D ultra shallow seismic imaging of buried pipe using dense receiverrray: Practical and theoretical considerations
an Bachrach1 and Moshe Reshef1
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ABSTRACT
Direct 3D imaging of a 6� pipe, buried at a depth of 1.5 m,using portable dense receiver array shows that small objectsassociated with large impedance contrast can be preciselyimaged. Detailed velocity analysis applied to backscatteredwavefield from small buried objects provides resolution ofless than 10 m /s. Comparison of backscattered wavefieldobservations to analytical solutions show a generally goodmatch. Theoretical calculations also show that the object canbe detected with wavelengths much larger than its size due tothe large contrast associated with its hollow shape. Densespatial sampling is needed to capture the energy emitted fromthe scattering object and successfully focus it by diffractionimaging. Portable dense receiver array can provide a cost-ef-fective solution for such tasks.
INTRODUCTION
Direct 3D seismic imaging of small-scale buried objects is notoutinely performed. The complexity of seismic waves scatteredrom small-scale objects in the heterogeneous shallow subsurfacerovides a major challenge for direct seismic detection and imagingf buried man-made objects such as utilities and foundations. Unlikemaging of geological structures, direct imaging of the ultra-shallowubsurface structures relies considerably on the ability to focus non-lanar, backscattered energy, mainly diffractions. This is, in manyases, a more challenging task, as the amplitudes of the diffractedaves are smaller than those of the reflected ones. Moreover, the het-
rogeneity of the very near surface strongly affects the high-frequen-y events and as a result, identification of the weak backscattered en-rgy becomes a more difficult task. Landa and Keydar �1998� recog-ize this issue and suggest using monitoring techniques to overcomehe subsurface complexity. In their pioneering work the diffractioninematics �travel time and ray path� are used to maximize energyssociated with diffractions. In general, standard seismic technology
Manuscript received by the Editor 3August 2009; revised manuscript rece1TelAviv University, Dept. of Geophysics and Planetary Sciences, Israel. E2010 Society of Exploration Geophysicists.All rights reserved.
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as not been the method of choice when trying to identify small-cale buried objects. Therefore, to our knowledge, the dynamics ofhe ultra-shallow wavefield �i.e., diffraction amplitudes� and specifi-ally the relation between the backscattered wavefield, the frequen-y content of the wavefield, and the observed energy have not beenddressed.
During the last two decades, most high-resolution near surfacemaging studies of small-scale heterogeneities has been done usinground penetrating radar �GPR�. Bachrach and Nur �1998� illustratehat seismic waves and GPR can both illuminate the subsurface in aomplimentary way using similar wavelength. However, seismicethods appear promising for near-surface investigation because
hey do not suffer from high attenuation and can be sensitive to me-hanical contrast rather than dielectric contrast. Furthermore, as theechanical state of the subsurface is often of interest for many engi-
eering applications, the detection and analysis of seismic wavesay provide a valuable tool for these applications. If seismic meth-
ds are to be considered as an alternative to GPR, it will be necessaryo better understand how to utilize seismic imaging techniques forear-surface studies in a cost-effective way.
In this study, we conducted a controlled experiment where denseeceiver array �Bachrach and Mukerji, 2001, 2004a, 2004b� wassed to image buried objects in 3D. Specifically, we produced andnalyzed an image of a 6� diameter pipe buried at a depth of �1.5 mnd carried out detailed velocity analysis of scattered wavefield us-ng advanced seismic-imaging procedures. The results successfullyompared to the analytical solution.
In the following, we first review the experimental procedure thenresent the analysis of the field data. Finally, we compare the resulto synthetic theoretical seismograms derived from the full elastody-amic solution of the elastic wave equation. We demonstrate the ef-ectiveness of using dense spatial sampling to obtain a seismic imagef a very small object. In the case of large contrast between the elas-ic properties of the scattering object and the surrounding media, wergue that large wavelengths �more than 10 times the size of the scat-ering object� can be used to successfully image the subsurface het-rogeneity.
