near-surface seismology: surface-based...

IntroductionSeismic methods are geophysical techniques that in-

volve the generation and recording of seismic waves forthe purpose of mapping the subsurface. Each method isbased on the propagation of waves from an artificial sourceto a set of receivers, followed by an analysis of therecorded wavefield in terms of subsurface properties. Al-though seismic methods are conceptually not limited toany particular macroscopic scale, the emphasis here is onsource-receiver separations that range from a few meters toa few hundred meters, and on depths of investigation thatfall approximately within the same range. These linear di-mensions define the domain of near-surface seismology,and focus attention on a portion of the uppermost crust thatis of great importance to other geologic disciplines, espe-cially geotechnical engineering and hydrogeology. Sitecharacterization and the delineation of aquifers constitutethe primary practical applications of near-surface seismol-ogy, thereby explaining the many references to engineeringand groundwater methods in the applied geophysical liter-ature.

For much of its early history, near-surface seismologywas dominated by analog seismographs and the seismic re-fraction method, with depth-to-bedrock probably being themost common objective. However, the introduction of af-fordable multichannel digital seismographs in the 1980s,along with the remarkable decrease in cost of powerfuldesktop computers, has led near-surface seismologists toembrace a broader variety of methods, including the seis-mic reflection method, the surface-wave method, and vari-ous borehole methods. The application of these methods tonear-surface problems has necessarily been accompaniedby an increased emphasis on numerical modeling of seis-mic wave propagation and the application of inverse the-ory. As a result, near-surface seismology is capable of rou-tinely providing more complete information on shallowstructure and stratigraphy than ever before. It is likely thatthe most important advances in the coming years will in-

volve wider application of 3D imaging, progress in relatingseismic measurements to geotechnical or hydrologic prop-erties, and enhancements in data acquisition that lead tolower costs.

This chapter provides a survey of those near-surfaceseismic methods that are based on the deployment ofsources and receivers at the surface on land. It builds on thereview and tutorial articles by Steeples and Miller (1990)and by Lankston (1990), which appeared in the originalSEG publication on geotechnical and environmental geo-physics (Ward, 1990). The tradition established by thoseauthors is continued here by pulling together essential con-cepts and presenting them at a uniform level with consis-tent notation and terminology. Although many details mustremain unstated because the subject area is extensive, alengthy list of cited references is provided to alleviate thisdifficulty.

The next section discusses the essential aspects ofsources, receivers, and digital seismographs that are com-mon to most field experiments. Separate sections are thendevoted to each of the surface-based seismic methods thatcurrently find significant use in a near-surface context onland — the refraction method, the reflection method, andthe surface-wave method. A supplementary reference list isincluded to guide the reader to many of the peer-reviewedjournal articles on near-surface seismology that have ap-peared in the interval 1990–2004 inclusive.

Seismic Sources and FieldInstrumentation

In general, a seismic method is most effective whenthe seismic wave of interest is recorded with a broad spec-tral bandwidth and large signal-to-noise ratio. Althoughthese desirable signal characteristics are limited by thephysics of wave propagation in the earth and the ubiquityof noise, much has been done in the design of seismicsources and field instrumentation to enhance the quality ofseismic data. This section provides an overview of com-monly available sources and instrumentation for a generalsurface-based seismic field experiment on land. Importantgeneral references for this section include the treatises onexploration seismic instrumentation by Anstey (1970),

219

Chapter 8

Near-Surface Seismology: Surface-Based MethodsJohn R. Pelton1

1Department of Geosciences, Boise State University, Boise, Idaho83725; Email: [email protected].

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Evenden and Stone (1971), Pieuchot (1984), and Evans(1997), and the companion papers on high-resolution re-flection profiling by Knapp and Steeples (1986a, b).

Seismic field experiments

Surface-based seismic experiments conducted on landrequire a source to generate seismic waves, one or more re-ceivers, and a digital recording system. The source is de-ployed at a specific location on the earth’s surface or in ashallow borehole. It generates a transient seismic wavefieldthat excites receivers deployed at points on the surface thatare (usually) in the far-field. The geometric pattern of thesource and the receivers on the surface is called the spread.The spread may be arranged along a straight or curved lineor it may be distributed areally over any portion of the sur-face. The horizontal distance between a source and re-ceiver is called the offset for that source-receiver pair. Aninline offset spread is arranged along a straight line withthe source located at one end but separated from the near-est receiver by nonzero offset; the inline offset spread issaid to be reversed if sources are located at both ends. Asplit spread is arranged along a straight line with the sourcelocated at the center of the receivers. Many other types ofspreads are possible; Figure 1 schematically illustrates someexamples.

A receiver is an electromechanical transducer (or setof interconnected transducers) that is fixed to the earth andconverts ground motion to an analog electrical voltagecalled the seismic signal. For each source effort, the seis-mic signal from each receiver is digitally recorded by arecording system called a seismograph. The digitally re-corded seismic signal from a given receiver for a givensource effort is called the recorded signal for that sourceeffort and receiver; the term trace is commonly used torefer to the recorded signal or its analog equivalent. Thecollection of all traces from a given source effort is calleda field record and is an example of a common-sourcegather or common-shot gather. The source effort may berepeated multiple times at each of multiple source loca-tions for multiple deployments of the receivers until suffi-cient data are collected for analysis. Although there is

considerable variation, the parameters for most near-sur-face seismic experiments on land will fall within the rangeof 1–1000 field records, with each record consisting of1–120 traces, and each trace consisting of 1000–10 000digital samples.

Sources

An ideal seismic source is a safe, cost-efficient, and re-peatable generator of a seismic wavefield of broad spectralbandwidth and adequate signal strength at each receiver.The development of a source approaching these characteris-tics is a difficult problem that has been addressed by manyseismologists and engineers. Of the numerous sources nowavailable, most can be classified as one of the following: asingle impulsive source, a swept frequency source, or a mul-tiple impulsive source.

A significant number of source comparison tests havebeen published to assess source characteristics in variousgeologic settings (Miller et al., 1986; Miller et al., 1992;Miller et al., 1994; Buhnemann and Holiger, 1998; Doll etal., 1998; Herbst et al., 1998; van der Veen et al., 2000).Perhaps the most important findings of these source testsand the many years of cumulative experience of near-sur-face seismologists are that the relative performance ofsources is site dependent, and that the best performance ofa given source is typically observed at sites characterizedby fine-grained water-saturated sediments.

A single impulsive source imparts a force of short du-ration across a small area at the earth’s surface or within asmall volume located inside the earth. These sources in-clude chemical explosives, weight drops (both free fallingand accelerated), projectiles from firearms, sudden re-leases of compressed air or water, and electrical dis-charges. The most commonly used single impulsive sourceis the sledgehammer which offers the advantages of lowcost, portability, ease of use, and relative safety. Keiswet-ter and Steeples (1995) studied the source parameters fora sledgehammer. They found that the area of the strikingplate and the hammer mass are more important in affect-ing source performance than hammer velocity or platemass, and that the effects depend on the site. Projectilesources are also common and include vertically orientedrifles and shotguns fired in boreholes or at the surface (e.g.,Steeples, 1984; Pullan and MacAulay, 1987; Parker et al.,1993). Baker et al. (2000) found in a test of sledgehammerand projectile sources (4.5-kg sledgehammer, 30.06 rifle,and .22-caliber rifle) at two sites that the least energeticsource (.22-caliber rifle) generated more desirable high-frequency characteristics (above 250 Hz) than did the themore energetic sources.

At the high-energy end of the available single impul-sive sources in near-surface seismology, Liberty (1998)compared a compressed-air source (75-in3 land air gun) to

220 Near-Surface Geophysics Part 1: Concepts and Fundamentals

Surface

Surface

Offset

Offset

Figure 1. Schematic illustrations of (a) a reversed inline off-set spread, and (b) a split spread. Receivers are black circlesand sources are black squares. Offset for a given source-re-ceiver pair is the horizontal distance between the source andreceiver of the pair; see examples marked in each illustra-tion.

a)

b)

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a small buried explosive (one-third pound) as part of a seis-mic reflection survey in an urban setting. He found that al-though the explosive gave superior results in testing, theland air gun produced data of adequate quality and was farless limited in the urban application.

A swept frequency source is a vibrator with a smallbaseplate that is maintained in continuous contact with theground surface. The baseplate ideally displaces the under-lying surface according to a pilot signal p(t) of continu-ously varying frequency and several seconds duration. Theswept frequency source was developed primarily in the pe-troleum industry to meet the demands of the reflectionmethod for a surface source with controllable spectralcharacteristics. The primary advantages of swept fre-quency sources in near-surface reflection seismology, andseveral example applications, are described by Ghose et al.(1998).

Each trace generated by a swept frequency sourcemust be crosscorrelated with the pilot signal p(t) to pro-duce a result that is equivalent to a trace from a single im-pulsive source. The process may be illustrated in a simpleway by assuming that a trace s(t) can be adequately repre-sented by a linear shift-invariant system with additivenoise. More precisely, suppose the generation of the seis-mic wavefield can be modeled as a linear shift-invariantsystem with the source p(t) as input, and further supposethat a portion r(t) of the impulse response can be isolatedwhere r(t) is of interest to the seismologist.

The classic example of r(t) is the series of Dirac deltafunctions representing the normally incident reflection re-sponse of a layered elastic earth to a perfectly impulsivesource. The desirable portion of s(t) is then the convolutionp(t) * r(t) , and the undesired balance of s(t) is noise and isrepresented by n(t):

. (1)

Source and propagation effects and the effect of the record-ing system are not shown in equation (1) for simplicity; seeYilmaz (2001, 219–222) for a more complete convolu-tional model. Crosscorrelation of s(t) with p(t) gives amodified signal s′(t):

(2)

where the operator ⊗ indicates crosscorrelation (or auto-correlation for like signals); see Appendix A. If the band-width of the noise does not significantly overlap the band-width of the pilot signal, then by the crosscorrelation theo-rem (see Apppendix A), the noise crosscorrelation is rela-tively small, and equation (2) becomes

, (3)

where k(t) = p(t) ⊗ p(t) is the autocorrelated pilot signal(sometimes called the Klauder wavelet), and n′(t) = p(t) ⊗n(t) is the remainder from the noise crosscorrelation. Assuggested by the example in Figure 2, the function k(t) isof much shorter duration than p(t), so that equation (3) issimilar to the trace generated by a single impulsive source.

Multiple impulsive sources rapidly deliver a series ofshort-duration forces over an extended time. Similar toswept frequency sources, crosscorrelation is used to con-vert each trace to a result that is analogous to a trace froma single impulsive source. The Mini-Sosie is the bestknown multiple impulsive source; see Barbier and Viallix(1974) and Barbier et al. (1976) for a review, and Steepleset al. (1986) and Miller et al. (1988) for example applica-tions. A recent contribution is the swept multiple impulsivesource described by Park et al. (1996), which combines theideas of swept frequency and multiple impulsive sources.

Some applications in near-surface seismology involvethe use of SH-waves. A suitable source of these waves is astout timber oriented normal to the direction of an inlineoffset spread and fixed to the earth’s surface with a hold-down weight or spikes. Traces recorded with blows in op-posite directions are subtracted to enhance SH-waves rela-tive to other waves. Two sources of this type are describedby Michaels (1998).

Vertical stacking

It is possible to reduce the effect of random noise on afield record by simply adding the records from repeatedsource efforts with no change in the source location, spreadof receivers, or the recording system. This practice isknown as vertical stacking or field summing, and is based

Near-Surface Seismology: Surface-Based Methods 221

Figure 2. Pilot signal p(t) of a swept frequency source ofduration T shown in (a) is autocorrelated to produce theKlauder wavelet k(t) shown in (b). Energy in the Klauderwavelet is compact in time relative to the pilot signal, and issymmetric about zero lag.

a)

b)


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on the assumption that the source-related portion of eachtrace will add constructively while random noise will berelatively diminished by destructive interference. An im-portant prerequisite for vertical stacking is the ability of thesource to produce the same seismic wavefield from eachsource effort, a source attribute known as repeatability.

