p -wave reflection imaging of submerged soil models using ultrasound

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p-Wave Reflection Imaging of Submerged Soil Models UsingUltrasound

Joseph Coe, S.M.ASCE1; and Scott J. Brandenberg, A.M.ASCE2

Abstract: An ultrasonic p-wave reflection imaging system is used to noninvasively image submerged soil models with embeddedanomalies and complex geometric layer contacts. The ultrasonic transducers emit compressive waves into water that subsequently transmitinto the underlying soil, and measurements of the reflections are used to construct the images. The properties of the transducers and dataacquisition hardware and software are explained. Fast signal stacking is used to improve signal-to-noise ratio and provide clearer images.Transducer directivity is explained as a wave passage effect, and transfer functions are derived for square and circular transducers toquantify directivity. The transfer functions agree reasonably with measured amplitude data. The cause of errors in the imaged position ofdipping reflectors is explained, and a Kirchhoff migration algorithm is implemented to correct these errors. A soil model consisting ofembedded high- and low-impedance anomalies, dipping soil layer contacts, and an undulating concrete base layer was imaged using 500-and 100-kHz transducers. The geometric features of the model are clearly visible in the images recorded with the 500-kHz transducers andless clear with the 100-kHz transducers. The lateral spatial resolution of the migrated images is shown to be much larger than onewavelength.

DOI: 10.1061/�ASCE�GT.1943-5606.0000346

CE Database subject headings: Soils; Ultrasonic methods; Transfer functions; Transducers; Imaging techniques; Signal processing;Submerging.

Author keywords: Reflection; Compression waves; Ultrasonic methods; Transfer functions; Transducers; Imaging techniques; Signalprocessing.

Introduction

Inadequate knowledge about the subsurface is among the biggestproblems in geotechnical engineering. Current standard of prac-tice site investigation techniques leave us with an incomplete un-derstanding of site conditions that is often inadequate to reliablyperform engineering predictions �Terzaghi 1947�. Medicine faceda similar challenge in the first half of the 20th century, whereinthe properties of the inside of the human body could only beobserved invasively. This problem was overcome by computer-assisted tomography that used inversion of X rays to “see” insidethe body without surgery �independently developed by Cormack�1963� and Hounsfield �1973��. A number of additional noninva-sive medical imaging techniques followed, including ultrasonicimaging, which utilizes reflections of compressive waves, or pwaves. p-wave reflection imaging is also used often by seismolo-gists to image geologic structures sometimes kilometers belowEarth’s surface, and is useful for locating faults or geologic fea-tures that contain oil �e.g., Yilmaz 1987�. Medical ultrasound and

1Graduate Student, Dept. of Civil and Environmental Engineering,Univ. of California, Los Angeles, CA 90095-1593. E-mail:[email protected]

2Assistant Professor, Dept. of Civil and Environmental Engineering,Univ. of California, 5731 Boelter Hall, Los Angeles, CA 90095-1593�corresponding author�. E-mail: [email protected]

Note. This manuscript was submitted on November 15, 2008; ap-proved on February 24, 2010; published online on February 26, 2010.Discussion period open until March 1, 2011; separate discussions must besubmitted for individual papers. This paper is part of the Journal ofGeotechnical and Geoenvironmental Engineering, Vol. 136, No. 10,
October 1, 2010. ©ASCE, ISSN 1090-0241/2010/10-1358–1367/$25.00.
1358 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN

J. Geotech. Geoenviron. Eng.

seismic reflection imaging utilize different tools �small handheldultrasonic transducers versus explosives ignited on the groundsurface� to construct images of vastly different scales; yet theunderlying principle is identical: Compressive waves reflect fromanomalies and the recorded reflections can be used to noninva-sively construct an image.

p-wave reflection imaging is a very mature field of study, withthousands of papers published in medical and geophysical jour-nals. It has tremendous potential as a geotechnical site investiga-tion tool, yet the technology has seen only limited application atthe scale of a typical geotechnical project, or at the scale of soilmodels often used in research. A handful of studies have beenconducted to demonstrate the potential of p-wave reflection im-aging. For example, Lee and Santamarina �2005� conducted asmall-scale laboratory test program that used 500-kHz ultrasonictransducers to image soil layers, embedded objects, and slurrysurface position during sedimentation. Grandjean �2006� used aseismic “multiapproach” that identified contaminants in the fieldusing a number of different types of waves, including p waves�Rayleigh waves and shear were also used�. Kase and Ross �2004�used reflection imaging in advance of tunnel excavation to iden-tify potentially difficult soil conditions. Nichols et al. �1988� lo-cated rebound fracture zones in Pierre shale using shallow seismicreflection imaging. More work is needed to adapt sensors and dataprocessing methods for p-wave reflection imaging at the geotech-nical scales of interest.