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FIELD EXPERIMENT
The experiment took place in Moss Landing beach, nearonterey Bay, CA. This site was chosen due to the excellent seismic
esponse from the beach sand and the extensive characterization of- and S-wave velocities available in Bachrach and Nur �1998�;achrach et al. �2000�. The experiment was conducted in 2002,here we buried a 6� pipe �length of 1.5 m� inside the beach sand.igure 1 depicts the 6� pipe �about 15 cm diameter� and the locationf the survey. The pipe was buried horizontally at a depth of about.5 m below the surface and the acquisition used a small, 0.25 kgammer as the seismic source. We used a 2D portable dense receiverrray �Bachrach and Mukerji, 2001, 2004a, 2004b�, arranged as aectangle, with receiver spacing of 25 cm in each direction to collectD seismic data over the buried object. The goal of the experimentas to evaluate the performance of the array and the use of the re-
orded data for imaging very small objects. The 3D acquisition ge-metry is presented in Figure 2. A single patch consisting of 72 re-eivers was used to record each of the 40 source locations �Figurea�. The patch acquisition was repeated after horizontally movinghe dense receiver array by a full patch length �2 m�. Figure 2b pre-ents the total horizontal coverage of the patches, and Figure 2c illus-rates the offset distribution �color map� associated with the CDP.he portable receiver array was moved within �5 minutes and thentire survey was acquired in about 40 minutes.
SEISMIC DATA PROCESSING AND QUALITYCONTROL
A typical raw seismic shot gather is presented in Figure 3. We fol-owed the approach outlined by Bachrach and Mukerji �2004a� andnalyzed the data quality using offset supergathers, generated bytacking traces with similar offsets from all shots. The overall signaluality was very good and the frequency bandwidth of the data wasell above 600 Hz, as can be seen in the radial gathers presented inigure 4. The water table reflection, below the target, provides an ex-ellent reference for data processing and signal analysis. The pro-essing included filtering, first arrival mute, velocity analysis andmaging using poststack and prestack depth and time migrations. Inhe following, discussed in detail are some of the issues related to im-ging strategies and results associated with this unique high-qualityataset.
igure 1. Experiment location in Moss Landing beach and the 6�ipe before burial.
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3D IMAGING RESULTS
The data were preprocessed using the flow described by Bachrachnd Mukerji �2004b� which include analysis on supergather, first-ar-ival mute and imaging. We applied several imaging algorithms tohe data set, including CDP stack and then poststack-phase shift mi-
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igure 2. Acquisition geometry. �a� Top-Asingle patch consisting of2 receivers and 40 shot locations with the CDP location. �b� Fullurvey geometry after moving the patch three times. �c� Offset CDPistribution associated with the full survey geometry.
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3D pipe imaging G47
ration, PSTM and PSDM using Kirchhoff/Born-based algorithms.ll of the imaging algorithms successfully focused the data, due to
ts excellent quality and the precise determination of the velocityunction. For example, Figure 5 presents a vertical slice through theD volume after stack �Figure 5a� and after poststack migrationFigure 5b�. Note that the diffraction energy decays relatively fastnd is nonsymmetric. Although visible on the stacked data, the dif-raction is less clear and energy is smeared. We note that the CDPpacing here is 12.5 cm; thus the whole diffraction pattern is visiblen a very short interval �less than 1 m�. However, it is clear from Fig-re 5 that the migration helps in focusing the energy associated withhe buried pipe and improves its seismic resolution and spatial posi-ioning.