Knapp and Steeples (1986b) and Steeples and Miller(1990) have discussed the repeatability of various sourcescommonly used in near-surface seismology in terms of thelogistics of duplicating both the source mechanics and theground conditions at the source point. All modern digitalseismographs suitable for near-surface seismology are ca-pable of vertical stacking during acquisition to reduce datastorage requirements.

A simple statistical analysis of vertical stacking illus-trates its dependence on the characteristics of the randomnoise present in the traces. Consider a seismic experimentin which a highly repeatable source at a fixed location isused to generate a sequence of n traces from a fixed re-ceiver. The trace Ai(t) associated with source effort i maybe modeled as the sum of a deterministic function S(t) anda random variable Ri(t):

. (4)

The random variable Ri(t) is of unspecified distribu-tion, but it is stationary for the duration of the trace withzero mean and finite variance q2

i. The function S(t) repre-sents the error-free system response to the source-gener-ated seismic wavefield, and is referred to here as the sig-nal; the remaining portion Ri(t) of the trace is not related tothe source and is therefore called the noise.

The size of the signal relative to the noise is given bythe signal-to-noise ratio (S / N), which is defined for thepurposes of this exercise to be the ratio of the signal to thestandard deviation of the noise. Thus, the signal-to-noiseratio of trace i is

, (5)

and the signal-to-noise ratio of the vertically stacked traceis

, (6)

where the denominator in equation (6) is obtained by as-suming that the random variables Ri(t) are mutually inde-pendent. The question of whether vertical stacking resultsin an improved signal-to-noise ratio can be answered bycomparison of equations (5) and (6) for a specified set ofvariances.

One easily investigated possibility is the case in whichnoise is stationary over the entire time interval required to

obtain the n source efforts. In that case, the variance of thenoise is the same from trace to trace:

. (7)

Substitution of assumption (7) into the signal-to-noiseequations (5) and (6) shows that vertical stacking gives asignal-to-noise ratio that is larger than the single-trace ratioby a factor of ��n:

(8)

However, if the noise is not stationary during the acquisi-tion of the n source efforts, then it is possible for verticalstacking to decrease the signal-to-noise ratio relative to theratio of a single trace. For example, under conditions ofsporadic vehicle traffic, it is common for noise bursts tooccur so that one trace with excessive noise can drasticallyreduce the signal-to-noise ratio for the vertically stackedtrace. Indeed, from equations (5) and (6), it may be con-cluded that the signal-to-noise ratio of one of the singletraces is always larger than the ratio of the verticallystacked trace unless

(9)

for i = 1, 2, …, n. Because it is not efficient to carefullymonitor noise during most field operations, trace summa-tion schemes have been devised that minimize the delete-rious effect of nonstationary variance. Of possible impor-tance to near-surface seismology is diversity stacking,which has the property that the signal-to-noise ratio of thesummed trace always increases with n (Gimlin and Smith,1980). If noise bursts are a problem, and the vertical stack-ing capability of the seismograph is being utilized duringacquisition, then it may be advisable to save the individualfield records (one for each source effort) also so that moresophisticated trace summation techniques can be per-formed during processing.

Geophones and seismometers

A geophone or seismometer is an electromechanicaltransducer that converts ground motion to an analog elec-trical signal. The term geophone refers to a small light-weight device with a natural frequency of perhaps 10 Hz orgreater, whereas a seismometer is a relatively large andheavy device with a natural frequency on the order of 1 Hz.The differences are illustrated by the products of a com-pany that offers a 10-Hz geophone with 20-cm3 volumeand 75-g total mass, and a 1-Hz seismometer with 600-cm3

volume and 2-kg total mass. The design of modern geophones and seismometers is



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such that their physical robustness decreases with decreas-ing natural frequency. As a result, geophones tend to bemore suitable for rugged field use whereas seismometersneed to be handled with greater care. Practitioners of thesurface-wave method may choose seismometers, becausethe maximum attainable target depth for that method de-pends on acquisition of relatively low-frequency data (per-haps 1 Hz at the low end), but refraction and reflection seis-mologists favor geophones because of the need to rapidlydeploy and retrieve up to several hundred receivers manytimes daily. Geophones and seismometers of the type usedin near-surface seismology are identical in terms of theirtheory of operation. Therefore, the following discussionapplies to both even though the term geophone is used inthe remainder of this section.

General design and function of a geophone

A geophone is designed to be securely attached to thesolid earth. The dimensions of the volume in which the at-tachment occurs are small relative to the range of seismicwavelengths. Thus, one speaks of the geophone as beingattached to a particle of the earth and moving with that par-ticle, so that the geophone case mimics the particle motionor ground motion during a seismic disturbance. A single-component geophone is constructed with a single trans-ducer and is either a vertical geophone (sensitive to verti-cal particle motion) or a horizontal geophone (sensitive toparticle motion in a specific direction in the horizontalplane). A three-component geophone contains three mutu-ally orthogonal transducers and is intended to provide in-formation on particle motion in three-dimensions.

Most three-component geophones need to be leveledand oriented with respect to a fixed horizontal direction toensure that one transducer is vertical and the others are ina consistent horizontal direction (i.e., the vertical, radial,transverse configuration). In the Gal’perin three-compo-nent configuration, the axis of each transducer makes anangle of approximately 54° with the vertical so that eachtransducer is affected by gravity in the same way and there-fore may be designed identically. The Gal’perin configura-tion is also somewhat easier to orient in the field.

The choice of geophone depends on the type of waveto be recorded and the direction of wave propagation.Common advice for the recording of body waves is basedon the theoretical result that in a homogeneous and iso-tropic linearly elastic material, simple plane P-waves arelongitudinal and simple plane S-waves are transverse. Thus,for example, if the direction of body-wave propagation isapproximately vertical, the P-wave should record best on avertical geophone and the S-wave should record best on apair of horizontal geophones. Vertical propagation is acommon assumption for reflected body waves returning to

the surface from depth because refraction in low-velocitynear-surface materials tends to bend the upgoing raypathtoward the vertical according to Snell’s law.

The SH-component of a plane S-wave should recordbest on a horizontal geophone with sensor axis orientedperpendicular to the direction of wave propagation; thischoice would also be the recommendation for recordingLove waves. An experiment to record Rayleigh waves wouldinvolve either a horizontal geophone aligned parallel to thedirection of wave propagation or a vertical geophone (orboth if a complete description of particle motion is de-sired). Three-component geophones may be used in anyterrestrial experiment to effectively record all wave typesand to aid in wave identification.

The transducer in nearly all modern geophones is themoving-coil electrodynamic type, and consists of a coilsuspended by one or more springs in a magnetic field thatis fixed relative to the geophone case. Motion of the earthcauses relative motion between the coil and the magneticfield and induces an analog voltage at the geophone termi-nals according to Faraday’s law. The geophone terminalsare connected via wires to a seismograph which amplifies,filters, and converts the analog voltage to a digital signal.In the following discussion, the differential equation gov-erning the relationship between particle motion and thegeophone output is presented in the time domain and solvedin the frequency domain to give the geophone frequencyresponse. An understanding of the geophone frequency re-sponse aids the proper design of field experiments, and isessential for the recovery of the original particle motion aseither displacement, velocity, or acceleration.

Geophone equation

Although the specific design and fabrication of a mov-ing-coil electrodynamic geophone varies with the manu-facturer, it is reasonable to represent any geophone of thistype as a damped harmonic oscillator. To see that this is in-deed the case, a detailed analysis of the vertical geophonemodel shown in Figure 3 is given in Appendix B. The re-sult of the analysis is the geophone equation which is asecond-order linear ordinary differential equation charac-teristic of damped harmonic oscillation:

, (10)

where V(t) is the voltage at the seismograph input, andmB(t) is the vertical velocity of the geophone case (a proxyfor vertical particle velocity). The constants h, C, and u0 =23f0 are the total damping constant (dimensionless), totaltransduction constant (V per m/s), and natural frequency(u0 in radian/s and f0 in Hz), respectively, and are defined


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in Appendix B in terms of the physical properties of thegeophone. It is convenient to view a geophone as a linearshift-invariant system governed by equation (10), with theinput and output given by mB(t) and V(t), respectively. Thisproperty is exploited in the following discussion to developthe geophone frequency response.

Geophone frequency response

The Fourier integral transform of the geophone equa-tion (10) is

(11)

where ~V(u) and ~mB(u) and are the Fourier integral trans-

forms of the corresponding time functions. Solving for~V(u) gives

. (12)

The geophone frequency response is denoted here by~H(u), and is given by equation (12) for the situation wherethe vertical case velocity mB(t) is an impulse represented bythe Dirac delta function d(t). If mB(t) = d(t), then ~mB(u) =1, and equation (12) becomes

. (13)

Notice from equation (13) that~H(u) is a well-defined com-

plex function for all u as long as the total damping con-stant h is nonzero.

Interpretation of the geophone frequency response(13) is best achieved by computing the amplitude response⏐~H(u)⏐ and phase response ∠ ~H(u):

(14)

which are shown in Figure 4 plotted as a function of u/u0for various values of the total damping constant h. The idealfrequency response would have ⏐~

H(u)⏐=C and∠ ~H(u) = 0,because the output voltage would then be a scaled versionof the vertical case velocity. However, because Figure 4 in-dicates that this ideal can only be achieved for u>>u0, avalue of the total damping constant h is sought with thefewest objectionable characteristics. Resonance near u0precludes choosing small h, whereas large h is undesirablebecause rolloff of ⏐~

H(u)⏐ is excessive and ⏐~H(u)⏐ flattens

at unacceptably high frequencies. As a result, geophonesare commonly designed with h = 0.7 as a compromise. Ath = 0.7, the amplitude response ⏐~

H(u)⏐ is reasonably flatfor frequencies u>1.5u0, but it should be kept in mind thatthe phase response ∠ ~H(u) remains nonzero and nonlinearin this frequency range. Nonlinear phase means that differ-


S

Terminals

CoilCase

A

B

Ring magnet

Pole pieces

S N

Spring

Figure 3. Schematic illustration of a moving-coil electrody-namic geophone. Structure is axially symmetric about axisAB. Magnetic flux lines are represented by closed loops.Polarity of magnetic pole pieces is indicated by N and S. Ahorizontally wrapped coil is suspended from a spring andconnected to geophone terminals via loose conductors thatpermit vertical coil movement relative to the case. Thespring shown is in an undeformed state.

Figure 4. Amplitude response (a) and phase response (b) fora geophone as functions of frequency u normalized to natu-ral frequency u0. Responses are shown for total dampingconstant h equal to 0.3, 0.7, and 2.0. Amplitude response isnormalized to total transduction constant C so that it is di-mensionless; phase response, in degrees.

a)

b)


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ent frequencies undergo different time shifts, so that V(t)will be a distorted version of mB(t), even at frequencieswhere the amplitude response is flat.

Natural frequency, damping, andtotal transduction constant

The natural frequency u0 can be adjusted by changingthe stiffness K of the spring, or the mass m of the coil, orboth; see equation (B-15):

. (15)

Geophones with low natural frequencies involve moremassive coils (larger m) and weaker springs (smaller K)which accounts for their heft and reduced tolerance torough handling. Some low-frequency geophones are pro-vided with a clamping mechanism to protect the mecha-nism during transportation and installation.

The total damping constant h can be expressed as thesum of an open-circuit damping h0 and an electromagneticdamping or coil-current damping hem; see equation (B-15):

and, (16)

where D is the mechanical damping coefficient, Rc is theresistance of the coil, RE is the equivalent resistance of theexternal circuit connected across the geophone terminals,and Jem is a constant related to the internal electromagneticproperties of the geophone. The equivalent resistance REdepends on the nature of the external circuit; see equation(B-8):

, (17)

where RA is the seismograph input resistance, RS is theshunt resistance, and RL is the line resistance between thegeophone and the seismograph.

Notice in equation (16) that the open-circuit dampingh0 depends only on internal geophone parameters, whereasthe electromagnetic damping hem depends on internal pa-rameters as well as the external circuit through resistanceRE. If the geophone is disconnected from the recording cir-cuit so that RE is infinite, the total damping is given by h0which is generally in the range 0.3–0.7, depending on thegeophone design. If the geophone is connected to the ex-ternal circuit, and the seismograph input resistance RA isvery large compared to the shunt resistance RS and the line

resistance RL, then equation (17) indicates that RE is ap-proximately equal to RS, and the electromagnetic dampinghem can thereby be controlled by the shunt resistance.