This paper used ultrasonic transducers to image a soil modelsimilar in scale to those often tested in large geotechnical centri-fuges. The properties of the transducers and data acquisition sys-tem are presented first, followed by a study of transducer
directivity and the ability of the transducers to measure dipping
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reflectors. A transfer function is derived to characterize the trans-ducer directivity, and compared with experimental measurements.The directivity study is then used to demonstrate errors that arisein the position of dipping reflectors in the recorded images, and aKirchhoff migration algorithm that corrects these errors is ex-plained. The ultrasonic system is then used to image a soil modelwith a geometry that was made deliberately complex, with a dip-ping soil layer interface, high- and low-impedance embedded ob-jects, and an undulating concrete base layer, to test the limits ofthe imaging system. Finally, the resolution of the system is testedby comparing the migrated image of the undulating concrete baselayer with hand measurements of its surface topography.

System Components

The system components for these experiments are the ultrasonictransducers, source pulser, receiver amplifier, receiver analog fil-ter, string potentiometer, terminal block �SCC-68�, data acquisi-

Table 1. Transducer Properties

Nominalfrequency�kHz� Product number

Length�mm�

Diameter�mm�

500 A3441 32 19

100 GRD100-D50 43 50

Table 2. Pulser Properties

Manufacturer Product number Input powe

JSR Ultrasonics PCU-QP3 PCU0021 5 Vdc

Fig. 1. Schematic of p-wave reflection imaging system components

JOURNAL OF GEOTECHNICAL AND GEO


tion cards mounted in a PXI chassis, and a personal computer�Fig. 1�. Many of the components were designed for implemen-tation on the nees@UCDavis geotechnical centrifuge, and wereinitially tested at Georgia Tech by Lee and Santamarina �2005�. Asteel housing contained the transducers, pulser, amplifier, and fil-ter �together, these components are hereafter called the ultrasounddevice� and was attached to a frame that held the tips of thetransducers in contact with water, and permitted the ultrasounddevice to smoothly glide horizontally.

Ultrasonic Transducers

Two different sets of piezoelectric ultrasonic transducers that op-erate at central frequencies of 500 and 100 kHz were used toattain the p-wave images in the laboratory �Table 1�. The 500-kHztransducers were described by Lee and Santamarina �2005�, andthe 100-kHz transducers were acquired for potential field appli-cation. The transducers are composed of a piezoelectric disk-shaped element, backing block, matching layer, and an insulatingcasing. Imposing a voltage across the source piezoelectric ele-ment causes it to rapidly vibrate, thereby inducing a compressivewave in the media to which it is coupled. The reflected waveenergy distorts the piezoelectric material in the receiver trans-ducer, producing a measurable voltage potential across the ele-ment. The nominal frequency of the transducer is controlled bythe thickness and stiffness of the disk. The pulse duration is con-trolled by the backing block, which effectively acts as a damperby absorbing some of the energy radiating from the piezoelectricdisk. Short pulse durations �from highly damped transducers� aredesired for imaging applications because “spiky” signals providebetter image quality than “ringy” signals. However, damping de-creases signal amplitude and therefore limits penetration depth ofthe ultrasonic waves. The matching layer optimizes the wave en-ergy that is transmitted from the transducer, and is configured tofavor the transducer’s central frequency thereby acting as a band-pass filter. The impedance of the matching layer is typically se-lected to be the geometric mean of the impedance of thepiezoelectric element and the material in contact with the match-ing layer to maximize energy transmitted from the transducer�i.e., impedance matching�. The casing electrically grounds thetransducer and provides a mechanical shield that prevents directarrival of compressive waves from source to receiver.

Selecting a central frequency for ultrasonic transducers mustbalance the conflicting goals of high resolution and the ability totransmit the waves large distances through heterogeneous attenu-ative materials. The resolution of the p-wave reflection images isproportional to the central frequency of the transducers, and a ruleof thumb is that resolution is equal to about one wavelength.Hence, high frequency is optimum for resolution. However, high-frequency waves attenuate more quickly in attenuative media, andtherefore cannot travel as far as low-frequency waves. Further-more, soil is a granular material and dispersion becomes signifi-cant when the wavelength becomes smaller than about ten particlediameters �Santamarina et al. 2001�. Therefore, the attainable res-olution for a particular application depends on the properties ofthe soil and the distance to the reflector.

Output voltage Input function

150 Vdc Square waveform 0–5-Vdc amplitude

r

ENVIRONMENTAL ENGINEERING © ASCE / OCTOBER 2010 / 1359

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Source Pulser

A custom pulser provided a 150-Vdc input signal to the sourcetransducer �Table 2�. A high voltage pulse was desired to maxi-mize the pulse amplitude to improve penetration depth and signal-to-noise ratio. The pulser receives +5-Vdc power, and is triggeredby a 0 to +5-Vdc step function from an arbitrary waveform gen-erator. The pulser outputs a step function to the transducer, whichsubsequently responds predominantly at its central frequency.This type of pulser does not permit tuning the frequency of thetransducers. More advanced pulsers can reproduce any arbitrarywaveform, which can be useful for developing transfer functionsusing frequency sweeps or chirp signals. A step wave durationequal to half of the natural period of the transducer was found tooptimize the output signal amplitude.