Figure 6 presents the results of imaging the data using KirchhoffSTM with two subsets of data. One with 150 Hz �Figure 6a� and thether �Figure 6b� with 450 Hz low-cut filter applied. We note that the50 Hz data provides a better definition of the buried object �markedith arrows� while the high-frequency panel provides inferior im-
ge. This is not surprising considering the bandwidth associatedith the 150 Hz wavelet is wider than that of the 450 Hz low-cutavelet. For a given frequency content in theata, the wavelet is better compressed as theandwidth increases and thus, if sufficient energys backscattered, wider bandwidth will have bet-er definition. Furthermore, our observations em-hasize the importance of low frequencies evenhen imaging very small objects buried at shal-
ow depth �note that in the study area, 150 Hzata is illuminating the 0.15 m pipe with wave-engths of about 1 m�. This issue to be further dis-ussed.
It is also interesting to note that although theMS velocity resolution at the watertable reflec-
ion was excellent, a non-linear velocity profile iseeded to correctly position the pipe in depth.his observation is in agreement with velocitiesithin sands as presented by Bachrach et al.
2000�.
elocity analysis and velocity resolution
Precise depth imaging depends on the ability toefine the subsurface interval velocity. Conven-ional velocity analysis techniques, which are based on flatteningvents in depth-migrated common image gathers �CIGs�, are oftennadequate for ultra-shallow data. This is due to the small number ofive traces in the CIGs as a result of low fold and application of top
ute. Residual moveout measurements are impossible in these situ-tions. In Figure 7, the effectiveness of velocity scans using iterativeD depth migration is demonstrated. Moving from slow velocity onhe right to high velocity on the left with increments of 10 m /s, onean easily see how the buried object is best imaged by the velocitysed to generate Figure 7d �surrounded by the black box�. In additiono the good-quality image of the pipe, the migration was able toharply define the side walls of the filled trench in which the pipe waslaced.
COMPARISON TO ANALYTICAL SOLUTION
To better understand the different wave types observed in the
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igure 5. �a� CDP-stacked data with bin size of 12.5 cm. �b� 3D mi-rated data. The pipe is located at �15 ms. Note the improvement inefinition and resolution after migration.
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field, and specifically the relation between thesize of the scattering object and the wavelength ofthe seismic wave, we compare our experiment toanalytical results obtained for the case of plane-wave scattering from a homogeneous cylinder.Here we use exact elastodynamic analytical re-sults of waves interacting with the buried cylin-der.
Analytical solution
The exact analytic solution of body-wave scat-tering from buried cylindrical objects in homoge-neous media have been studied extensively �Yingand Truell, 1956; White, 1958; Pao & Mow,1973; Miklowitz, 1978; Veksler et al., 1999; Liuet al., 2000�.
In this study we adopt the analytical solutiongiven by Veksler et al. �1999� and Liu et al.�2000�, and calculate the time domain syntheticseismogram for a wavefield backscattered from aburied cylinder. The seismogram is given in termsof the radial displacements associated with P- andS-wave �ur1
P �t� and ur1S �t�� and the tangential dis-
placements associated with the P- and S-bodywaves �u� 1
P �t� and u� 1S �t�� by the following series
expansion �Liu et al., 2000�:
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igure 6. 3D PSTM images of buried pipe with 150 Hz and 450 Hz data. N
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igure 7. The results of migration velocity scan with increments of 10 m /s.ndicates that buried pipe is best imaged in the section marked by the black bocity of 150 m /s. Each panel is a vertical section through a depth migrated
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3D pipe imaging G49
here G��� is the Fourier transformed source wavelet, r is the radialistance from the center of the cylinder, kc1�� /VP1, ks1�� /VS1
re the P- and S-wave number in the medium, VP1, VS1 are the P- and-wave velocities in the medium, Hm
�1� is the mth order Bessel func-ion of the first kind, and Am and Bm are coefficients which are deter-
ined from the boundary conditions associated with the buried cyl-nder. Detailed calculations of Am and Bm are given in Veksler et al.1999�. We note that there is no free surface associated with the ana-ytical solution; thus we will evaluate only the observed body waves.or the homogeneous background the values were chosen according
o the average velocity observed in the field to be VP1�150 m /s,S1�75 m /s and density of 1.6 gr /cc. We note
hat a Vp /Vs ratio of two and density of 1.6 gr /ccs within the range of values observed for dryand �Bachrach et al., 2000�.