Finally, as shown in equation (B-15), the total trans-duction constant C also depends on the external circuit, butit is reasonable to expect values for C in the range 1-10 Vper m/s.

Geophone considerations in near-surface seismology

Effects not included in the geophone theory outlinedabove can result in departures from an otherwise flat am-plitude response at spurious frequencies or parasitic reso-nance frequencies that are well above the natural fre-quency. However, geophones are now available with a nat-ural frequency of 10 Hz with flat amplitude response freeof spurious or parasitic defects to at least 400 Hz. A geo-phone with these specifications is consistent with the rec-ommendations of a 1997 workshop on the near-surface seis-mic reflection method (Steeples et al., 1997), and wouldalso be a good selection for the refraction method. How-ever, the same workshop recommended 100-Hz geophonesfor seismic frequencies that extend above 400 Hz.

Single geophones are used in most near-surface seis-mic experiments because geophone arrays (geophones con-nected in series and/or parallel arrangements to produce asingle seismic signal) can adversely affect the recording ofhigh frequencies (Knapp and Steeples, 1986b). However,some practitioners use arrays of not more than three geo-phones distributed over a distance of 1–2 m oriented paral-lel to the predominant wind direction to help attenuatewind noise (Steeples and Miller, 1990).

If geophones are connected in series and/or parallelarrangements, it is necessary to evaluate the effect of theseinterconnections on electromagnetic damping. Unless theelectromagnetic damping is adversely affected, series con-nections in geophone arrays are recommended so that theindividual geophone voltages sum (Steeples and Miller,1990).

It is very important to fully push the geophone spikeinto firm soil (if possible) with no organic debris (grass,leaves, etc.) between the geophone base and the soil. Thispractice helps ameliorate the well known high-cut filteringeffect associated with geophone-soil coupling (Krohn,1984). Even if the advice of Krohn is followed, the cou-pling cannot be perfect because the earth is not perfectlyrigid and the geophone does not have zero mass. Othershave investigated the problem of geophone-soil couplingboth theoretically and experimentally; see Spikes et al.(2001) for a recent experimental study that includes a fullsummary of previous work.



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Recent developments in receiver technology

Attention has been given recently to the speed of re-ceiver deployment with innovations such as mounting anentire geophone spread on a board, piece of channel iron,or other mount to facilitate mass deployment and move-ment of the spread (Steeples et al., 1999a, b; Schmeissneret al., 2001; Bachrach and Mukerji, 2001), and gimbaledgeophones in a land streamer that can be towed into posi-tion (van der Veen and Green, 1998; van der Veen et al.,2001). A new velocity sensor designed to operate in thehorizontal orientation for detection of SH-waves is de-scribed by Sambuelli et al. (2001).

A new variable capacitance micromachined silicon ac-celerometer has been developed that includes an internalintegrated circuit that measures and digitizes the ac-celerometer response for output (Goldberg et al., 2001).Sensors of this type utilize MEMS technology (micro-electromechanical systems), and are seen as possibly lead-ing to an era of full-wavefield systems in which MEMSdigital accelerometers are routinely deployed to record thevector ground motion (Dragoset, 2005). Sensors based onMEMS technology are three-component accelerometersthat are insensitive to deployment tilt, but automaticallysense the direction of gravity and provide a tilt measure-ment for component rotation.

In addition, MEMS sensors produce a fully digital 24-bit output that completely eliminates the difficulties asso-ciated with analog transmission, and provide a flat ampli-tude and linear phase response from approximately 1 to800 Hz (Mougenot, 2004). Because MEMS sensors arelikely to be deployed as single units and not as noise-can-celing arrays, the petroleum industry is currently debatingthe merits of the new technology. The impact of MEMSsensors on the methods of near-surface seismology, whichnormally use single sensors but are governed by a muchlower capital expense threshhold, remains to be seen.

Traditional and distributed seismographs

A modern seismograph is a field-portable electronicsystem that amplifies, filters, and digitally records the ana-log seismic signals produced by the receivers. The evolu-tion of seismograph design has been driven by the de-mands of increasingly sophisticated seismic imaging tech-niques and by advances in digital electronics such as thedevelopment of microprocessors, compact mass data stor-age devices, and digital communication systems. At thepresent time, seismographs used in near-surface seismol-ogy may be classified as either traditional seismographs ordistributed seismographs, and most near-surface seismicdata are collected with traditional seismographs.

A traditional seismograph is a self-contained multi-channel system designed to digitally record on a separatechannel the output from each receiver that is active during

a given source effort. The seismic signals from the activereceivers are delivered to the channel inputs via analogtransmission over thinly insulated small-diameter wires(28 AWG) bundled in thick, durable cables with poly-urethane jackets. Traditional seismographs are usually (butnot necessarily) structured in blocks of 12 channels withthe total number of channels selected to match project re-quirements.

For example, it is common for projects designed tomap the bedrock interface at shallow depths with the re-fraction method to utilize 12- or 24-channel seismographs.As another example, the reflection method applied to mapa groundwater aquifer might employ a 48- or 96-channelseismograph. As a final example, the spectral analysis ofsurface waves (SASW) method was originally designed touse only two channels. Regardless of the number of chan-nels, a traditional seismograph handles at a central loca-tion the amplification, filtering, digital conversion, andrecording of the analog seismic signals from all active re-ceivers.

A distributed seismograph involves a collection of in-dividual seismographic units dispersed at intervals amongthe spread of receivers. Each unit handles the amplifica-tion, filtering, and digital conversion of the analog signalsfrom a nearby subset of the active receivers. The actualrecording of the digital signals may take place within theunit or at a central recording point after digital transmis-sion via radiotelemetry or fiber-optic cables. Distributedseismographs ameliorate problems such as crosstalk andinterference from power lines that are associated with ana-log signal transmission through seismic cables over largedistances. Distributed seismographs also promote the useof large numbers of receivers in special projects such as 3Dreflection surveys in rough terrain because the receiverspreads are easier to deploy. Although distributed seismo-graphs were introduced in the late 1970s and are now inwidespread use in the petroleum industry, they are still rel-atively uncommon in near-surface seismic applications.

Amplification and filtering

The analog seismic signal produced by each receiverneeds to be prepared for input to the analog to digital con-verter (A/D converter), which is at the heart of a modernseismograph. Although the details of the analog signalpreparation vary considerably from one seismograph to thenext, the nominal steps are initial amplification (alsoknown as preamplification), filtering, and final amplifica-tion with gain control. The initial amplification adjusts thelevel of the seismic signal to account for the strength of thesource relative to the location of the receiver, and is doneby a fixed-gain linear amplifier of very low noise and verylow distortion. Filtering removes high frequencies that aresusceptible to aliasing (see “Bandwidth and sampling,”below) and optionally attenuates noise associated with cer-



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tain frequency bands. The final amplification with gaincontrol adjusts the level of the initially amplified and fil-tered signal so that it is within the input range of the A/Dconverter.

Gain control known as instantaneous floating point orIFP refers to amplification that applies gain at each sampletime based on the signal level at that sample time; the gainis recorded as part of the output of the A/D converter. Gaincontrol is necessary if the dynamic range of the analog sig-nal at the input to the A/D converter exceeds the dynamicrange of the converter (see “Dynamic range” below).

Although IFP seismographs are highly regarded andwidely used, the most recently introduced seismographs donot include gain-control amplification in the preparation ofthe analog seismic signal. These newer seismographs useinnovative 24-bit sigma-delta A/D converters that have amuch larger dynamic range than the 16-bit A/D converterstypical of IFP seismographs. Also, because the sigma-deltaA/D converters sample at very high sampling rates (e.g.,256 kHz), filtering can be done digitally followed by re-sampling at the lower sampling rates used to represent eachdigital trace. The potential advantages of the newer sys-tems include simplicity of design, lower electronic noise,and lower power consumption, because there are feweranalog electronic components.

Bandwidth and sampling

The bandwidth of the amplified and filtered analogseismic signal A(t) is the interval fl < f < fu on the positivefrequency axis within which the power spectrum of the sig-nal has significant magnitude. Because the phrase signifi-cant magnitude is imprecise, many mathematical defini-tions are used to identify the lower frequency fl and upperfrequency fu of the bandwidth. Rather than explore thesedefinitions, it is sufficient to state that in the context ofnear-surface seismology, the bandwidth of a seismic signalproduced by a surface geophone located in the far field ofa near-surface source usually lies well within the 0–1000Hz range. A reasonable feel for the typical bandwidth ofseismic signals in near-surface seismology can be obtainedby examining the numerous spectra published in the seriesof source comparisons cited earlier.

A discrete-time signal A(nT) is obtained from the am-plified and filtered analog seismic signal A(t) by samplingat a finite number of discrete times t = nT, where n = 0, 1,2, …, N and the sampling interval T is assumed constant.The inverse of the sampling interval

(18)

is called the sampling rate or sampling frequency. In near-surface seismology, T and fs are usually specified in ms andHz, respectively. For example, if the sampling interval is 0.5

ms, then the sampling frequency is 2000 Hz. Sampling in-tervals on modern seismographs are selectable by the oper-ator in a range that can be as broad as 0.02–16.0 ms whichcorresponds to sampling frequencies of 62.5–50 000 Hz.

A well-known result from linear system theory knownas the sampling theorem states that a strictly band-limitedanalog signal A(t) can be recovered from the correspondingdiscrete-time signal A(nT) if the sampling frequency fs is atleast twice the frequency fu of upper end of the bandwidthof the signal:

. (19)

The undesirable condition fs < 2 fu is referred to as aliasing,and causes signal content at frequencies above fs / 2 to beimproperly represented as signal content at lower frequen-cies; the frequency fs / 2 is called the Nyquist frequency orfolding frequency in near-surface seismology (but Nyquistfrequency refers to the sampling frequency in some otherfields). To prevent aliasing of a band-limited signal, eitherthe sampling frequency needs to be increased or the analogsignal must be low-pass filtered so that condition (19) ismet. Analog low-pass filters aimed at fulfilling condition(19) are known as alias filters or antialias filters, and arefound on many seismographs prior to the conversion of thesignal to digital form.

Quantization

A digital signal is obtained from a discrete-time signalby quantizing the sampled values. Recall that A(nT) repre-sents the sampled values of the amplified and filtered ana-log seismic signal A(t), and suppose that the sampled val-ues fall within the range [–Amax, Amax], where Amax is a fi-nite positive number. Quantization is the process of as-signing a sampled value A(nT) to one level Am of a finitenumber M of levels representing the range [–Amax, Amax]:

. (20)

The step size of a quantizer is the difference between twoadjacent levels and is given by

. (21)

In a uniform quantizer, the step size does not depend on mand may be represented by ∆. Figure 5 shows an exampleof uniform quantizer where the sampled value A(nT) is as-signed level Am if the following rule is satisfied:

. (22)

The quantization error E is the difference between the sam-pled value A(nT) and the level Am chosen to represent it:



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. (23)

The quantization error for an assignment rule such as equa-tion (22) cannot exceed ∆/2, which implies that the maxi-mum quantization error can be reduced by reducing thestep size. Reducing the step size for a given Amax can be ac-complished by increasing the number M of levels. Also,notice that for a uniform quantizer, the maximum quanti-zation error expressed as a percentage of the sampled valueA(nT) decreases with increasing A(nT).

Each amplitude level Am is represented by a code thatis amenable to digital electronic systems. Binary codes arecommonly chosen because the binary digits 0 and 1 (alsoknown as bits) are resistant to electronic noise in transmis-sions systems. The number K of unique code words in a bi-nary code depends on the number of bits Nb in a binaryword:

. (24)

For example, if Nb = 8 in a binary code, then the number Kof unique code words is 256. Clearly, the number of re-quired bits Nb depends on the number M of levels availablein an A/D converter. A larger M, which requires a largerNb, corresponds to a reduced step size (and hence reduced

quantization error as mentioned previously) and/or an ex-panded input range limit Amax (and hence expanded dy-namic range as explained below).