Receiver Amplifier and Filter

An inline amplifier and analog filter were used to record the volt-age signal from the receiver transducer �Table 3�. The amplifierwas located near the receiver transducer in the casing to minimizecable length for the unamplified signal thereby reducing noise andminimizing loss of charge in the cable from the capacitive trans-ducer. The amplified signal was subsequently filtered using a low-pass antialiasing filter with corner frequency of 2.5 MHz.

String Potentiometer

A linear string potentiometer �Table 4� measured the horizontalposition of the transducers and was used to trigger pulses at speci-fied positions as the ultrasonic device was slid by hand on a railfrom one end of the model to the other. Triggering intervals assmall as 1 mm were used successfully using the string potentiom-eter. The automated triggering mechanism facilitated rapid acqui-sition of hundreds of pulses in only a few seconds, compared withhours that would have been necessary to manually advance thetransducers and stop each time an acquisition was desired.

Computer Hardware and Software

Data acquisition was controlled by National Instruments cardsmounted in a PXIe chassis �NI PXIe-1062Q� connected to a per-sonal computer running LabView software. The pulser was trig-gered by an arbitrary waveform generator card �NI PXI-5412�,and the receiver was sampled at 5 MHz by a high speed digitizercard �NI PXI-5620�. The string potentiometer was connected to aNI SCC-68 terminal block expansion slot and sampled using amultifunction card �NI PXI-6259�. These three cards were syn-chronized through the internal clock of the PXIe chassis.

Custom LabView software was written to trigger the ultrasonicdevice based on readings from the string potentiometer. A single

Table 3. Receiver Filter and Amplifier Properties

Component Manufacturer Product number Input po

Amplifier Mini-Circuits ZFL-500LN 15 Vd

Filter Mini-Circuits BLP-1.9 N/A

Table 4. String Potentiometer Properties

Manufacturer Product number Input power

Unimeasure, Inc. LX-PA-25 15 Vdc



recorded pulse for the 500-kHz transducers exhibited low signal-to-noise ratio, so signal stacking was used to improve signal qual-ity. Traditional signal stacking involves exciting a pulse, waitingfor all of the reflections to attenuate below the measurable level,repeating this process many times, and subsequently averagingthe recorded signals. Averaging reduces the noise amplitude,which is presumably random, while preserving the amplitude ofthe desired portion of the signal, which is presumably correlatedamong the recorded signals. The amount of time required to per-form traditional stacking would be too large to be feasible for thistest system, so a fast stacking algorithm �Brandenberg et al. 2008�was adopted in which a rapid succession of 5,000 pulses withsystematically varying time intervals between pulses was used toreduce the amount of time required to perform the stacking. The“noise” in fast stacking therefore consists of ambient vibrationsand electrical noise, and also first arrivals and reflections from the5,000 pulses. Hence the noise is not random, and does not attenu-ate as much for a given number of stacks compared with tradi-tional stacking. However, a large number of stacks can becompleted very quickly using fast stacking, and the additionaltime required to perform fast stacking did not affect the rate atwhich the device could be advanced along the length of the model�at an approximate rate of about 15 mm/s�. Traditional stackingwould have required a slower, more inconvenient approach inwhich the transducers were held in one place while the stackingprogressed, which would have significantly impeded data collec-tion and image construction.

Fast stacking was not applied for the 100-kHz transducers be-cause �1� the signal-to-noise ratio of a single pulse was alreadyhigh and stacking was not required to obtain high-quality signalsand �2� fast stacking is not appropriate for signals with an alreadyhigh signal-to-noise ratio because the large-amplitude first arriv-als and reflections appear as noise in the stacked signal. Tradi-tional stacking could improve the already good signal-to-noiseratio, whereas fast stacking could degrade it. The recorded pulseswere written to file at each specified trigger point, and metadatacontaining the sampling frequency, trigger points, and other sa-lient information were written as a header and appended to therecorded voltage vectors.

Transducer Directivity

Transducer directivity characterizes the amount of wave energyomitted and recorded at inclined angles from the transducer axis,and can be conceptualized by analogy to a flashlight that can beadjusted to emit a narrow focused beam of light �narrow directiv-ity� or a wider beam �broad directivity�. As a general trend forultrasonic transducers, higher diameter-to-wavelength ratios ex-hibit narrower directivity patterns �e.g., Krautkramer and Krau-

