 30 m to 10 m over this distance.As discussed, the anomaly is well resolved, with a lateral resolution at 10–12 m depth better than 10 m throughout most of the model and better than 7.5 m through much of it ͑Figure 8c͒. The outline of the low-velocity Figure 9. East-west cross sections through the preferred final model at y-positions as labeled. The clay layer from the well data overlays the model in white. Arrow indicates known water table at 9–10 m. Contour interval is 100 m/s; thick contour is 1000 m/s. Unsampled regions are white. Figure 10. Raypaths through the preferred final model projected into the x-y and y-z planes. For clarity, every 200th raypath is shown. H74 Zelt et al.
  9. 9. anomaly is consistent with the general shape of the paleochannel from the well data ͑Figure 8a͒, suggesting the paleochannel incised into the clay layer influences the long-wavelength velocity structure. At a given depth, the velocities are generally higher at the south end of the model than at the north ͑Figure 8a͒, perhaps because the sur- face elevation is roughly 1 m higher in the south, resulting in greater consolidation and higher velocities. Fresnel zones The size of the first Fresnel zone and the picking uncertainty pro- vide insight into the smoothness of the final model because they are related to the spatial resolution. For first-arrival traveltime tomogra- phy, the Fresnel zone is the volume within which any scattered wave will arrive within one-quarter period of the dominant frequency of the first arrival — roughly 3.3 ms for these data.As a result, any het- erogeneity within the Fresnel zone is averaged, although overlap- ping Fresnel zones from different source-receiver pairs makes it pos- sible for traveltimes to resolve details that are nearly 60% of the Fresnel zone’s dimensions ͑Pratt et al., 2002͒. Ray-theoretical Fresnel zones are calculated by summing the first-arrival-time fields from the source and receiver points and by contouring the traveltime corresponding to the first-arrival time between the two points, plus one-quarter of the dominant period. The volume within the contour corresponds to the first Fresnel zone because it represents all subsur- face points from which scattered energy between the source and re- ceiver will arrive within one-quarter period of the first arrival. Consider four representative Fresnel zones for refracted raypaths through the final model with offsets of 15, 30, 60, and 90 m that bot- tom above, within, and beneath the paleochannel ͑Figure 13͒. The greater heterogeneity in the upper 4 m of the model ͑Figure 9͒ could be a good representation of the true structure, given the more local- ized shape of the Fresnel zones in the upper 4 m, although contami- nation of the short-offset first arrivals by the airwave for this experi- ment must be factored in. The results of the checkerboard tests indi- cate lateral resolution exceeds 5 m in the upper 5 m throughout most of the model. Figure 11. The preferred final model and eight alternative final mod- elsat10 m depth,displayedasperturbationswithrespecttothestart- ing model. The reference velocity at this depth in the preferred start- ing model is 1150 m/s.The preferred final model is in the center; the other models are obtained using ͑a͒ starting model B, ͑b͒ starting model C, ͑c, e͒ ␭o = 10 000, ͑d͒ ␭r = 1.4142, ͑f͒ ␣ = 0.95, ͑g͒ sz = 0.3, ͑h͒ Nlsq = 325, and ͑i͒ model above 3 m fixed at starting-mod- el values ͑see text for details͒. The preferred starting model ͑e͒ is produced using starting modelAin Figure 6 and free-parameter val- ues ␭o = 5000, ␭r = 1.3173, ␣ = 1.00, sz = 0.4, and Nlsq = 250. Black contour interval is 100 m/s. Depth-to-clay contours ͑green͒ from the well data for 7–11 m overlay the models. White edges are unsampled regions. Figure 12. Recovered checkerboard anomaly patterns ͑top row͒ and corresponding semblance values ͑bottom row͒ at z = 10 m for the five anomaly sizes: 5, 7.5, 10, 15, and 20 m. The boundaries of the true checkerboard pattern overlay the recovered perturbations. In the semblance plots, the contour interval is 0.1; the 0.7 contour is white. 3D seismic refraction tomography H75
  10. 10. The Fresnel zones are thickest and broadest approximately half- way between the source and receiver, where they are as much as 15–20 m vertically and 15–30 m horizontally for raypaths that sam- ple the paleochannel.Although large, the overlapping Fresnel zones at the target depth of about 10 m, arising from many different source-receiver pairs, make it possible to resolve lateral variations in the paleochannel on a length scale consistent with the resolution de- rived from the checkerboard tests ͑Figure 8c͒. However, for vertical resolution at the target depth ͑approximately 10 m͒, every Fresnel zone with an offset of 25–40 m that bottoms near the target depth will average the structure over the entire depth range of interest.As a result, the traveltime data will only sense a very smooth vertical gra- dient. It is not possible to determine from the traveltime data whether the final model accurately describes a smooth velocity increase at the clay contact or the water table or whether a sharp velocity contrast exists but is smoothed out because of the size of the Fresnel zones. Thus, it is prudent to refrain from viewing the velocity values in the final model as localized point measurements. Regardless of the in- ability to determine the precise nature of the velocity increase result- ing from a change in lithology or the water table, the lateral geometry of the paleochannel is resolved within the final model at a length scale of 7.5–10 m. We estimate that a dominant frequency of ap- proximately 200 Hz and a picking error of about 2 ms would be re- quired to infer anything about the nature of the clay contact or the water table. Comparison with reflection data and waveform inversion Figure 14 compares a slice at z = 10 m from the preferred final model with results