Once the quantizer has assigned a level Am to the sam-pled value A(nT), the final step is to represent A(nT) by thebinary word Bm that uniquely represents Am. The A/D con-version of an amplified and filtered analog seismic signalA(t) of duration NT can therefore be summarized as fol-lows:

(25)

where the specific characteristics of the quantization andcoding steps depend on the many different digital seismo-graph designs that have been developed over the years.

Dynamic range

Dynamic range is a general term that refers to therange of positive values that can be accurately measuredand recorded by a measuring system. For example, the dy-namic range for a meter bar marked in increments of 1 mm,and used to measure lengths, is reasonably given as0.2–1000 mm, where 0.2 mm is considered the smallestlength that can be judged to be different from zero with theunaided eye. If Smin > 0 and Smax > Smin are the minimumand maximum values of the dynamic range, respectively,then it is common to express the dynamic range as the ratioSmax/Smin, where the ratio is converted to the decibel scale(dB) by the following standard formula:

. (26)

Applying equation (26) to the example of the meter bargives a dynamic range of 74 dB. It is useful to recognizethat because 20log10(2) is 6.02 dB, every 6 dB increase inthe dynamic range corresponds very closely to an increaseby a factor of two in the Smax/Smin ratio. Thus, the dynamicrange 74 dB corresponds to a ratio of maximum to mini-mum measurements greater than 212.

The dynamic range of a seismograph is measured andreported in a variety of ways and depends on numerousfactors. Perhaps the most useful general definition is theinput dynamic range defined by Pieuchot (1984, 326), andgiven in terms of the decibel scale as follows:

(27)

where Smax is the maximum input signal, and Ninput is thesystem noise which masks any smaller input signal. BothSmax and Ninput are measured in volts at the input terminalsof the seismograph at a particular gain setting for the ini-


A1

A4

A2

A3

A6

A7

A5

A8

Amax

-Amax

Input

Output

Figure 5. Schematic operation of a uniform quantizer ofstep size ∆ with eight output levels. Sampled value A(nT)must fall along the input axis between –Amax and Amax, andis mapped into one of eight discrete levels along the outputaxis. The smallest positive input value that is mapped into anonzero output level is ∆/2 which is mapped into outputlevel A5 = ∆. Input values greater than or equal to –∆/2 butless than ∆/2 are mapped into output level A4 = 0. Thelargest positive input value that can be mapped is Amax =3.5∆ which is mapped into output level A8 = 4∆. The largestnegative input value that can be mapped is –Amax = –3.5∆which is mapped into output level A1 = –3∆. The code forthis quantizer requires eight unique code words (one foreach output level) so that the number of bits Nb in each codeword for a binary code is three bits.


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tial amplification (i.e., measured at the gain setting of thepreamplifier).

For example, suppose the maximum positive inputvoltage at zero preamplifier gain is 1.4 V, and the systemnoise is given as 0.20 2V at a preamplifier gain of 36 dB.Assuming that the 1.4-V maximum input is prescribed bya device after the preamplifier, the value of Smax that can beinput to the 36-dB preamplifier is estimated to be 0.022 V(i.e., the 1.4-V maximum divided by the 26 gain of the pre-amplifier set at 36 dB). Thus, with Smax given by 0.022 V,definition (27) gives an estimate of 101 dB for the inputdynamic range of the seismograph at the 36-dB preampli-fier setting. If the maximum voltage of the seismic signalis aligned with the maximum allowable input of the seis-mograph (0.022 V), this dynamic range is sufficient torecord the 84-db seismic signal estimated by Pieuchot(1984, 54–55) for the most demanding case of a near-source receiver.

Sometimes the dynamic range of a fixed-gain seismo-graph is estimated from the number of bits produced by theA/D converter as follows:

, (28)

where Nb is the number of bits in the binary code. This for-mula stems from the idea that if one bit is reserved for thealgebraic sign, then the smallest through largest positivesignal amplitudes are represented by the range of binarynumbers associated with the remaining bits. Thus, a fixed-gain seismograph with a 16-bit A/D converter, where 1 bitrepresents algebraic sign, has an estimated dynamic rangeof 90 dB. The primary disadvantage of the dynamic rangeestimate in equation (28) is that it ignores the effect of sys-tem noise.

Refraction MethodThe refraction method is the oldest of the near-surface

seismic methods and continues to be widely used for map-ping the geometry of shallow geologic interfaces in a vari-ety of applications. Accurately timed first arrivals on fieldrecords are the basic data, and correct identification of thewaves responsible for the first arrivals is of critical impor-tance. This section focuses on the simplest possible two-di-mensional case where a single shallow interface separatessurficial material from an underlying material of contrast-ing physical properties. If the seismic velocity of the surfi-cial layer is less than the velocity of the underlying layer,then beyond a certain distance from the source, the first ar-rival will be a head wave generated at the shallow interface.At lesser source-receiver distances, the first arrival is gen-erally expected to be a body wave propagating in the surfi-cial layer. First-arrival times at a series of receivers de-ployed along a line of sufficient length between two sur-face sources usually provide adequate data for estimating

depth to the interface. The determination of depth to bed-rock beneath an unconsolidated overburden is the classicapplication of the refraction method.

A refraction survey can be carried out with field equip-ment that is relatively simple. A fixed-gain digital seismo-graph with at least 12 channels, a selection of acquisitionfilters, and the capability to vertically stack repeated sourceefforts would probably be considered adequate by mostpractitioners. Geophones should be suitable for ruggedfield work with a clean passband of perhaps 10–200 Hz.Appropriate sources are the single impulsive type such asa sledge hammer, a small explosive, or a trailer-mountedaccelerated weight drop. The required source energy in-creases as the interface depth increases because greatersource-receiver distances are needed to observe the headwaves.

The theory of the refraction method is based on thetracing of critically incident rays, and is therefore governedby the assumptions implicit in geometric ray theory. Alarge number of interpretation methods have been pub-lished over the years, but they are all closely relatedthrough their common dependence on Snell’s law. Al-though a fairly sophisticated interpretation can be carriedout entirely with pencil, graph paper, and hand calcula-tions, it is also possible to apply state-of-the-art computer-based inversion routines that are available both commer-cially and in the public domain. Indeed, modern seismo-graphs designed for near-surface seismic applications arenow bundled with refraction interpretation software. Noneof this advanced software, however, relieves the seismolo-gist from the responsibility of making correct identifica-tions of the waves represented on the traveltime curves.

Outside of the many textbooks on applied geophysics,some of the important general references for the near-sur-face refraction method are Redpath (1973), Palmer (1980,1981, 1986), Haeni (1988), and Lankston (1989, 1990).The volume of papers edited by Musgrave (1967) is de-rived mostly from refraction applications in the petroleumindustry, but contains a history of early refraction work andalso an extensive bibliography. The American Society forTesting and Materials (ASTM) has published standardD5777-00 for the refraction method (“Standard Guide forUsing the Seismic Refraction Method for Subsurface In-vestigations”). Published case histories also constitute avaluable source of information (see supplementary refer-ences at the end of this chapter).

Single plane dipping interface and the slope-intercept method

The slope-intercept method of interpretation for a sin-gle plane dipping interface illustrates many of the basicfeatures of the refraction method. Consider a plane dippinginterface separating two materials of contrasting seismic



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velocity as shown in Figure 6. Suppose the velocity V1 ofthe upper material is less than the velocity V2 of the lowermaterial, and that receivers are distributed along the sur-face on a straight line between source locations A and B.The horizontal distances from A and B to a given receiverG are x and y, respectively, where x + y = d, and constant dis the total length of the profile. The traveltime equationsfor the direct waves that travel from A and B to G are sim-ply the horizontal distances divided by the velocity of theupper layer:

and

(29)

The corresponding traveltime equations for the headwaves that travel from A and B to G are derived by tracingthe critically incident rays from source to receiver, and thenputting the resulting traveltime expressions in a standardform:

and

(30)

where v is the dip angle and oc is the critical angle of inci-dence:

. (31)

Parameters zA and zB are the depths measured normal to theinterface beneath source locations A and B, respectively.Because of reciprocity (i.e., the principle that the travel-time does not change if the source and receiver switch po-sitions), the direct-wave traveltime Tdw (A → B) must equalTdw (B → A), and the head-wave traveltime Thw (A → B)must equal Thw (B → A); these requirements of equations(29) and (30) are easily checked by substituting d for x andy and noting that zA = zB + d sin v.

Equations (29) and (30) are observable linear func-tions of x and y with measurable slopes and intercepts thatprovide complete characterization of the single plane dip-ping interface. Specifically, equation (29) indicates that theupper layer velocity V1 may be estimated by the inverse ofthe slope of the direct-wave traveltime equation. Further-more, inpsection of equation (30) shows that the other un-known subsurface parameters are related by the followingformulas to the head-wave traveltime slopes and intercepts:

(32)

and

. (33)

The expressions in equation (32) can be solved for the crit-ical angle oc and dip angle v in terms of the slopes:

and

. (34)

Similarly, the expressions in equation (33) can be solvedfor the depths zA and zB in terms of the intercepts:

and

. (35)

intercepts:

bz

V

bz

V

AA c

BB c

=

=

⎧

⎨⎪⎪

⎩⎪⎪

2

21

1

cos

cos

o

o

V1

V2

G yx

zA

zB

SurfaceA B

d

oc ococ oc

v

Figure 6. Raypaths for analysis of head-wave traveltimesfrom sources A and B to receiver G for single plane dippinginterface beneath a plane surface. Dip of interface is v andcritical angle of incidence is oc. Variable x is updip distancemeasured along surface from A to G, variable y is downdipdistance measured along surface from B to G, and constant dis distance measured along surface from A to B. All heavierdashed lines are normal to the subsurface interface. Veloci-ties above and below the interface are V1 and V2, respec-tively.


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Velocity V2 of the lower layer may be obtained from equa-tion (31) by substituting the critical angle of incidence es-timated by application of equation (34). Thus, if the slopesand intercepts of the traveltime curves [equations (29) and(30)] are determined by direct-wave and head-wave travel-time measurements made between source points A and B,it is straightforward to construct a complete map of the sin-gle plane dipping interface.

Notice that the single plane dipping interface problemmay be viewed as having four unknowns (for example, V1,V2, zA, and zB), and four independent equations. The inde-pendent equations are one direct-wave traveltime equation(29), both head-wave traveltime equations (30), and Snell’slaw (31) for the critical angle. Clearly, unless the interfaceis horizontal so that zA equals zB and there are only threeunknowns, it is not possible to obtain a unique solutionwithout both the updip and downdip head-wave traveltimeequations. The seismic refraction method is therefore al-ways characterized by forward and reverse data acquisi-tion, corresponding to source locations at each end of a lin-ear spread.

Single undulating interface and the reciprocal method

The reciprocal method is an elegant solution to theproblem of mapping an undulating interface that separatestwo materials of contrasting seismic velocity beneath anundulating surface; the description of the method byHawkins (1961) is adapted for presentation here. In the re-ciprocal method, quantities known as the time-depth tG andvelocity analysis function tv are defined for a receiver G interms of measured head-wave traveltimes:

and

(36)

where A and B are the locations of two surface sources, andreceiver G is located on the surface between A and B (seeFigure 7). The time-depth and velocity analysis functionare significant because tG can be related to the interfacedepth h beneath G, and tv can be used to infer the velocityV2 of the lower layer.

To find the relationship between tG and h, the head-wave traveltimes in equation (36) are expressed in terms ofthe raypath segments defined in Figure 7 to give the fol-lowing result:

. (37)

If �D�F is a straight line representing a plane segment of theinterface, then triangle GDF is an isosceles triangle, andequation (37) simplifies as follows:

. (38)

Using simple trigonometric relationships evident in Figure7, and Snell’s law sin oc = V1/V2 for the critical angle oc,equation (38) can be rewritten to give a linear relationshipbetween tG and the depth h, where h is measured normal tothe interface beneath receiver G:

. (39)

Equation (39) may be solved for h, and cos oc is written interms of the velocities to give

, (40)

where the conversion factor Cf is defined as follows:

. (41)

The depth h is computed directly from the time-depth tGassuming that Cf is known. Once h has been computed fora number of receivers along the profile between A and B,the interface is drawn as the envelope of the set of arcs ofvarying radius h centered on each receiver position.


o

o

oo

Surface

Figure 7. Raypaths for analysis of time depth tG and veloc-ity analysis function tv in the reciprocal method. Sources atA and B, and receiver at G. Head-wave arrivals reach re-ceiver G by traveling raypaths �A�C�D�G and �B�H�F�G. Line seg-ment �G�E of length h is normal to subsurface interface. Vari-able x is the distance from A to G along the surface. VariablexI is the distance from C to D to E along the subsurface in-terface. Angle oc is the critical angle of incidence. Alldashed lines are normal to the subsurface interface. Veloci-ties above and below the interface are V1 and V2, respec-tively.