Pass band Low-pass corner frequency Gain

0.1–500 MHz N/A 24 dB min

N/A 2.5 MHz N/A

Range Linearity Sensitivity

625 mm �25 in.� �0.5% 1.546 mV/V/mm

wer

c


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tkramer 1990�. The diameter-to-wavelength ratios for thetransducers in this study were 6.33 and 3.33 for the 500- and100-kHz transducers �assuming p-wave velocity of 1,500 m/s�,respectively; hence the 500-kHz transducers have a narrower di-rectivity pattern. Directivity can affect p-wave reflection imagesin a number of important ways that must be understood wheninterpreting results from an image. First, transducers with strongdirectivity may not receive returns from off-axis or dipping re-flectors. Strong directivity may be desirable when the goal is toimage a spatially limited region perpendicular to the axis of thetransducers because less postprocessing is required to identify theposition of the reflector, and the reflected signal amplitude islarge. Weak directivity may be desirable for imaging off-axis ordipping reflectors, but more postprocessing is required since re-flectors could lie in a larger geometric region and the signal am-plitude is smaller due to geometric attenuation. Second, theamplitude of a reflected signal provides information about thedomain because the reflection and transmission coefficients at aninterface are functions of the impedance contrast. Hence, the re-flection amplitudes can potentially be used to independently mea-sure the impedance of a reflector, which can be combined withtravel time to measure depth to the reflector. However, transducerdirectivity also affects the amplitude of the recorded signals, andthis effect must be removed to obtain an accurate measure ofimpedance.

To quantify directivity, consider Fig. 2, which shows an in-clined harmonic incident wavefront �represented in complex no-tation� approaching a transducer. The recorded signal can beexpressed as the average of the incident wavefront over the lengthof the transducer. The arrival time of the wavefront depends onthe horizontal position along the sensor, as given by Eq. �1�,where �t�x� is the delay in travel time at position x relative to theinitial arrival of the signal at x=0

�t�x� =x · sin��

Vp�1�

The phase lag associated with the time delay in Eq. �1� isshown in Eq. �2�, where k=� /Vp=wave number

��x� =� · x · sin��

Vp= k · x · sin�� 2�

The wavefield at position x on the transducer can then becomputed by incorporating the phase lag into the complex har-monic equation, and the recorded signal can be obtained as theaverage of the waves on the surface of the transducer, as shown inEq. �3�, where w�x� is the width of the transducer in the out-of-plane direction in Fig. 2

Recorded�x,t� =�0

Lei��·t−k·x·sin��w�x�dx

�Lw�x�dx�3�

Fig. 2. Inclined wavefront approaching sensor surface

0



For a square transducer, w�x�=L, and Eq. �3� can be solved inclosed form �Eq. �4��. For a circular transducer, w�x�=2�L ·x−x2, and the closed-form solution to the integral becomesunwieldy but can be easily solved by numerical approximation

Recorded�x,t� =�0

Lei��·t−k·x·sin��Ldx

�0LLdx

= ei�t ·i�e−i·L·k·sin�� − 1�

L · k · sin��

�4�

A transfer function can be computed between the recorded andincident waves by dividing Eq. �4� by the incident wave as fol-lows:

TF =Recorded�x,t�Incident�x,t�

=i�e−i·L·k sin�� − 1�

L · k · sin��5�

The transfer function in Eq. �5� provides a convenient meansof quantifying the wave passage effect on a square transducer ofspecific diameter and central frequency, and its amplitude is plot-ted versus L ·k · sin�� in Fig. 3. Also plotted in Fig. 3 is thetransfer function for a circular transducer, which was obtained bynumerically approximating Eq. �3� by the trapezoidal rule withw�x�=2�L ·x−x2, and dividing by the incident wave. The ampli-tude of both transfer functions is near unity when L ·k · sin�� issmall, which is in reasonable agreement with the general under-standing that small-diameter low-frequency transducers act essen-tially as point sources while large-diameter high-frequencytransducers exhibit strong directivity. For square transducers, theamplitude of the transfer function is equal to zero whenL ·k · sin��=N ·2�, where N is any nonzero integer. This corre-sponds to the condition where the transducer length is equal toone wavelength. For the circular transducers, the zero values areat slightly higher values of L ·k · sin��. The zero values indicateperfect destructive interference of the incident waves on the sur-face of the transducer. The zero values are not a problem forconvolution �i.e., when the incident wave is known and the re-corded wave is desired�, but render deconvolution �i.e., when therecorded wave is known and the incident wave is desired� nu-merically unstable �e.g., Strang and Nguyen 1997�. The transferfunctions were derived for an incident wavefield striking a re-ceiver transducer, but also reasonably characterize the far-fieldresponse of the source transducer based on the principle that eachpoint on the transducer surface is a wavefront point source.Hence, for an identical source/receiver pair, the transfer functionshould be applied twice to account for directivity of the sourceand receiver transducers.

The directivity pattern was measured for the 500- and 100-kHz

Fig. 3. Amplitude of transfer functions for square and circular trans-ducer shapes

transducers using the experimental setup shown in the inset in


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Fig. 4. An aluminum plate of thickness 9.5 mm was used as areflector in an acrylic container filled with de-ionized water. Theangle of the aluminum plate was varied and the transducers wereslid across the length of the model while p-wave reflections weremeasured at 5-mm horizontal displacement intervals. The peak-to-peak amplitude of the record from the center of the plate wasnormalized by the peak-to-peak amplitude of the record from theflat plate �i.e., �=0°�. The results clearly show that the 100-kHztransducers have a broader directivity pattern than the 500-kHztransducers. They detect more off-axis energy from reflected sig-nals and are able to see the plate at higher angles. The amplitudeversus angle relation was also estimated using Eq. �3� by �1�taking the Fourier transform of the reflection recorded with theplate at �=0°; �2� multiplying the Fourier coefficients by the cir-cular transducer transfer function twice to account for convolu-tion of the signal through the source and receiver; and �3� settingthe transducer width and frequency �see Table 1� to their respec-tive values and varying the reflection angle from 0° to 45°. Thelines on Fig. 4 exhibit similar trends with the recorded data, andgenerally overpredict the measured amplitudes. Additionalsources of amplitude reduction in the experiment may arise frommodes of wave propagation inside the transducer �not accountedfor in Eq. �3�� and mode conversion of the inclined p waves as pand s waves at the aluminum/water interface.

