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GEOPHYSICS, VOL. 73, NO. 3 �MAY-JUNE 2008�; P. G1–G6, 9 FIGS.10.1190/1.2901215

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ield investigation of Love waves in near-surface seismology

obert Eslick1, Georgios Tsoflias1, and Don Steeples1

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ABSTRACT

We examine subsurface conditions and survey parameterssuitable for successful exploitation of Love waves in near-surface investigations. Love-wave generation requires theexistence of a low shear-velocity surface layer. We examinedthe minimum thickness of the near-surface layer necessary togenerate and record usable Love-wave data sets in the fre-quency range of 5–50 Hz. We acquired field data on a hillsidewith flat-lying limestone and shale layers that allowed for thedirect testing of varying overburden thicknesses as well asvarying acquisition geometry. The resulting seismic recordsand dispersion images were analyzed, and the Love-wavedispersion relation for two layers was examined analytically.We concluded through theoretical and field data analysis thata minimum thickness of 1 m of low-velocity material isneeded to record usable data in the frequency range of inter-est in near-surface Love-wave surveys. The results of thisstudy indicate that existing guidelines for Rayleigh-wavedata acquisition, such as receiver interval and line length, arealso applicable to Love-wave data acquisition.

INTRODUCTION

Surface-wave methods are a subset of near-surface seismic tech-iques. First introduced for near-surface applications in the 1950sJones, 1958�, surface-wave methods became viable along withore conventional near-surface seismic techniques, i.e., reflection

nd refraction, in the early 1980s �Steeples, 2005�. Since that time,urface-wave methods have improved and expanded from the spec-ral analysis of surface waves �SASW� �Nazarian et al., 1983� to

ultichannel analysis of surface waves �MASW� �Park et al., 1999�;he latter includes procedures for both passive and active sourcesPark et al., 2007� as well as methods of utilizing higher-mode ener-y �Xia et al., 2000a�.

To date, surface-wave techniques have focused mostly on the ac-uisition and inversion of Rayleigh-wave data. A strong foundation

Manuscript received by the Editor 17 May 2007; revised manuscript receiv1University of Kansas, Lawrence, Kansas, U.S.A. E-mail: rocyes@yahoo.2008 Society of Exploration Geophysicists.All rights reserved.

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f theoretical and field studies has proven these methods reliable andseful in many geotechnical and environmental applications �Xia etl., 2000b; Miller et al., 1999a; Miller et al., 1999b�. Very limitedork on the use of Love waves has been reported in the literature

Lee and McMechan, 1992; Li, 1997�.Love waves are seldom used in near-surface investigations be-

ause of the relative difficulty in systematically producing a shear-ave signal and because they require horizontal geophones. Loveaves typically are considered an unwanted signal in near-surface

hear-wave reflection surveys �Miller et al., 2001�. At early times oneismograms collected with horizontal geophones, Love waves rou-inely dominate the seismic record and appear in the same phase-ve-ocity range as reflections of interest. With increasing capability andecreasing cost of technology, it is becoming more viable to designhear-wave or multicomponent surveys in the near-surface.

Potentially, Love waves can yield shear-wave velocity profilesith little change to the Rayleigh-wave procedure. Zeng et al. �2007�

nd Song et al. �1989� show that Love waves generally are more sen-itive to S-wave velocity changes and layer thickness changes thanayleigh waves. An inherent difference is that Love-wave methodsstimate horizontal shear-wave velocity, whereas Rayleigh-waveethods estimate vertical shear-wave velocity. Joint inversion ofove and Rayleigh data may yield information about subsurface an-

sotropy �Safani et al., 2005�, such as the presence of fractures.Extensive literature about Love waves, including the mechanics

f propagation and dispersion, comes from earthquake seismologynd theoretical physics �e.g., Sezawa and Kanai, 1937; Anderson,962; Drake, 1980; Kelly, 1983; Kim, 1992; Guzina and Madyarov,005�. However, Love-wave surveys in the near-surface have beensed and reported on only a few occasions �Jones, 1958; Song et al.,989; Safani et al., 2005�. The utility of the method and acquisitionuidelines have not been investigated thoroughly. Several studiesddressing these issues have been completed for Rayleigh wavesBeaty and Schmitt, 2003; Zhang et al., 2004�. As surface-waveechniques continue to become attractive alternatives to other inva-ive and geophysical methods for near-surface site characterization,t is important to understand their applicability.