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Equation (41) indicates that the conversion factor Cf isdependent on velocities V1 and V2. A value for V1 may beobtained from the inverse slope of direct-wave traveltimes;see equation (29). The problem of determining V2 can beapproached by using the velocity analysis function.Rewriting the definition of tv in terms of raypath segmentsshows that tv is the head-wave traveltime from source loca-tion A on the surface to position E on the interface:

. (42)

Because �A�C/V1 is a constant, tv may be regarded as a func-tion of distance xI, where xI is the distance measured along�C�D�E and its extension on the interface. Thus, writing xI for�C�D�E in equation (42), the velocity V2 is given by the in-verse of the derivative of tv with respect to xI:

. (43)

Of course, the distance xI is unavailable initially, so tv isplotted as a function of the distance x measured from A toG along the surface. The inverse slope of this plot yields anapproximate V2 (which becomes exact if the surface andinterface are parallel):

. (44)

This approximate velocity yields an approximate Cf and aset of approximate h-values computed from equation (40).The resulting approximate interface may then be used toestimate the distance xI. Replotting tv as a function of the xIestimate leads to a refined V2 estimate. Thus, if necessary,an iterative approach can be used to determine both V2 andthe interface.

The conversion factor Cf can also be determined di-rectly from equation (40) if the interface depth h is knownat one or more locations along the profile (perhaps fromborehole data), and the corresponding time-depth tG is alsoknown at those locations. This alternate procedure of de-termining Cf can directly account for lateral velocity varia-tion and provide quality control through independent depthinformation.

Single undulating interface and the generalized reciprocal method

The generalized reciprocal method (GRM) was devel-oped by Palmer (1980, 1981), and includes the reciprocalmethod as a special case. Like the reciprocal method, theGRM is used to map an undulating interface that separates

two materials of contrasting seismic velocity beneath anundulating surface. However, the GRM differs from the re-ciprocal method in that it generalizes the definitions for thetime-depth tG and the velocity analysis function tv:

and

(45)

where A and B are the locations of two surface sources, Xand Y are two receivers on the surface between A and B,point G is midway between X and Y, and x is distancemeasured along the surface from A to G (see Figure 8). No-tice that the GRM definitions for the time-depth and the ve-locity analysis function reduce to the reciprocal methoddefinitions if receivers X and Y occupy the same position aspoint G [equation (36)]. Thus, as stated above, the recipro-cal method is a special case of the GRM.

The following analysis shows that the GRM time-depth tG and velocity analysis function tv are related to theinterface depth h and velocity V2, respectively, in ways thatare identical to the reciprocal method. Start by expressingthe head-wave traveltimes in equation (45) in terms of the


Figure 8. Raypaths for the analysis of time depth tG and ve-locity analysis function tv in the generalized reciprocalmethod. Sources at A and B, and receivers at X and Y. PointG on the surface is midway between X and Y. Head-wavearrivals reach receiver Y from source A by traveling raypath�A�H�E�Y. Head-wave arrivals reach receiver X from source Bby traveling raypath �B�K�C�X. Line segment �G�D of length h isnormal to subsurface interface. Constants hX and hY are thelengths of the line segments drawn normal to the extensionof line segment �C�E from X and Y, respectively. Variable x isthe distance from A to G along the surface. Angle v is theangle between line segments �X�Y and �C�E. Angle oc is thecritical angle of incidence. All dashed lines are normal tosubsurface interface. Velocities above and below the inter-face are V1 and V2, respectively.


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raypath segments defined in Figure 8, so that tG and tvmaybe written as follows:

and

(46)

Next assume that the geometric figure XCEY may be ap-proximated by a quadrilateral. Under this assumption,which is equivalent to assuming that portions of the surfaceand interface are approximately planar, straightforwardtrigonometry may be applied to equation (46) to give

(47)

where v is the angle between quadrilateral sides �X�Y and�C�E. Although tv is not shown in equation (47) as an explicitfunction of the distance x, it is possible to compute dtv /dxusing the definition for the derivative:

, (48)

where ∆x is an infinitessimal increment in distance x, and∆tv is the corresponding increment in the velocity analysisfunction. Rewriting equation (48) gives V2 in terms of theinverse of the derivative dtv /dx:

. (49)

Equations (48) and (49) indicate that the inverse slope of tvoverestimates the velocity V2 by the factor 1/cosv, but theerror is within 3.5% of the true velocity if the angle v is lessthan 15°. The cosv term in equation (49) can be viewed asa correction factor that is missing in the approximation ex-pressed by equation (44) for the reciprocal method.

The derivative (48) may be substituted into equation(47) to give the GRM relationship between time-depth andinterface depth:

, (50)

where the depth h = (hx + hy)/2 is measured normal to the

interface beneath G. Solving equation (50) for h, and writ-ing cosoc in terms of V1 and V2, gives the following result:

, (51)

where the conversion factor Cf is defined by Cf = V1V2 /��V2

2 �– V12. Equations (50) and (51) are identical to equa-

tions (39) and (40) for the reciprocal method. Thus, as inthe reciprocal method, the depths h are estimated accord-ing to equation (51) using the measured time-depths for anumber of points on the surface, and the interface is drawnas the envelope of the set of arcs centered on the surfacepoints, with the arc radii given by the estimated depths.

Although the reciprocal method and the GRM lead tothe same basic relationship between time depth and inter-face depth, the GRM analysis can be carried out for a vari-ety of �X�Y-separations. Palmer (1980, 1981) argues that thebest �X�Y-separation (denoted here by �X�Yo and called the op-timum �X�Y-separation) is the separation that corresponds tocoincidence of points C and E in Figure 8. Coincidence ofthese points eliminates the planar element assumptionalong the interface, and presumably leads to a more de-tailed description of the interface. Using the results of ex-tensive modeling as a guide, Palmer (1980, 1981) givesprocedures for deducing �X�Yo from plots of time-depth andthe velocity analysis function for a range of �X�Y-separa-tions. If the value of �X�Yo inferred from the plots does notagree with the optimum �X�Y-separation computed from theinterpreted model, then this inconsistency may indicate thepresence of undetected layers (i.e., layers not representedas first arrivals in the head-wave traveltime data). Palmer(1980, 1981) advocates the use of an average velocity ap-proach to estimate the depth to an interface even thoughundetected layers may occur above it. Recently, some au-thors have critically examined the difficulties associatedwith determining the optimum �X�Y-separation (e.g., Leung,2003).

Single undulating interface and inversion for delay times

Another traditional approach to the interpretation ofseismic refraction data is the delay-time method originallyproposed by Gardner (1939). A modern version using dis-crete linear inverse methods to estimate delay times isdemonstrated by Michaels (1995) and is summarized here.As in the description of the reciprocal and generalized re-ciprocal methods, consider an undulating interface thatseparates two materials of contrasting seismic velocity be-neath an undulating surface (Figure 9). Further consider ahead wave that travels between surface positions Pk and Plalong the path �P�

k�C�D�Pl. The head-wave traveltime can be

written as a linear function of the distance ckl measuredfrom Ik to Il along the interface:



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, (52)

where ∆t(Pk) and ∆t(Pl) are the delay times defined interms of traveltimes along certain raypath segments:

and

. (53)

Notice that the delay times approach zero if Pk and Pl areallowed to approach their counterparts Ik and Il on the in-terface (C must approach Ik and D must approach Il tomaintain the critical angle of incidence). Thus, the delaytimes represent the “delay” associated with the raypathsegments through the upper layer.

Next, introduce the assumption that the interface seg-ment beneath any source or receiver is planar over a largeenough area that the delay time is not dependent on the az-imuth of the head-wave raypath. Notice that this assump-tion does not require a horizontal interface but does implythat triangles APkC and DPlF are isosceles triangles, andthat the planar bases of the cones formed by rotating trian-gle APkC about �PkIk, and triangle DPlF about �Pl Il both lieon the interface. Using this somewhat simplified geometry,and Snell’s law sin oc = V1/V2 for the critical angle, it isstraightforward to deduce the following expressions for thedelay times:

and

. (54)

Solving equation (54) for h, and writing cosoc in terms ofV1 and V2, gives the familiar result:

and

, (55)

where the conversion factor Cf is defined by

. Comparison of equation (55) with equations (40)

and (51) shows that the delay times are related to the inter-face depths in precisely the same way as the time-depths inthe reciprocal and generalized reciprocal methods. If theconversion factor and the delay times are known, then re-sult (55) gives the interface depths.

To make further progress, let xkl be the distance meas-ured from Pk to Pl along the surface, and assume that thesurface and interface topography is sufficiently subduedthat ckl may be approximated by xkl in equation (52):

. (56)

The velocity V2 and the delay times in equation (56) areviewed as unknowns, whereas the head-wave traveltime isconsidered known by measurement. Because there arethree unknowns and only one constraining equation, it isnecessary to acquire additional data in the form of head-wave traveltimes measured along different interface ray-paths but involving the same delay times.

Consider a refraction survey with multiple sources andreceivers (not necessarily on the same linear profile).Using the head-wave traveltime data of the survey, supposeN equations of the form (56) can be written, and furthersuppose that these equations involve NP < N distinct sur-face positions serving as end points for head-wave travelpaths. Because each distinct surface position is associatedwith a unique delay time, the linear system of N equationsinvolves NP + 1 ≤ N unknowns, where the unknowns arethe NP delay times and the velocity V2. The system of equa-tions can be written in matrix form as follows:

, (57)

where Thw is an N × 1 column vector of observed head-wave traveltimes, parameter vector m is an (NP + 1) × 1column vector listing all of the unknown delay times plusthe slowness 1/V2, and K is an N × (NP + 1) matrix con-taining the distances xkl in the first column, with zeros andones indicating the participating delay times in the remain-ing columns.

As a simple example, consider a reversed inline spreadas shown in Figure 10. The details of equation (57) for thisexample are as follows:


PkPl

A

D

CIl

hk

V1

V2

xkl

Ik F

h l

Surface

χ kl

oc oc

ococ

Figure 9. Raypaths for delay-time method. The head wavetravels between source-receiver pair Pk-Pl along �PkC �DPl ray-path (or reverse). Line segments �PkIk and �PlIl are normal tothe subsurface interface and of lengths hk and hl, respec-tively. Constant xkl is the distance measured along the sur-face from Pk to Pl. Constant ckl is the distance measuredalong the subsurface interface from Ik to Il. Angle oc is thecritical angle of incidence. All dashed lines are normal tosubsurface interface. Velocities above and below the inter-face are V1 and V2, respectively.


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. (58)

Of course, additional equations could be added by usingadditional sources and the same set of surface positions,but only if head-wave traveltimes are recorded from the in-terface of interest. Methods to solve a system of equationsof the form of equation (58) are well known and are dis-cussed by Menke (1989). Once the delay times are known,interface depths may be computed using equation (55) withthe conversion factor Cf determined by any of the methodsdescribed previously.

Other considerations

All of the traditional interpretation procedures used inthe refraction method assume that the head wave from aparticular interface has been correctly identified on thefield records. This aspect of the interpretation is funda-mentally important, and is carried out primarily by in-specting the first-arrival times for crossover points markedby changes in apparent velocity. Identification of thecrossover from the direct wave to the first head-wave isoften reasonably certain because it is usually characterizedby a very abrupt increase in apparent velocity with in-creasing offset, and also by a waveform change.