from waveform inversion of the 2D reflection data along each east-west line and a migrated stack of the 3D reflec- tion data. The waveform result is presented in the form of depth to the 800-m/s velocity contour, interpreted by ͑Gao et al., 2004͒ to be the clay top. The 3D reflection data are presented as a depth slice at 10 m from a poststack 3D depth-migrated volume ͑Fradelizio et al., 2004͒. Although the waveform isovelocity surface shows artifacts related to contouring the results from independent 2D inversions of the 45 east-west lines, the paleochannel is clearly defined from 7–11 m depth, in good agreement with the well data. The 3D reflec- tion data show generally enhanced reflectivity within the channel as defined by the well data, although this reflectivity fades out between about y = 30 and y = 40 m. In the north, all three images show the channel curving to the east. This is where the strongest anomaly is in the traveltime model, the deepest point is in the waveform surface, and the largest patch of enhanced reflectivity is in the reflection im- age. South of about y = 80 m, the results are inconsistent. The low- velocity anomaly disappears in the preferred traveltime model; the channel defined by waveform inversion is generally consistent with the well data, and the high reflectivity is shifted east of the channel as defined by the well data. South of y = 80 m is an area where the al- ternative models show considerable variation ͑see models 4 and 8, Figure 11, d, i͒. This is not surprising, given the relatively poor reso- lution at the south end of the model ͑Figure 8c͒. The generally favorable comparison of the 3D velocity model with the waveform and reflection results lends credibility to the in- terpretation of the north-south low-velocity anomaly being an ex- pression of the topography on the clay surface and the low-velocity sediments within the paleochannel. The waveform and reflection re- sults have higher resolution than the traveltime result, as expected, but all three methods image the channel structure in close agreement with the well data. We estimate that the amount of experiment, com- puter, and human time necessary to produce the refraction model is a factor of 5–10 less than the time to produce the other two results. Figure 13. Comparison of first Fresnel zones in the final model for a center frequency of 75 Hz and source-receiver offsets of 15, 30, 60, and 90 m. ͑top͒ Vertical cross section through the Fresnel zones at x = 0 m. ͑bottom͒ Horizontal cross sections at 4, 10, and 16 m depth. The 10-m depth-to-clay contour from the well data overlays the 10 -m cross section in gray. Figure 14. ͑a͒ Horizontal slice of the preferred velocity model per- turbations at 10 m depth. ͑b͒ Depth to the 800-m/s isovelocity sur- face from 2D full waveform inversion of the 45 east-west 2D reflec- tions lines ͑Gao et al., 2004͒. ͑c͒ Horizontal slice of the poststack 3D depth-migrated reflectivity from the reflection data at 10 m depth ͑Fradelizio et al., 2004͒. The 7- and 10-m depth-to-clay contours from the well data are labeled.White edges are unsampled regions. H76 Zelt et al.
  11. 11. CONCLUSIONS The 3D seismic refraction experiment at HAFB and the applica- tion of 3D first-arrival-time tomography were a feasibility study for shallow seismic investigations at environmental remediation sites. Imaging the velocity structure of the near-surface environment pro- vides encouraging results, despite less-than-ideal seismic data re- sulting from airwave contamination, onsite noise from ongoing re- mediation activities, and a relatively low dominant frequency for such a shallow target. Regularized first-arrival-time tomography obtained a minimum- structure velocity model that outlines the shape of the low-velocity fill in the paleochannel at the top of the clay formation. The north- south low-velocity structure appears to mimic the paleochannel as determined from over 100 wells, generally consistent with the re- sults of waveform inversion and 3D poststack depth migration of the reflection data. The low-velocity anomaly may represent the shape of the paleochannel accurately at length scales of about 10 m, ac- cording to checkerboard tests and considering the Fresnel zones. The results suggest that first-arrival traveltime tomography can constrain the long-wavelength features of a rapidly changing, near- surface heterogeneous environment. A higher center frequency in the data would have meant smaller Fresnel zones and, along with a better S/N ratio, a smaller picking error, which in turn would have justified a closer fit to the data, increasing model resolution. In any shallow seismic study, the center frequency is dictated by site condi- tions and the need to propagate energy to and from the target. In com- parison to the 3D seismic reflection method, the seismic refraction method was relatively simple, quick, and inexpensive. In addition, the analysis and interpretation of refraction data is potentially less subjective than conventional reflection processing.There is minimal data processing and objective arrival picking, assuming low noise, and solving for a minimum-structure model minimizes the subjec- tivity of the interpretation. Compared to waveform inversion, travel- time inversion is robust, even in the presence of considerable noise or spatial aliasing. Finally, the velocity model obtained by first-ar- rival-time tomography can be used as a starting model for waveform inversion and as an independent check on the images obtained from processing reflection data. ACKNOWLEDGMENTS Hans Meinardus of Duke Power acted as our liaison with HAFB, and Jon Ginn at HAFB made possible our access to OU2. We thank the volunteer field crew members from nine countries for their great teamwork. D. Dana and I. Morozov helped to prepare the data for analysis. G. Fradelizio and F. Gao provided figures from their work. 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