Our objective is to determine the limiting thickness for a low-ve-ocity layer in order to record a usable Love-wave data set in near-

ptember 2007; published online 1 May 2008.flias@ku.edu; don@ku.edu

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urface seismology. By recordable, we mean that Love waves can bebserved in the seismic record; by usable, we mean that the recordan yield a well-formed dispersion image. We create the imagesrom multichannel records with the process used by Park et al.1998� for Rayleigh waves. Acquisition parameters for Love-waveurveys follow Rayleigh-wave acquisition guidelines described inhe MASW method �Park et al., 1999�.

THEORETICAL CONSIDERATIONS

Surface waves travel mostly within one seismic wavelength of thearth’s surface. They spread two-dimensionally and undergo energyecay at a rate of 1/r, where r is the radial distance from the source.ody waves spread three-dimensionally, and their energy decays at/r2. Rayleigh waves result from the interference of P- and SV-aves below a free surface. Their particle motion is retrograde ellip-

ical and is confined to a nearly vertical plane in the direction of prop-gation. Love waves consist of only interfering SH-wave energy andave particle motion transverse to the direction of propagation. Ray-eigh waves can exist in a half-space, although they are not disper-ive if it is homogeneous and isotropic. Love waves are guidedaves that are totally internally reflected. They require that a low-

igure 1. Two-layer model. Medium 1 is the waveguide; medium 2s the half-space. The properties of each medium are described byheir P- and S-wave velocities � and � , respectively, and density �.he thickness of the waveguide is H.

igure 2. Theoretical dispersion curves for the model in Figure 1.he modes are numbered from the fundamental mode �0� to the

ourth-higher mode �4�.

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elocity layer �or waveguide� of some thickness H be present �seeigure 1�.One form of the Love-wave dispersion relation for the two-layer

ase is given by Aki and Richards �2002� as

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here propagation is in the x-direction; � is angular frequency; cx ishase velocity; � 1, � 2, �1, and �2, are the shear-wave velocities andhear-moduli of the waveguide and half-space, respectively; and Hs the thickness of the waveguide.

We can see by examining this relation that Love-wave dispersionor horizontal layers is independent of P-wave velocity �; given theelation cx�� /�x, there are corresponding wavenumber � andhase velocity pairs that satisfy the relation for any given frequency.he solution with the lowest phase velocity is the fundamentalode; other solutions constitute higher modes. The solution to the

elation must also satisfy � 1 �cx �� 2. This implies the phase veloc-ties of low frequencies will approach the shear-wave velocity of thealf-space � 2, and at high frequencies Love-wave phase velocitiesill approach the velocity of the waveguide � 1.We evaluated equation 1 with typical near-surface parameters �� 1

150 m/s, �1 � 1600 kg/m3, � 2 � 500 m/s, �2 � 1800 kg/m3, and H4 m� and plotted the dispersion curves for this model, including

igher modes, in Figure 2. Our analytical models agree with pub-ished results from Pelton �2005� and are further verified by replicat-ng results from Stein and Wysession �2003� and Aki and Richards2002�. Multiple frequency/phase-velocity pairs satisfy equation 1,hich gives rise to higher modes. The separation between the modes

s given by the cutoff frequency � �Stein and Wysession, 2003�:

� �

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We show the effect of changing H, when only the fundamentalode is considered, in Figure 3.As H approaches zero m, the disper-

igure 3. Theoretical fundamental mode dispersion curves for the

odel in Figure 1 as a function of waveguide thickness H.

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ion curve extends well beyond the frequency range obtainable inhe field �commonly �50 Hz�. As H increases, the dispersion curverops into the frequency range of interest; when H is greater than 1, the entire curve can be observed from 5 to 100 Hz.As H increas-

s beyond 1 m, the slope of the dispersion curve becomes steepernd the frequency range at which cx approaches � 2 becomes increas-ngly narrow.

Figure 4 illustrates the effect of H on the formation of higher-ode energy. As H increases, � decreases such that at greater

hicknesses the separation between the fundamental mode and high-r modes decreases. Smaller values of H give the fundamental modewider frequency range over which to exist before there is the possi-ility of higher mode contamination, i.e., small waveguide thick-esses are favorable in terms of avoiding higher-mode contamina-ion.