However, additional crossovers at greater source-re-ceiver distances are commonly observed and are moretroublesome to interpret. These additional crossovers canbe caused by any of the following circumstances: (1) acrossover to a new head-wave arrival from a deeper inter-face; (2) a lateral change in the dip of an interface; (3) alateral change in the velocity of the material beneath the in-terface. In order to distinguish between a deeper interfaceand a lateral change in dip and/or velocity, many authorsrecommend multiple source locations with differing inlineoffsets. For example, if the source is moved to greater off-set for an inline profile, a deeper interface will be revealedby a comparable lateral shift in the crossover point towardthe new source location. However, if the crossover is theresult of a lateral change in dip and/or velocity, it will re-main fixed in absolute location. See Lankston (1990) for il-lustrations of these examples.

Another very common problem is lack of adequateforward and reverse overlap of head-wave first arrivalsfrom the same interface. As an extreme example, it is pos-sible for head-wave first arrivals from the same interface to

be accurately timed in both the forward and reverse direc-tions, but not have any receivers that recorded the headwave in both directions. Thus, in the reciprocal or general-ized reciprocal methods of interpretation, it may not bepossible to compute time-depths at the desired number ofsurface locations. The solution to this problem is to com-pute phantom arrival times using data acquired for sourcepositions at greater inline offsets (see Redpath, 1973;Lankston and Lankston, 1986; and Lankston, 1990 for afull explanation).

It is possible for a head wave to be generated at an in-terface but not be observed as a first arrival. Because head-waves arriving after the first motion are rarely distinctiveenough to reliably recognize and time, the layer beneaththis type of interface is hidden from the interpreter. A layerthat constitutes a velocity inversion also will not be rep-resented by a head wave from its upper surface, becausehead-wave generation requires a velocity increase. Thepresence of hidden layers and/or velocity inversions be-tween the surface and the interface of interest can causesignificant errors in the depth calculations to that interface;this difficulty is known as the undetected layer problem. Asalready mentioned, Palmer (1980) has suggested using anaverage velocity approach with the generalized reciprocalmethod to alleviate depth errors of this type. The use ofpostcritical reflections to constrain the undetected layerproblem is discussed by Sain and Reddy (1997).

Multiple interfaces and more general subsurface models

The reciprocal method and generalized reciprocalmethod can be applied in the case of multiple undulatinglayers (Hawkins, 1961; Palmer, 1980, 1981). The interpre-tation is carried out sequentially for each interface, begin-ning with the uppermost interface, or more commonly byusing an average velocity to represent the layers overlyingthe interface of interest. Alternatively, fast raytracing algo-


Forward

P1P2 P3 P4

Reverse

P1P2 P3 P4

Figure 10. Hypothetical refraction survey used to illustrateinversion of delay times. Black squares indicate positions ofsources; black circles indicate positions of receivers. Thesurvey consists of forward and reverse field records withsources located at the end receiver locations.


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rithms and numerical eikonal solvers have led to the im-plementation of inversion schemes for traveltimes of wavestraversing a general two-dimensionally heterogeneous sub-surface (e.g., Zelt and Smith, 1992; Lanz et al., 1998). Aninitial velocity model is specified using some parameteri-zation of the subsurface. The parameterization may includeundulating interfaces marking discontinuous velocities,and continuous velocity variations may occur in the layersbetween interfaces.

Theoretical traveltimes derived from intermediate sub-surface models are compared with observed traveltimes,and the current velocity model is adjusted based on themismatch. Subsequent iterations are used to deduce a finalmodel which produces traveltime residuals meeting prede-fined stopping criteria. Interpretation procedures of thistype should include estimates of resolution, uncertainty,and uniqueness of the model parameters.

Reflection MethodThe reflection method in near-surface seismology is an

adaptation of theory and procedures pioneered in the pe-troleum exploration industry. A significant literature nowexists describing near-surface reflection methodology, andnumerous case studies are available illustrating diverse ap-plications. Most practitioners of the reflection method usecommon midpoint (CMP) acquisition and data reductionbecause it takes full advantage of currently available digi-tal recording systems and seismic processing algorithms.This section is therefore focused on an introductory expla-nation of the essential elements of the CMP reflectionmethod. The discussion includes the hyperbolic signatureof a reflection on a field record and CMP gather, the opti-mum window concept, normal moveout corrections, andhorizontal stacking. Sequential processing of a CMPgather is shown to illustrate the basic process leading to astacked trace. An example of a fully processed reflectionprofile from a seismic hazard study is presented, and thesection concludes with comments on static corrections, theimportance of confirming interpreted reflections, and abrief description of recent developments in near-surface re-flection methodology.

Readers interested in a systematic exposition of the re-flection method through the literature of near-surface seis-mology are well advised to begin with the classic paper onthe optimum window by Hunter et al. (1984). Tutorials onvarious aspects of the CMP method are given by Knappand Steeples (1986a, 1986b), Steeples and Miller (1990),and Baker (1999). Important updates from a special work-shop held in 1996 are provided by Steeples et al. (1997)with further elaboration by Steeples and Miller (1998). Nu-merous recent case histories are given in the supplemen-tary references of this chapter and provide the critical linkbetween the tutorials and actual experience in a wide vari-

ety of geologic settings. Historical summaries of the near-surface reflection method are given by Hunter and Pullan(1989), Steeples et al. (1995), and Steeples (1998).

Hyperbola on a split-spread field record

A reflection is distinguished on a split-spread fieldrecord by the hyperbolic shape of its travel-time curve.Consider an idealized subsurface with a plane dipping in-terface separating two materials of contrasting seismic ve-locities V1 and V2 as shown in Figure 11. Simple geomet-ric analysis of the reflected raypaths shows that the re-flected-wave traveltime is a hyperbolic function of offset x:

, (59)

where v is the interface dip, h is the depth measured nor-mal to the interface from the source location at x = 0, andT0 = 2h/V1 is the traveltime for the normally incident ray-path. If the derivative dTrw/dx is set equal to zero, the min-imum traveltime is found to be T0cosv, which occurs updipat x = 2h sin v. In the case of a horizontal interface, the dipv is zero and equation (59) reduces to a hyperbola that issymmetric in x with minimum traveltime T0 at x = 0:

. (60)

Equation (60) is commonly rewritten by squaring bothsides and simplifying terms to obtain the following expres-sion for the reflection traveltime from a horizontal inter-face:

. (61)

Although equations (59)–(61) are strictly applicableonly to the idealized subsurface model shown in Figure 11,they are among the most robust results in seismology. Hy-perbolic reflection signatures have been observed oncountless field records acquired in a wide variety of geo-logic environments over a remarkable range of interfacedepths. An example showing a reflection hyperbola for anear-surface dipping interface is shown in Figure 12.

Optimum window

The range of offsets on a field record for which a near-surface reflection is observed with minimum interferencefrom other seismic waves is known as the optimum window(Hunter et al., 1984). An idealized subsurface model witha plane horizontal interface separating two materials withcontrasting seismic velocities provides a useful illustration



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of the optimum window concept (Figure 13). It is assumedthat the velocity of the surficial layer is less than the ve-locity of the underlying layer (V1 < V2), and that the large-amplitude surface-wave modes are limited to an approxi-mately triangular region of relatively low apparent veloc-ity. The optimum window for this simple case lies betweenthe surface waves and the critical distance marking theemergence of the head wave.

It is possible to recover reflections from receivers in-side the region of surface-wave interference by digital fil-tering. Steeples and Miller (1998) report that in their expe-rience using the reflection method at over 100 sites, thedominant frequency of near-surface reflections — reflec-tions with traveltimes less than 100 ms — is approximatelydouble the dominant frequency of the surface waves. Thus,assuming sufficient dynamic range in the recording sys-tem, the interference represented by surface waves at nearoffsets can often be lessened by high-pass filtering. Expan-sion of the optimum window at large offsets is complicatedby interference between the reflected waves and the directand head waves; separation of these arrivals is problematicbecause their frequency content and apparent velocities aresimilar.

At offsets comparable to the reflector depth, Pullanand Hunter (1985) note that the reflection will undergophase changes in response to reflection and transmission inthe vicinity of the critical angle.

Small offset hyperbola on a common midpoint gather

Consider a configuration of source-receiver pairs sym-metrically placed about a point on the surface known as thecommon midpoint (CMP); see Figure 14. The set of tracesassociated with source-receiver pairs S1 – R1, S2 – R2, andso on, when plotted against offset x, is a common midpointgather or CMP gather. Following Hubral and Krey (1980,70), it is possible to develop a hyperbolic approximationfor the traveltime T(x) of a reflected wave recorded on thetraces of the CMP gather. It is this hyperbolic approxima-tion that is exploited in the CMP reflection method.

Development of the hyperbolic approximation beginsby writing T2(x) as a Taylor series expansion about x = 0:

, (62)

where the constants bi are the Taylor series coefficients.The traveltime T(0) at zero offset is called the normal inci-dence time, because a reflected raypath starting and endingat a coincident source-receiver pair must be normally inci-dent on the reflecting interface (Figure 15). Reciprocity re-quires T2(x) to be an even function of x. Thus, the odd-in-dexed coefficients (b1, b3, and so on) must be zero, and theTaylor series [equation (62)] reduces to even powers of x:

v > 0

x > 0

Trw

x < 0

hV1

V2

hsinv

Surface

T0cosv

2

Figure 11. Raypaths and traveltime curve for a reflectionfrom a plane dipping interface (dip v) separating two materi-als of contrasting seismic velocities V1 and V2. The source(black square) and receivers (black circles) are located at thesurface along the x-axis, with the source at the origin and re-ceivers symmetrically located about the source. Distance his depth measured normal to the interface from the source.Constant T0 is the normally incident traveltime 2h/V1. Thereflection traveltime Trw is a hyperbola with minimum trav-eltime T0cosv occurring at distance 2hsinv updip from thesource.

0

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

0204060 4020 60Offset (m)

Trav

eltim

e (m

s)

Reflection

Figure 12. Reflection from a dipping interface recorded ona split spread. The interface is at a depth of about 35 m be-neath the source, and dips approximately 25° with the down-dip direction to the left in the diagram (same geometry andorientation as Figure 11). The source is an 11.4-kg verticalslide hammer located at zero offset, and the receivers aregeophones with 10-Hz natural frequency. Each trace hasbeen band-pass filtered with a 15-30-350-500 Hz trapezoidalpassband. (Courtesy L. M. Liberty.)


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. (63)

It is important to keep in mind that in general, the remain-ing Taylor series coefficients (b2, b4, and so on) are com-plex functions of the subsurface velocity structure.

The properties of a Taylor series expansion of a con-tinuous function ensure that the first two terms in equation(63) represent T2(x) to arbitrary accuracy for small enoughoffset. Therefore, if x < ∆x, where ∆x is a sufficiently smallpositive number, terms beyond the x2 term may be neg-

lected, and the traveltime of a reflected wave observed ona CMP gather is given by the small-offset hyperbola (alsocalled the small-spread hyperbola):

. (64)

For reasons that will become clear shortly, it is customaryto denote the Taylor coefficient b2 by 1/V2

NMO, so that thesmall-offset hyperbola [equation (64)] is written as fol-lows:

, (65)

where VNMO has dimensions of velocity and is called thenormal moveout velocity. It turns out that the normalmoveout velocity is given by simple exact expressions forseveral subsurface models involving homogeneous layers.In the following equations, VNMO is the normal moveoutvelocity for the reflection from the base of the indicatedlayer(s):

(66)

, (67)

and

, (68)

where V1 is the velocity of the single layer, v is the dip ofthe single dipping layer, and Vk and ∆hk are the velocityand thickness of layer k, respectively, of N horizontal lay-ers; see Figure 16. Formulas for VNMO for more compli-cated subsurface models that include the results in equa-tions (66)–(68) as special cases are developed by Hubraland Krey (1980).


CMPS1 S2 S3 R3 R2 R1

x

Figure 14. Source-receiver pairs of a common midpoint(CMP) gather with three pairs. Offset x is the distance be-tween the source (black square) and receiver (black circle)of a source-receiver pair (shown for the S2-R2 pair). By con-vention, the algebraic sign of x reverses if the positions ofthe source and receiver are interchanged.