The influence of directivity on the character of the recordedsignals is further explored in Fig. 5. Each plot shows a singlevoltage signal from the reflection at the plate for three values ofthe plate angle. For the 500-kHz transducers, the amplitude de-cays rapidly as the plate angle increases, and by an angle of 10°,the signal has diminished so much that significant amplification isnecessary to discern the signal quality. The 100-kHz transducershave a broader directivity pattern and the resulting signals are lessaffected by plate inclination.

Migration

Consider a sequence of p-wave reflection recordings from asource/receiver pair at the same position along a line on theground surface with a point reflector embedded below the ground�Fig. 6�. When the source-receiver pair is directly over the pointreflector, the travel time of the reflection will equal the ray pathlength divided by the p-wave velocity of the soil �i.e., Point 1�,where the ray path length is two times the depth of the reflector toaccount for two-way wave passage. However, the point reflectorwill also reflect waves when the source/receiver pair is at a pointon the ground surface that is offset horizontally from the point

Fig. 4. Measured and predicted amplitudes for 500- and 100-kHztransducers for various reflector plate inclination angles

reflector. The reflection will arrive at a later time �i.e., at Point 2�



because the ray path is longer due to the vertical and horizontalcomponents. An image of the subsurface can be constructed byplotting each reflection at its recorded position along the horizon-tal axis, and by converting the timescale to depth by multiplyingby half of the p-wave velocity �to account for two-way wavepassage�. Imaged in this manner, a point reflector will appear as ahyperbola with the apex at the reflector position. By postprocess-ing the recorded image using migration, the hyperbola can becollapsed to a single point, thereby locating the true-reflector po-sition.

The simplest form of migration, called Kirchhoff migration,involves summation of reflection records over the possible reflec-tor positions. For the recording at Point 2 in Fig. 6, the possiblereflector positions lie on a semicircle that extends to the groundsurface if the seismic source is a point source, and intersects thehyperbola at the apex �i.e., at the true-reflector position�. Thesemicircles of possible reflector positions for each point along thehyperbola also pass through the apex of the hyperbola. The sum-mation of the semicircles for each point in the record results inconstructive interference of the records at the true-reflector posi-tion, and destructive interference at nonreflector positions, asshown in Fig. 7 for superposition of three separate semicircles

Fig. 5. Signals recorded at various plate inclination angles for the500- and 100-kHz transducers

Fig. 6. Diffraction hyperbola for a point reflector, and semicirculararc of possible reflector positions for recording above Point 2


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along a dipping reflector. The result is a high-amplitude signal atthe true-reflector position, and low-amplitude signals at other po-sitions. Summation over the semicircles of possible reflector po-sitions is an intuitive way to understand this simple form ofmigration, but for ease of implementation in practice, migration istypically performed by summing over diffraction hyperbolas foreach point in the migrated section �e.g., Gray et al. 2001�. Migra-tion collapses diffraction hyperbolas to single points, and alsorepositions dipping reflectors to their true positions. The premi-grated image of a dipping reflector renders the reflector with aflatter angle and larger length, and migration moves the dippingreflector up-dip and shortens it �e.g., Yilmaz 1987�.

Several forms of migration exist including Kirchhoff�Schneider 1978�, finite difference �Claerbout and Doherty 1972�,reverse time �Baysal et al. 1983�, and frequency-wave-numbermigration �Gazdag 1978�. All of the aforementioned methods intheir own ways attempt to resolve aspects of the wave equation inorder to model wave paths within the domain and properly imagethe subsurface, and each has its limitations. Kirchhoff migrationcannot account for horizontal variations in wave velocity, or forcurved ray paths due to diffraction. Finite-difference migrationcan account for these aspects, but at an increase in computationalcost and effort. This study implemented a Kirchhoff migrationalgorithm that sums over diffraction hyperbolas because it is thesimplest form of migration and offers a robust level of versatilityand accuracy �e.g., Gray et al. 2001�. The algorithm proceeds bydefining a position in the migrated image �x1 ,z1�, and solving forthe diffraction surface by representing the depth z2 as a functionof horizontal position x2, as defined in Eq. �6�, where dx is thespacing between sensors. Directivity of the transducers limits theangles at which reflectors can be “seen,” so an aperture angle of16° was used to limit the horizontal extent of the diffraction sur-faces �i.e., reflector positions more than 16° off center from thesensor positions were omitted in the migration algorithm�. Thepoint in the migrated image is treated as a pixel, where the pixelvalue is equal to the sum of the pixel values along the diffractionsurface. The pixel values are subsequently mapped to an 8-bitgrayscale image �i.e., with values ranging from 0 to 255� by firstthresholding the pixel values by setting negative values to zero,and subsequently linearly mapping to the 8-bit values