We also examined the effect of velocity contrast between the low-elocity waveguide and the underlying half-space using equation 1.igure 5a shows a plot where H and � 1 are held constant at 4 m and50 m/s, respectively, and where � 2 varies from 1.01 to 10 times � 1.aintaining constant waveguide velocity while changing � 2 does

ot significantly change the range of frequencies at which cx ap-roaches � 1 or � 2, but it does change the slope of the dispersionurve between the minimum and maximum values. As the slope ofhe dispersion curve becomes increasingly steep �or as the velocityontrast becomes increasingly large�, the frequency band overhich it occurs becomes increasingly narrow and more difficult to

ecord. Varying the waveguide velocity, i.e., contouring � 1, andolding � 2 constant �Figure 5b� exhibits broader changes in theange of frequencies at which cx approaches � 1 or � 2 as well as in thelope of the dispersion curve.

Phase velocity ultimately controls the wavelengths in the record-d data. Wavelength � is related to the phase velocity and frequency

f by � � cx/f . Recording long wavelengths necessitates longer re-eiver lines, which increases the subsurface area being averaged andan introduce far-field effects during dispersion-curve extractionnd inversion. In high-velocity environments, wavelengths can

igure 4. Cutoff frequency for the model in Figure 1 as a function ofaveguide thickness H.

engthen and at some point become impractical for near-surfaceove-wave surveys.It is important to consider these relations because they have sig-

ificant implications when acquiring and interpreting Love-waveata.

FIELD METHOD

A field site over a road cut south of Clinton Lake dam in Douglasounty, Kansas, allowed for the direct testing of the effect of H on

he ability to collect Love-wave data in the field. For the currenttudy and based on a priori information, the site is parameterizedith two layers. The top layer consists of unconsolidated soils and

roded shale that form a hill that slopes at 25° to 35° and has a maxi-um accessible thickness of 4 m. It is underlain by the Plattsmouthimestone, which has an exposed thickness of 5 m below the hill-

orming overburden. The limestone layer is laterally continuousver a large area and constitutes a horizontal layer. The limestoneayer was assumed thick enough, relative to time and offset range ofnterest, to be considered a half-space for this study. The field site is

a)

b)

igure 5. Theoretical dispersion curves for varying layer velocityontrast while maintaining waveguide thickness constant: �a� � 1 iseld constant at 150 m/s and � 2 varies from 1.01 to 10 times � 1.aintaining constant waveguide velocity while changing � 2 does

ot significantly change the range of frequencies at which cx ap-roaches � 1 or � 2. �b� Varying � 1 and holding � 2 constant exhibitsroader changes in the range of frequencies at which cx approaches

or � as well as in the slope of the dispersion curve.

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n excellent analog to the model described by the dispersion relationiven in equation 1.

We acquired several data sets at the field site to test the effect of Hnd acquisition parameters on Love-wave data usability. Using theop of the limestone as the zero elevation datum �H � 0 m�, welaced receiver lines at H � 0.5, 1.0, 2.0, and 4.0 m �see Figure 6�.ach line consisted of 144, 4.5-Hz horizontal geophones at an inter-al of 0.25 m. A 5-lb sledgehammer and a shear block were used ashe seismic-energy source, which was located 0.25 m off the northnd of each line.

RESULTS AND DISCUSSION

Raw, relative-amplitude seismograms acquired over varyingaveguide thicknesses are shown in Figure 7. We can observe Loveaves on all records; however, the offset range over which they

xtend and their frequency content change significantly with wave-uide thickness H. At H � 0.5 m, the relative energy of the Love-ave component of the record dissipates within 10 m of offset and

he dominant frequency in the seismic record is roughly 35 Hz.As Hncreases, the offset range at which Love waves are present increas-s, and the dominant frequency decreases.At H � 4 m, Love wavesominate the entire record from 0 to 36 m of offset, and the domi-ant frequency is 20 Hz.

Analysis of the first arrivals gives � 1 and � 2 estimates of 100 and00 m/s, respectively. Although the first arrival appears before theove waves, it is difficult to interpret because of the low signal-to-oise ratio. However, dispersion images created from all recordsive reliable estimates in accordance with direct arrivals for � 1 of00 m/s. Figures 8 and 9 show the dispersion images and interpretedispersion curves for the lines at H � 1.0 and 4.0 m, respectively.he shape of these curves is consistent with the analytical models

igure 6. Field experiment setup. Receiver lines consisting of 144,.5-Hz horizontal geophones at an interval of 0.25 m and a near-off-et distance of 0.25 m were used to collect data at four differentaveguide thicknesses.

igure 7. Raw, relative-amplitude seismic records corresponding toifferent waveguide thicknesses. Love-wave energy dissipates by00 ms and 10 m of offset on the first record �H�0.5 m�; on the lastecord �H�4 m�, it persists over the entire range of offsets to about50 ms.

igure 8. Dispersion image created from the receiver line at H�

igure 9. Dispersion image created from the receiver line at H�.0 m with interpreted dispersion curve.