Optimumwindow

Distance from source (x)

Trav

eltim

e (T

)

V1

V2

h

Surfacewaves

DirectwaveReflection

Head wave

Source

dc

hwdw

dx

T0

rw

Figure 13. Optimum window for a single horizontal inter-face at depth h separating two materials of contrasting seis-mic velocities V1 and V2. Abbreviations rw, dw, and hwrefer to reflected wave, direct wave, and head wave, respec-tively. Constant T0 is the normal incidence time for the re-flection and is observed by a hypothetical receiver at thesource (x = 0). Constants dc and dx are the critical distanceand crossover distance for the head wave, respectively. Headwaves will not exist unless V1 < V2. S-R

Reflecting interface

Surface

Normally incident raypath

Figure 15. Normally incident raypath for a reflection gener-ated and recorded at the same surface point (i.e., coincidentsource-receiver pair).


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Normal moveout

The normal moveout or NMO of a reflection recordedon a CMP gather at offset x is defined to be the differencebetween the reflection traveltime T(x) and the normal inci-dence time T(0) for that reflection:

. (69)

Substituting T(x) from the small-offset hyperbola (65) intoequation (69) gives the NMO under the small offset as-sumption:

. (70)

As can be seen from equations (65) and (70), the normalmoveout velocity is the key parameter at small offsets indetermining the the shape of the reflection hyperbola andthe size of the normal moveout. In other words, as the nor-mal moveout velocity VNMO increases without limit, thenormal moveout ∆tNMO decreases toward zero, and thesmall-offset hyperbola flattens to a horizontal straight linegiven by T(x) = T(0).

Stacking hyperbola and velocity analysis

It has been shown above that under the small offset as-sumption, the traveltime T(x) of a reflection observed on aCMP gather can be represented by the small-offset hyper-bola defined by equation (65). However, as offset in-creases, the agreement between T(x) and the small-offsethyperbola generally deteriorates in a manner that dependson the subsurface structure. The discussion below de-scribes an empirical procedure used to obtain a better over-all hyperbolic approximation to T(x) over the full range ofCMP offsets. Unlike the small-offset hyperbola, this newhyperbolic approximation is not guaranteed to match T(x)over any offset range, but it does lead to the very usefulprocedure known as horizontal stacking that is almost uni-versally employed in reflection data processing.

Suppose the reflection traveltime T(x) is measured onM traces of a CMP gather to give traveltime data [xi, T(xi)],where subscript i = 1, 2, …, M indicates the trace number.These traveltime data may be used to constrain the param-eters of the stacking hyperbola which is defined as follows:

, (71)

where TST(0) and VST are adjustable stacking parameters,and VST is known as the stacking velocity. Extension of ahyperbolic approximation for traveltime T(x) to all offsetsof the CMP gather (not just small offsets) can be accom-

plished by finding the values of the stacking parametersTST(0) and VST that provide some best fit to the [xi, T(xi)]traveltime data. In general, the stacking parameters TST(0)and VST will not equal T(0) and VNMO of the small-offsethyperbola, although they are often considered to be ap-proximations to them.

Perhaps the simplest way to determine the stacking pa-rameters is to plot T2(xi) as a function of x2

i, and then per-form a linear least-squares fit to obtain T2

ST(0) as the inter-cept and 1/V2

ST as the slope. However, this procedure is justone method of velocity analysis, a term used to describe awide variety of processes developed over the years for de-termining the stacking parameters for each reflection on aCMP gather; see Yilmaz (2001) for a thorough discussionand summary. The key point underlying velocity analysisis that a properly determined stacking hyperbola closelyfollows a reflection on the CMP gather and thereby guidesconstructive trace-by-trace summing of the reflection sig-nal. Regardless of the details involved in velocity analysis,the final result is the definition of a stacking velocity, andhence a stacking hyperbola, for each time increment on thezero-offset axis of a CMP gather.

Flattening a reflection by the normal moveout correction

Once the stacking velocities are determined for a CMPgather, the reflections on that gather may be flattened by aprocess known as the normal moveout correction. For a


∆h1

∆h2

∆hk

∆hN

V1

V2

Vk

VN

Layer 1

Layer 2

Layer k

Layer N

Surface

Figure 16. Subsurface consisting of N horizontal layers.The velocity Vk and thickness ∆hk are uniform within agiven layer, but in general, the velocity and thickness varyfrom layer to layer.


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given time Tj(0) on the zero offset axis, equation (71) isused to compute TST(xi), where xi is the offset of trace i ofthe CMP gather, TST(0) is given by Tj(0), and the stackingvelocity VST is the stacking velocity associated with Tj(0):

. (72)

The trace value at offset xi and time TST(xi) is then mappedto offset xi and time Tj(0). By repeating this operation forall traces, a reflection with a hyperbolic traveltime curveapproximated by equation (72) is aligned or flattened at atime that closely corresponds to its normal incidence time.Because coherent events that are not aligned with a stack-ing hyperbola are not flattened, the normal moveout cor-rection is seen as a mechanism for separating reflectionsfrom all other events, including multiple reflections. Figure17 provides an example of the result of normal moveoutcorrections applied to a CMP gather acquired in Oregon.

Application of the normal moveout correction to re-flection waveforms of finite duration results in a waveformdistortion known as NMO stretch (Barnes, 1992). The ef-fect is most serious at small normal incidence times andlarge offsets and therefore has considerable significancefor near-surface CMP data. The problem can be handled bycareful selection of allowable stretch parameters in a pro-cessing algorithm that mutes unacceptably stretched re-flections (Miller, 1992).

CMP reflection method

The preceding development of the hyperbolic repre-sentation of reflection traveltime curves and the normalmoveout correction is a sufficient basis for summarizingthe CMP reflection method. Although vast in its details, theCMP method may be viewed as consisting of the five es-sential steps listed below.

1) Aquisition of CMP gathers is carried out for a sequenceof common midpoints along a profile on the earth’s sur-face. A highly efficient procedure known as roll-alongacquisition is used to acquire the necessary data.

2) Stacking hyperbolas for each CMP gather are deter-mined using velocity analysis.

3) Each reflection on each CMP gather is flattened by ap-plication of the normal moveout correction.

4) The flattened traces of each CMP gather are summed toachieve one stacked trace for each gather. This processis known as horizontal stacking and has the effect of en-hancing reflections while canceling those events that donot align properly as a result of the normal moveoutcorrections. The number of traces summed to get astacked trace is known as the fold; the fold is typically6–30 in near-surface applications.

5) The stacked traces are plotted side-by-side in CMPorder to obtain a seismic section of the subsurface.Alignments of reflections on the seismic section markcontinuous geologic interfaces with significant reflec-tion coefficients; interuptions of these alignments mayindicate faults.


Figure 17. Sequential processing of a common midpoint (CMP) gather. (a) Original CMP gather. (b) After application of atrapezoidal band-pass filter (40-80-500-800 Hz). (c) After NMO corrections with stretch mute. (d) After top and bottommutes. In each panel, traces are shown with trace gain applied (i.e., each trace is normalized to its maximum amplitude).(Courtesy L. M. Liberty.)

a) b) c) d)


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An example of a seismic section acquired as part of aseismic hazards study in Oregon is given in Figure 18. Thereflection alignments are clearly visible in the uninter-preted section in the upper part of the figure; a geologic in-terpretation is superimposed on the section in the lowerpart.

Static corrections

The hyperbolic shape of a reflection traveltime curveon a field record or CMP gather may be distorted by vari-ation in the elevation of sources and receivers, and by lat-eral changes in velocity in the very shallow subsurface (es-pecially above the water table). These distortions corre-spond to higher order terms in the Taylor series expansion(63) and are therefore not represented by the small-offsethyperbola. Because the distortions are also not representedby the stacking hyperbola, reflections are not adequatelyflattened prior to horizontal stacking. The result can be aserious degradation of the quality of the seismic section.Static corrections are time shifts used to adjust the tracesin a field record or CMP gather toward an ideal conditionwhere the terrain is flat and without shallow lateral veloc-ity variations.

Whole-trace shifts in time that represent vertical trans-lation of the source and receiver to a common elevation ordatum are called elevation static corrections or datumstatic corrections. The accuracy of elevation static correc-tions is critically dependent on choosing the correct aver-age velocity to represent the material between the surfaceand the datum. Refraction static corrections are used tocorrect for lateral variations in the thickness and velocity ofthe surficial low-velocity layer. In the simplest and perhapsmost reliable situation in which the low-velocity layer isthe unsaturated zone above the water table, refraction staticcorrections are determined from deviations in the arrivaltime of the water-table head wave (Hunter et al., 1984).Residual static corrections are used to correct short wave-length variations in shallow velocity beneath individualsources and receivers. Regardless of the type of static cor-rection, Steeples and Miller (1998) caution that static cor-rections on near-surface seismic reflection data requireconsiderable care because the time shifts are comparable tothe dominant periods of the reflections.

Borehole ties to lithology

The interpretation of reflection data in terms of geo-logic interfaces requires development of a correspondencebetween normal incidence time on the seismic section anddepth in a borehole with lithologic control. A comprehen-sive discussion of the experimental aspects of this problemis provided by Hunter et al. (1998), who describe downholeseismic logging techniques for both P-waves and S-waves.

Other considerations

Numerous pitfalls exist in the acquisition and process-ing of seismic reflection data in the near-surface environ-ment. These pitfalls are summarized concisely by Steeplesand Miller (1998) in an article describing experiencegained during 25 years by the authors and their colleaguesat numerous field sites representing many geologic envi-ronments. Perhaps the single most important action thatcan be taken to avoid problems is to confirm interpreted re-flections on the seismic section by comparison with theminimally processed field records or CMP gathers. If aninterpreted reflection cannot be confirmed in this way, thenthere is the possibility that it has been created as an artifactof acquisition and/or processing.

The treatise by Yilmaz (2001) is a very complete andreadable exposition of the most important results from themassive literature on seismic data processing. Although thecontext of Yilmaz (2001) is the reflection method as prac-ticed by the petroleum industry, it nonetheless serves as avaluable reference for processing reflection data acquiredfor near-surface investigations. Adaptation of the process-ing methods from the petroleum exploration industry to thenear surface requires careful examination of the underlyingassumptions.

For example, Steeples and Miller (1998) report thatdeconvolution does not work properly on most near-sur-


Figure 18. Seismic section from seismic hazards study inOregon. Traveltimes along the vertical axis of each sectionhave been converted to estimated depths by applying a uni-form average velocity. Colors are used to represent trace po-larity and amplitude. Vertical scale exaggerated by a factorof 1.5, approximately. The unmigrated and uninterpretedsection is at the top; the migrated and interpreted section isbelow. (Courtesy L. M. Liberty).


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face reflection data, because the reflection wavelet variesboth laterally and with depth, and because the series of re-flection coefficients is not modeled well as a random timeseries. As another example, Black et al. (1994) find that mi-gration of near-surface seismic sections is often not re-quired for low subsurface velocities and small reflectordepths relative to spread lengths. Migration is the processof repositioning dipping reflectors properly in time andspace on a seismic section; examples of successful migra-tions are demonstrated by Bradford et al. (1998) andPasasa et al. (1998). Migration has been carried out for theinterpreted seismic section in the lower part of Figure 18.

Recent developments

Sustained effort in the acquisition and processing of3D near-surface reflection data is probably the most no-table of the recent developments; see the examples byBuker et al. (1998, 2000), Siahkoohi and West (1998),Spitzer et al. (2001), Spitzer et al. (2003), and Bachrachand Mukerji (2004a, b). Coupled with previously men-tioned attempts to speed the deployment of receivers (see“Seismic Sources and Field Instrumentation”), this work issignificant because the application of 3D reflection meth-ods is often stymied by high costs. More difficult process-ing problems are also being addressed, such as those asso-ciated with very large subsurface velocity gradients thatcan occur, for example, in the change from unsaturated tosaturated conditions near the water table (see Miller andXia, 1998 and Bradford, 2002a, b). Another important de-velopment is the combined use of both ground-penetratingradar and very high-resolution seismic reflection methodson the same imaging problem; for example, see Cardimonaet al. (1998), Baker et al. (2001), and Liberty et al. (2003).Similarly, Ghose and Goudswaard (2004) examine theprocess of integrating S-wave reflection data with conepenetration tests.