z2 = ��x1 − �x2 + dx/2��2 + z12 + ��x1 − �x2 − dx/2��2 + z1

2 �6�

Fig. 8 shows the results of the Kirchhoff migration algorithmimplemented in this study for the case of a 70-mm-long alumi-num plate at an angle of 10° in an acrylic container filled withde-ionized water using the 500-kHz transducers. Figs. 8�b and c�are reflection images of the unmigrated and migrated data, respec-

Fig. 7. Constructive interference of waves at true-reflector positionduring Kirchhoff migration

tively. In the unmigrated section, the plate appears to lie in the



horizontal range between 60 and about 180 mm at an angle ofabout 9°. The migrated image moves the dipping reflector up-dipto its true position between 100 and 170 mm at its true angle of10°. The accuracy in the reflector’s size and position comes at theexpense of noisy artifacts from the migration algorithm, wheredestructive interference of records at nonreflector positions hasfailed to render zero signal amplitude. The upper right corner ofthe plate acted as a point source and produced a diffraction hy-perbola that was collapsed by migration, rendering a sharper edgein the migrated image.

Soil Model Imaging

Fig. 9 illustrates the three-dimensional soil model used in thisstudy, which was constructed to observe the ability of the systemto image objects with irregular surfaces, dipping soil layer con-tacts, and to measure spatial resolution. The material properties ofthe model constituents are summarized in Table 5. The internaldimensions of the model were approximately 550 mm in length,

Fig. 8. �a� Schematic of directivity experiment; �b� recorded section;and �c� migrated section

420 mm in width, and 300 mm in depth. Uniform 60-mesh silica


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sand was air pluviated to form two distinct layers with loose sandover medium-dense sand with a horizontal contact on the rightside of Fig. 9, and a dipping contact on the left side. The differ-ence in densities was achieved by varying drop height. A concretebase with an undulating surface of varying spatial frequency wasplaced at the bottom of the model to test the resolution of thesystem, a high-impedance anomaly composed of concrete formedinto an irregular cylindrical shape was embedded into the loosesand layer, and a low-impedance anomaly composed of an emptylow-density polyethylene �LDPE� water bottle was embedded inthe medium-dense sand layer �Fig. 10�. The properties of theLDPE were based on manufacturer specifications because thewall thickness of the bottle was too small to accurately measureits properties. These embedded objects extended through onlyhalf of the width of the model so that the soil layer contacts on theother half could be imaged without embedded anomalies. Themodel was saturated by placing the inside of the container undervacuum, and subsequently dripping deaired water through tubesto the bottom of the model. The LDPE water bottle collapsedwhen the vacuum was released from the container, and its ap-proximate shape and position before and after saturation areshown in Fig. 9. Collapse of the bottle also caused the soil surfaceto settle.

Fig. 11 compares two unmigrated sections measured using the500-kHz transducers to show the influence of fast signal stacking.Fig. 11�b� shows the stacked section, which is a much cleanerimage compared with the unstacked section in Fig. 11�a�. Thenoise in Fig. 11�a� somewhat obscures the soil-water interface,dense-loose sand interface, and the concrete base, all of which areclearer in the stacked section. Fast signal stacking was not per-formed for the 100-kHz transducers because it did not improvethe already good signal-to-noise ratio.

Figs. 11�a and c� and , a and c� show images obtained usingthe 500- and 100-kHz transducers from the half of the model

Table 5. Material Properties

Material type GS

D50

�mm� USCS symbo

Dense sanda 2.67 0.31 SP

Loose sanda 2.67 0.31 SP

Concretea — — —

LDPEb — — —aMeasured.b

Fig. 9. Schematic of three-dimensional model with inclined soillayer interfaces, undulating concrete base, and embedded anomalies

Reported by manufacturer.



without, and with the embedded anomalies, respectively. Thequality of the 500-kHz image is superior due to the higher fre-quency �and shorter wavelength� and associated higher resolution,which renders thinner black lines for each reflection, and higherdamping �and less ringy signals�, which manifests as fewer blacklines for each reflection. Clearly the 500-kHz transducers aremore appropriate for imaging the model studied in this paper, andgenerated superior images compared with the 100-kHz transduc-ers. However, 100-kHz transducers render larger amplitude re-flections that might be superior for larger models or for modelswith larger particles, where the reflection amplitude of the 500-kHz transducers might become immeasurable. This illustrates theinherent trade-off between resolution and the distance the wavescan propagate, and shows that the optimum frequency is the high-est frequency that can transmit measurable waves to the desireddepth.