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Figure 3�, where at H � 1.0 m the curve has a gentler slope over aarger range of frequencies and at H � 4.0 m it becomes steeperver a smaller range of frequencies. Both of these curves aresymptotic to about 100 m/s �� 1� at higher frequencies but becomembiguous at low frequencies, making � 2 difficult to interpret. Fromhe dispersion curve at H � 4 m it is possible to independently inter-ret � 2 to be approximately 700 m/s at 10 Hz, which agrees with theefraction velocity. However, there is increasing uncertainty in fre-uencies less than 12 Hz where the phase velocity is 400 m/s, yield-ng a � of approximately 33 m — about the length of the receiverine.

The energy below 28 Hz in Figure 8 and below 12 Hz in Figure 9s distorted because of misrepresented longer wavelengths relativeo the receiver line length and other noise such as incidentally in-luded body-wave energy, which obscures the upper boundary � 2.he layer thickness is a controlling factor in producing usable dis-ersion curves from Love-wave data at low frequencies. Figure 8hows the dispersion curve from H � 1 m; at a phase velocity of00 m/s, the frequency is 28 Hz, giving a � of approximately 7 m.ven though the receiver line was five times that length, frequencieselow 28 Hz are practically unusable.

Smaller waveguide thicknesses effectively restrain the lower fre-uencies or longer wavelengths from being generated. Theoretical-y, as shown in Figure 3, at thicknesses less than 1 m, the frequencyange over which the dispersion curve is asymptotic to � 2 becomesarge and should be relatively clear. However, in field data collectedhere H is less than 1 m, the low-frequency component is missing

nd the range of offsets over which Love waves propagate becomesmall. This essentially makes � 2 impossible to interpret from a dis-ersion curve created from data collected where the overburdenhickness is less than about 1 m.

CONCLUSION

Love-wave generation is dependent upon the presence of a slowhear-velocity waveguide below the free surface. The thickness ofhat layer directly relates to the ability to record usable data. We ob-erved Love waves on seismic records where the thickness was asmall as 0.25 m, but they did not become usable until waveguidehickness was greater than 1 m. The two-layer case study providesnsight into the conditions that must exist for near-surface Love-ave surveys to be viable. If waveguide thickness is small, regard-

ess of the velocity trend or layering within it, low-frequency energys not generated within the layer and Love waves will not propagateo the offsets needed to produce the low-frequency component of theispersion image. This cannot be overcome during data acquisitionnd constitutes the limiting case for which Love waves are applica-le.

The acquisition-parameter guidelines for Rayleigh-wave dataorked well for Love waves in this study.Any difference in field pa-

ameters between the two methods is accounted for by consideringhe corresponding shear-wave velocities and the resulting wave-engths. The most significant factors in surface-wave survey designre the highest and lowest velocity and frequency expected. Theighest velocity and lowest frequency yield the longest wavelength,hich should be approximately equal to the total line length, al-

hough there are other considerations such as the far-offset effect andhe averaging effect of the inversion procedure. The near-offset dis-ance should be greater than or equal to one-half of the longest wave-ength to avoid the near-field effect. The lowest velocity and highest

requency yield the shortest wavelength and determine receiverpacing, which should be less than or equal to one-half of the shortestavelength.Literature addressing Love waves on a global scale and from a

heoretical standpoint is widely available, and procedures for acquir-ng and utilizing Love-wave data are analogous to those for Ray-eigh-wave data, which are well studied in the near-surface. Howev-r, continued research, including procedural, numerical, feasibility,nd case studies, are needed so a basis for Love-wave surveys can beuilt and relied upon for near-surface site characterization.

ACKNOWLEDGMENTS

The authors thank Kwan Yee Cheng, Michael Christie, Gerardzarnecki, Michael McGlashan, and Steve Sloan for assistance in

he field. The authors also thank Julian Ivanov, Jianghai Xia, andick Miller at the Kansas Geological Survey for access to softwarend their helpful insight into surface waves. This research was sup-orted by the Office of Science �BER�, U.S. Department of EnergyDOE�, grant DE-FG02-03ER63656. However, any opinions, con-lusions, or recommendations expressed herein are those of the au-hors and do not necessarily reflect the views of the DOE.

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