We performed numerical calculations and gen-rated a synthetic seismogram for each of thehree basic configurations: A plane wave scatter-ng from a cylindrical cavity; a plane wave scat-ering from an elastic cylindrical object whose P-nd S- velocities are lower than the backgroundy 25% �with VP2�112 m /s, VS2�65 m /s, andensity of 1.5 gr /cc�; and a plane wave scatteringrom buried elastic cylinder whose properties areimilar to concrete �with VP2�3800 m /s, VS2
1900 m /s, and density of 2.45 gr /cc�. Therst and third configurations represent the case ofiffraction associated with large contrast in mate-ial properties. In the first case, the sharp changes from elastic medium with finite elastic modulio cavity with zero stress condition on the surfacef the cylinder. The third case represents a stiffiffractor whose elastic properties are more than0 times larger than those of the surrounding me-ium. In the second case, the diffractor propertiesre not drastically different from the background.n all cases the cylinder radius was 7.5 cmnd was located below the surface at a depthf 1.5 m.
The vertical seismogram was calculatedrom the radial and tangential displacementelds using the relations: uy1
P �t��ur1P �t�cos�� �
u� 1P �t�sin�� �, ur1
S �t��ur1S �t�cos�m� ��u� 1
S �t�sin�� �.Figure 8 presents the vertical displacement
eismogram obtained by numerically evaluatinghe analytical solution for the three different cas-s. A minimum phase wavelet with unit ampli-ude was used for the simulation. We calculatedour theoretical seismograms for each of the mod-ls. Each synthetic seismogram was calculated bysing a different central frequency for the wave-et. We used frequencies of 50 Hz, 150 Hz,00 Hz, and 600 Hz, which correspond to-wavelengths �P of 3 m, 1 m, 0.5 m and 0.25 mespectively, and S-wavelengths which are half ofP. The ratio of P-wavelength to object diameter
n our numerical experiments varies from 20:1 forhe 50 Hz wavelet to about 1.5:1 for the 600 Hzavelet. We note that the domain where the scat-
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Figure 8. Syn7.5 cm buriedP-wave with ccases: �a� hollinder. Colorbaamplitude of t
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ering object is smaller than the wavelength is known as Rayleighcattering domain �Mavko et al., 1998�.
The two events diffracted from the buried cylinder are P- and-waves. For all frequencies we can identify these modes for eachne of the test cases.As expected, the 50 Hz response is much weak-r than the higher frequencies response, due to the lower scatteringower associated with Rayleigh scattering from small-size objects.ecall that in the Rayleigh scattering domain the scattering power isroportional to �P
�4, and thus larger wavelength will backscatterith lower power as demonstrated numerically in our analytical re-
ogram for cylindrical cavity
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P- and S-backscattered wavefield from a cylinder with a radius ofbelow the receiver line, which is being illuminated by a plane
frequency of 50 Hz, 150 Hz, 300 Hz and 600 Hz for the followinginder; �b� weak contrast low velocity cylinder; and �c� concrete cyl-nts the amplitude of the data. Note the colorbar which represents thescattered energy associated with buried scatterrer.
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ults. However, if we compare the case of low elastic contrast to thewo high contrast examples, it can be seen that the amplitudes of thecattered wave at low frequencies �50 Hz and 150 Hz� are mucheaker. Figure 9 demonstrates this effect by plotting the same seis-ograms as Figure 8, using a common scale factor. We also note that
t low frequency the relative amplitude of the converted P- to-wave diffraction increases.A comparison between the theoretical seismogram and the pro-
essed field data is presented in Figure 10. We extracted a subset ofhe data, located very close to the scattering cylinder �Figure 10a�nd projected it along offset to try to capture the backscattered ener-y while still enhancing S/N. In Figure 10b and c, we present themall supergather which tries to capture the very near-offset scatter-ng from the pipe using 150 Hz and 300 Hz low-cut filters and super-ose the theoretical seismogram on the data. In general, we obtainood agreement between the observed and calculated P-wave dif-raction, while the S-wave diffraction is not clearly observed on theeld data.