Figs. 12�b and d� and 13�b and d� show the migrated sections,where each section was migrated in two dimensions by summingover diffraction hyperbolas. The influence of migration is clearlyevident for the 500-kHz transducers, while little difference is evi-dent for the 100-kHz transducers. Comparing the images from the500-kHz transducers in Figs. 13�a and b�, the most strikingchange caused by migration was the quality of the concrete baselayer. The concrete base layer in the unmigrated section exhibiteda bowtie pattern that is characteristic of unmigrated images ofundulating reflectors �e.g., Yilmaz 1987�. Migration untied thebowties and rendered an accurate image of the undulating con-crete base layer. Furthermore, the diffraction hyperbola from thetop of the water bottle apparent in the unmigrated image col-lapsed to nearly a point at the top of the bottle. Migration had alittle influence on the quality of the concrete cylinder, and intro-duced a small amount of undesired noise into the 500-kHz im-ages. Regarding the images from the 100-kHz transducers, theundulations in the concrete base layer are not readily apparent and

e�

�kg /m3�VP

�m/s�Z=�VP

�kg /m2 s�

0.69 1,990 1,556 3.10106

0.92 1,870 1,532 2.86106

— 2,237 2,588 5.79106

— 920 1,950 1.79106

Fig. 10. Photo of textured concrete base, high-impedance concreteanomaly, and low-impedance LDPE bottle out of the model aftertesting

l


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would likely go unnoticed without a priori knowledge of the ge-ometry of the base. The ringiness and lower frequency of the100-kHz transducers are responsible for the poorer image quality,and clearly illustrate the importance of transducer selection inp-wave reflection imaging.

Fig. 14 illustrates the results of overlaying the migrated imagefrom the 500-kHz transducer signals with measurements taken byhand of the surface of the concrete base layer, with the verticalaxis expanded to more clearly show detail. The migrated imageaccurately characterized the geometry of the concrete base layer,particularly for the low-frequency spatial undulations on the rightside of the figure. The image on the left side of the migratedsection is less clear, though the undulations are evident even forthe shortest spatial period of about 40 mm �left side of Fig. 14�. Ingeneral, the peaks and valleys are clearly evident, while theslopes in between are less clear. This is due to the influence ofdirectivity and the fact that the peaks and valleys act essentially asflat reflectors. A general rule of thumb for locating the depth of areflector is that transducer resolution is equal to one wavelength,but Fig. 14 indicates that lateral resolution is poorer. The wave-length for the 500-kHz transducers was approximately 3 mm�wavelength=Vp / f�, but the concrete base layer was already be-coming unclear at a spatial period of 40 mm. Furthermore, thewavelength for the 100-kHz transducers was approximately 15mm, but the concrete base layer was not clear in the images evenat the largest spatial period of more than 100 mm. Hence, the ruleof thumb that resolution is equal to one wavelength should not beapplied for horizontal resolution, and the resolution of a testing

Fig. 11. Image of one plane of three-dimensional soil model using500-kHz transducers �a� without fast signal stacking; �b� with fastsignal stacking

Fig. 12. Images of one plane of three-dimensional soil model with-out embedded anomalies using ��a� and �b�� 500-kHz transducers and��c� and �d�� 100-kHz transducers ��a� and �c�� before migration and��b� and �d�� after migration



system should be carefully characterized prior to any experimen-tal study to verify that experimental requirements are met.

A three-dimensional image of the model was constructed bycollecting two-dimensional scans at 5-mm intervals along thewidth of the model, forming a 5-mm square grid of measurementsin plan view. The voltage values were mapped to voxels �i.e.,three-dimensional pixels� using the software package Voxler�manufactured by Golden Software �Golden, Colo.��. The shadeof each voxel was proportional to the amplitude of the voltagevalue from the migrated sections of the records. Fig. 15 showstwo snapshots of the three-dimensional image generated by the500-kHz transducers. Fig. 15�a� is a side view of the model simi-lar to those presented in Figs. 12 and 13, and Fig. 15�b� is aperspective view from one corner of the model. All of the majorfeatures of the soil model are clearly visible, including the con-crete base layer, water bottle, concrete anomaly, and soil layercontact. Shadowing artifacts are apparent in Fig. 15�b� on theconcrete base and soil layer contacts where the embedded anoma-lies reflected so much of the energy from the compressive wavesthat the amplitude of the transmitted waves was too low for im-aging purposes. The concrete anomaly is clearer in the three-dimensional image in Fig. 15�a� than in the two-dimensionalsection �see Fig. 13�, which is caused by superposition of voxelshades in the direction perpendicular to the plane of Fig. 13. Thewater bottle was imaged approximately as a line above the loose/dense sand interface, which is consistent with the shape of thecollapsed bottle. The bottle also rotated as it collapsed, becoming

Fig. 13. Images of one plane of three-dimensional soil model withembedded anomalies using ��a� and �b�� 500-kHz transducers and ��c�and �d�� 100-kHz transducers ��a� and �c�� before migration and ��b�and �d�� after migration

Fig. 14. Comparison of 500-kHz p-wave reflection image of con-crete base superposed on shaded region of hand measurements �ver-tical scale is exaggerated to show detail�


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higher near the center of the model than at the boundary. Thisinformation would be difficult to discern from multiple two-dimensional sections, but is clear in the three-dimensional image.Finally, Voxler permits the user to rotate the three-dimensionalimage to observe it from any desired perspective, and the abilityto move the image renders a clarity of the embedded objects thatcannot be captured in a still shot �which cannot be demonstratedin this paper�.

Discussion

The p-wave reflection imaging system and postprocessing meth-ods presented in this paper are admittedly simplistic comparedwith the more advanced methods that are often used in geophys-ical and medical imaging applications �e.g., Stotzka et al. 2005;Fata and Guzina 2007�. The purpose of the paper is not to ad-vance the state of the art of acoustic imaging methods, but ratherto advance a largely unexplored application of such methods forgeotechnical physical models. These simple methods have con-siderable potential for application to soil models on the samescale as those typically tested on large geotechnical centrifuges,provided that the models can be submerged. Model geometriesare often meticulously measured by hand before testing on a cen-trifuge, and then again after testing during model dissection.However, changes that occur during testing, for example, due to asequence of simulated earthquakes, are not typically measuredand must be interpolated. This system provides a method to non-invasively monitor model geometry during testing. More ad-vanced methods that utilize tunable source transducers, pulserswith controllable arbitrary waveform outputs, more advancedpostprocessing algorithms, and tomographic imaging could pro-vide even more information and higher quality images.

Saturation of the sand is crucial for p-wave reflection imagingbecause unsaturated soil pockets have significantly lower p-wavevelocity than saturated soil at the same relative density, and there-fore pose an impedance contrast that scatters the seismic waves.In the study presented in this paper, such a high degree of satu-ration could be obtained by vacuum saturating the models, but notby water pluviation. The surface of the soil was visible in imagesof the water-pluviated soil, but reflections from the interior of the

Fig. 15. Three-dimensional p-wave reflection image using 500-kHztransducers showing �a� side view; �b� isometric view

model were not recorded, presumably because air bubbles scat-



tered the waves. In this regard, the ultrasonic testing system mayalso prove useful for verifying whether a soil model is adequatelysaturated. p waves are often used to verify saturation in soil mod-els, and the waves are often generated using p-wave hammers orby striking a plate on the soil surface with a hammer. For ex-ample, Naesgaard et al. �2007� generated p waves with frequencyin the range 3,500–7,000 Hz in a soil model with air bubbles ofcontrolled size, and found that high p-wave velocities were mea-sured even when Skempton’s B values were low �indicating poorsaturation� when the air bubbles were large. They explained thatthe p waves may propagate through a saturated soil matrix, by-passing and masking unsaturated pockets. The ultrasonic systempresented in this paper would not mask unsaturated pockets, butrather could potentially be used to image the size and position oflarge air bubbles �at least as small as about 40 mm for the 500-kHz transducers based on Fig. 14�.

The 500-kHz transducers produced high-resolution images,while the 100-kHz transducers produced ringy images with com-paratively poor resolution. Clearly the 500-kHz transducers aremore appropriate for the particular models tested in this paper, butlower frequencies may be desired for larger or more attenuativemodels. Spiking deconvolution �e.g., Stotzka et al. 2005� can im-prove the resolution of p-wave reflection images by compressingthe recorded signal in time with the goal of replacing the reflec-tion with a “spike” at the reflector position. Spiking deconvolu-tion could potentially improve the ringiness of the 100-kHzsignals, but was beyond the scope of this paper.

Conclusions

An ultrasonic p-wave reflection imaging system was used to con-struct images of submerged soil models with embedded anomaliesand complex geometric layer contacts. The transducers were heldin contact with water above the soil model, and manually slidacross the model while p waves were transmitted and recorded atspecified positions. Fast signal stacking was used to improvesignal-to-noise ratio and provide clearer images. Transducer di-rectivity was shown to affect the recorded images, and transferfunctions were derived for square and circular transducers toquantify directivity. The transfer functions agreed well with mea-sured data. A Kirchhoff migration algorithm was implemented toproperly image dipping reflectors. High- and low-impedanceanomalies were clearly visible in the recorded images, as were thecontact between loose and medium-dense sand layers and theundulating concrete base layer. The lateral spatial resolution ofthe migrated images was shown to be worse than one wavelength�a common rule of thumb for vertical resolution�. p-wave reflec-tion imaging has significant potential in geotechnical site investi-gation for imaging laboratory soil models �as demonstrated in thispaper� and also in the field. More work is required to transitionthis well-established imaging technique to the geotechnical fieldand laboratory scale.

Acknowledgments

The writers would like to thank Navid Shirazi for helping tocharacterize the sand properties by various air pluviation tech-niques. Funding for the project was provided by UCLA and
nees@UCLA.

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2010.136:1358-1367.

p -wave reflection imaging of submerged soil models using ultrasound

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