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igure 9. Same as Figure 8 but with absolute scal-ng to show relative strength of reflection. Note thatow contrast diffractors emit lower energy than theigh contrast example.
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DISCUSSION
The pipe we imaged was buried 1.5 m below the surface and thepparent velocity of 150 m /s best focused its diffraction. With suchvelocity, a 150 Hz wavelet will have a wavelength of 1 m, whichill propagate 1.5 times its length before being scattered by the bur-
ed object. For a 450 Hz wavelet, a wavelength of 33 cm will beackscattered from the buried object while a 50 Hz signal will notropagate even a single wavelength before encountering the hetero-eneity and scattering of the object. Thus, at low frequencies we areractically collecting “near field” data, which travels few wave-engths.
We note that for all frequencies discussed, the wavelength is larg-r than the pipe’s diameter. However, we are still able to collect aarge amount of energy from this buried object, as can be seen in theeld and synthetic data. This important observation is related to theontrast in elastic properties between the hollow pipe and the sur-ounding dense sand. The larger the material contrast, the higher thecattering power associated with the heterogeneity. Although the
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3D pipe imaging G51
ize of the disturbance is small compared to wavelength, the highontrast causes sufficient energy to be backscattered and imaged. Weemonstrate this phenomenon through analytical solution to theroblem of buried pipe in homogeneous medium, where same sizebjects scatter different amounts of energy due to the overall con-rast in the elastic properties of the scatterrer.Although in general thecattering power should decrease as �P
�4, which means that for a re-uction of frequency by a factor of two will decrease the scatteringower by a factor of 16, large material contrast will scatter more en-rgy and therefore may be detected with sufficient S/N. The denseavefield sampling used in this study enabled us to collect energyith sufficient S/N that could be successfully imaged by standard
eismic processing techniques.Due to the scalability of the problem in terms of wavelengths and
epth of burial, it can be argued that if a 15 cm pipe, buried 1.5 m be-ow the surface, can be detected with frequencies of 150 Hz and50 Hz, it should be possible to detect larger and deeper objects withelatively low frequencies, as long as the contrast in elastic proper-ies between the objects and their surroundings is sufficiently large.
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Shot and Receiver locationsa)
igure 10. Comparison between field data and theoretical seismo-rams. �a� Map of location of buried pipe and traces selected for gen-ration of supergather for scattered wavefield analysis. �b� Synthetic- and S-backscattered wavefield superposed on field observationssing 300 Hz data and model; �c� same as �b� but with 150 Hz datand model predictions.
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CONCLUSIONS
We were able to image in 3D a 15 cm hollow pipe buried in sand atdepth of 1.5 m below the surface using dense receiver array. The
ollowing are our findings:
� The key factor in successful imaging of shallow-buried smallobjects is the use of very dense receiver array which enables thecapture of energy scattered from the objects through low-veloc-ity sand.
� The velocity resolution is very good and within �10 m /s. Thissuggests that monitoring velocity changes around the buriedobject is feasible with standard velocity analysis techniquesaimed at enhancing diffractions focusing.
� We successfully imaged the pipe with energy associated withwavelengths much larger than the pipe’s diameter.
� When large contrast in material properties is present, largewavelengths are also backscattered and can be used to improveimage resolution.
It is our opinion that the use of small scale dense receiver arrayay provide a valuable tool for ultra-shallow imaging and to moni-
or variations in subsurface properties, associated with nongeologi-al man-made objects.
ACKNOWLEDGMENTS
We would like to thank Brad Artman for assistance in data collec-ion and the reviewers who contributed to clarifying the manuscript.
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