Some investigators are working on the relationshipsbetween seismic reflection measurements and materialproperties, e.g., Bachrach and Mukerji (2004c). Finally,there has been interest in defining a practical minimum re-flector depth. Recent experiments have shown that reflec-tions from a depth of approximately 1 m may be recordedwith a dominant frequency of about 600 Hz using surfacesources and receivers (Steeples, 1998).

Surface-Wave MethodThe surface-wave method was developed in response

to needs in geotechnical engineering and S-wave reflectionseismology for a noninvasive technique for estimating thein situ S-wave velocity of near-surface materials. Conven-tional implementation of the method involves the recording

of Rayleigh waves on vertical-component receivers, usingthe Rayleigh-wave data to estimate the phase-velocity dis-persion curve, and then applying the methods of geo-physical inversion to the dispersion curve to obtain the S-wave velocity as a function of depth.

The SASW method (spectral analysis of surfacewaves) and the MASW method (multichannel analysis ofsurface waves) are the two primary techniques that haveemerged for field data acquisition and subsequent estima-tion of the dispersion curve. Surface waves of broad band-width are desirable to ensure that the recorded dispersion isrepresentative of the full depth range of interest. Maximumdepths depend on the application and vary from a fewdecimeters in pavement systems to a several decameters insite investigations.

Most of the inversion schemes in current use adopt ahorizontally layered earth model in which each layer is ahomogeneous and isotropic, linearly elastic medium.These inversion schemes differ primarily in the computa-tion of the forward model and the method of optimization.Applications of near-surface S-wave velocity informationinclude foundation dynamics, pavement analysis, soil im-provement, liquefaction potential, and static corrections forS-wave reflection data.

Spectral analysis of surface waves method

The spectral analysis of surface waves method(SASW) is distinguished by the use of cross-spectral tech-niques to determine a phase-velocity dispersion curve forRayleigh waves. A typical field experiment uses a pair ofidentical vertical-component receivers G1 and G2 of lownatural frequency (e.g., f0 = 1 Hz) placed symmetricallyabout a fixed point on the surface (Figure 19). A sourcesuitable for the generation of Rayleigh waves is placedalong the line established by the two receivers. The sourceis activated at both forward and reverse source points withoffset to the nearest receiver equal to the receiver separa-tion. The seismic signals from G1 and G2 for each sourceactivation are recorded by a dual-channel digital recordercapable of spectral analysis in the field; storage of eachtrace pair for future processing is usually on a portablecomputer. Data are acquired for several different receiverseparations where each separation is generally twice theprevious separation. The corresponding offset increaseusually requires an increase in source energy to providesufficiently strong surface waves at the receivers.

The reduction of SASW data is based on spectralanalysis of each trace pair. Stochastic estimates of the crossspectrum and coherence function are of particular impor-tance. However, to understand the use of the cross spec-trum in the SASW method, it is possible to disregard thestochastic nature of the recorded signals and consider a de-


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terministic (nonrandom) pair of continuous traces G1(t)and G2(t) that record the Rayleigh wave from a singlesource activation. The crosscorrelation function G12(t) forG1(t) and G2(t) is defined as follows (see Appendix A):

(73)

The cross spectrum∼G12(u) is the Fourier integral trans-

form of G12(t), and may be expressed in polar form as fol-lows:

, (74)

where f12(u) denotes the phase spectrum of the cross spec-trum. The cross spectrum may also be written in terms ofthe individual Fourier integral transforms

∼G1(u) and

∼G2(u)

of traces G1(t) and G2(t), respectively, by using the cross-correlation theorem (see Appendix A):

, (75)

where the asterisk indicates the complex conjugate. Thesignificance of equation (75) is clarified by writing

∼G1(u)

and ∼G2(u) in polar form with phase spectra f1(u) and

f2(u), respectively:

and. (76)

Substitution of the polar forms (76) into the crosscorrela-tion theorem (75) gives

. (77)

Comparison of equations (74) and (77) shows that thephase spectrum f12(u) of the cross spectrum gives thephase difference of trace G2(t) relative to trace G1(t):

. (78)

As is discussed next, the result in equation (78) permitsf12(u) to be used to compute the phase-velocity dispersioncurve c(u) of the Rayleigh waves recorded by receivers G1and G2.

The vertical component uz of a single mode of theRayleigh wave displacement at receivers G1 and G2 can bewritten for frequency u as follows:

and

(79)

where G1 and G2 are located at horizontal positions x + dand x, respectively, the fundamental mode is assumed withwavenumber k0(u), constant w is the fundamental modeamplitude for frequency u, and both receivers are on thesurface z = 0. It is important to realize that the fundamen-tal mode is used here only as an example. Any mode canbe used in the discussion, but there is an implicit assump-tion that a single mode dominates the displacement at thereceivers.

It is evident from the cosine functions in equation (79)that the phase difference ∆f(u) of the displacement at re-ceiver G2 relative to the displacement at receiver G1 is theproduct of the geophone separation d and wavenumberk0(u):

. (80)

Dividing both sides of equation (80) by frequency u andrearranging gives the Rayleigh-wave phase velocity c(u):

. (81)

The displacements in equation (79) are converted into thetraces G1(t) and G2(t) by convolution with the impulse re-sponse of the field recording system. Because the phasechanges introduced by the recording system can be as-sumed to cancel in the subtraction in equation (78), the


G1 G2

G1 G2

G1 G2

P

P

d∆x ∆x

Figure 19. Typical data acquisition scheme for SASWmethod. Three individual spreads are shown with eachspread centered on the same point P on the surface. Eachspread is a reversed inline offset spread. Black squares aresources and black circles are receivers (identified as G1 andG2 in text). For each spread, the offset between each sourceand the nearest receiver equals the receiver separation (i.e.,the near offset ∆x equals the receiver separation d as shownfor the third spread). The spacing between the sources andreceivers for a given spread is twice that of the precedingspread.


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phase spectrum f12(u) is equivalent to ∆f(u). Thus,estimation of the phase-velocity dispersion curve can bereduced to determining f12(u):

. (82)

Although presentation of the dispersion curve as afunction of frequency is common in seismology, the con-version of c(u) to a function of wavelength c(l) is oftenused in geotechnical engineering. The conversion is ac-complished by recalling that the wavelength l for a givenfrequency u is given by l = 23c(u)/u.

Estimation of the dispersion curve in the SASWmethod is subject to limitations on the longest usablewavelength. Because of near-field effects, Stokoe et al.(1994) recommend that any wavelength l for which aphase-velocity estimate c(l) is obtained should satisfy thefollowing criterion:

, (83)

where ∆x is the offset between source and nearest receiver(recall that ∆x = d in the normal SASW field protocolwhere d is the distance between receivers). For pavementsystems, Sanchez-Salinero et al. (1987) suggest a muchstricter criterion:

. (84)

As a consequence of these restrictions on wavelength, thedispersion curve is composed of overlapping segmentswith greater offsets used for measuring phase velocities forlonger wavelengths. A smoothing procedure is used to con-vert the overlapping segments to a single composite disper-sion curve.

It is well known that surface wave propagation in-volves multiple modes and each mode is generally associ-ated with a different dispersion curve (Tokimatsu et al.,1992). Thus, an assumption implicit in the procedure out-lined above is that Rayleigh waves of a single mode domi-nate the seismograms at all wavelengths so that this domi-nant mode is the primary determinant of the dispersioncurve. Analysis of wave propagation in an elastic half-space with shear modulus increasing with depth was car-ried out by Vrettos (1991). One finding of the Vrettos(1991) study is that the phase velocity of the fundamentalmode Rayleigh wave approximates the phase velocity ofthe total half-space response beyond a short source-re-ceiver distance (a few wavelengths). However, Gucunskiand Woods (1991a,b) stress that higher mode Rayleighwaves can dominate surface wave propagation for subsur-face profiles with a low-velocity layer between higher ve-locity layers.

Use of the coherence function in the SASW method

The coherence function g2(u) is used as a measure ofdata quality in the SASW method and is defined as follows(Jenkins and Watts, 1968, 352):

, (85)

where the traces G1(t) and G2(t) are now viewed as sto-chastic processes. The functions

∼G11(u) and

∼G22(u) are the

power spectra of traces G1(t) and G2(t), respectively, and∼G12(u) is the cross spectrum.

The use of the coherence function as a measure of dataquality can be explained by supposing that G2(t) is the con-volution of G1(t) with some impulse response h(t) (such asa simple delay) plus independent noise N(t):

. (86)

The ratio of the power spectrum of the signal at receiver G2to the power spectrum of the noise for this model can beexpressed in terms of the coherence function (Jenkins andWatts, 1968, 351–352):

, (87)

where~NNN(u) is the power spectrum of the noise. Thus, at

a particular frequency u, if the signal at G2 is all noise,then the ratio in equation (87) is unity and the coherencefunction is zero; but if the noise is zero at G2, then the ratiois infinite and the coherence function is unity.

As a simple example, suppose G1(t) = scG(t), where scis a positive real number and G(t) is a stochastic processthat constitutes the essential aspects of the surface-wavesignal, and further suppose that G2(t) is a delayed versionof G1(t) plus independent noise:

, (88)

where G(t) and N(t) have zero mean and equal variance.Scaling factor sc is introduced as a way of adjusting thestrength of the signal relative to the noise. The coherencefunction in this case can be shown to be independent offrequency and totally dependent on the scaling (Jenkinsand Watts, 1968, 357):

. (89)

Thus, if the signal is small relative to the noise (sc ap-proaches zero), then the coherence function also ap-proaches zero. On the other hand, if the signal is large rel-



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ative to the noise, (sc approaches infinity), then the coher-ence function approaches unity.

Phase velocities at frequencies with g2(u) significantlyless than one are disregarded in the SASW method. An ex-ample of the typical use of the coherence function in theSASW method is given by Nazarian and Desai (1993).

Recent developments in the SASW method

Notable advances in the traditional application of theSASW method include automation of dispersion curve de-termination (Nazarian and Desai, 1993), and automation ofthe inversion process (Yuan and Nazarian, 1993), includingthe incorporation of multiple modes in the inversion (Ganjiet al., 1998). Underwater applications of the SASWmethod are discussed by Luke and Stokoe (1998). The po-tential of the SASW method to detect a subsurface obsta-cle such as a cavity is investigated numerically by Ganji etal. (1997). Rix et al. (2000) and Lai et al. (2002) have ex-tended the SASW method to the determination of thedamping ratio.

Multichannel analysis of surface waves method

The multichannel analysis of surface waves method(MASW) is distinguished from the SASW method by theanalysis of field records acquired with considerably morereceivers than the pair of receivers used for SASW acqui-sition. According to Park et al. (1999), the primary advan-tages of using multiple channels are the recognition andisolation of noise (defined as all wave types other than fun-damental mode Rayleigh waves) and the speed and redun-dancy of data acquisition. In addition, multichannel dataprocessing can be used to separate the dispersion curvesfor the fundamental and higher modes. The dispersioncurves for higher modes can be used to help constrain theinversion for the shear-wave velocity-depth profile.

A typical field experiment uses a vertical impulsive orswept frequency source to generate Rayleigh waves thatare recorded by an inline offset spread of identical re-ceivers of relatively low natural frequency (1 < f0 < 10 Hz).As in the SASW method, it is important that wavelengthsshould be smaller than twice the smallest inline offset toavoid near-field effects and to promote dominance of thefundamental mode in the recorded data. The far offset islimited by the distance at which higher frequency surfacewaves are significantly contaminated by reflected bodywaves. In the ideal case in which a single Rayleigh modedominates the noise and all other modes, a multichannelswept frequency record (acquired with a swept frequencysource or transformed from an impulsive record) will showa distinctive trace-to-trace linear waveform coherency(Park et al., 1999). Any breakdown in this coherency servesas a guide to modifications in the acquisition and subse-quent data-processing protocols. Comparison of results

from the MASW method with those of downhole measure-ments have been carried out by Xia et al. (2000).

Several forms of multichannel analysis can be used todeduce the phase-velocity dispersion curves. Park et al.(1999) point out that it is possible to simply measure thelinear slope of each frequency component on the fieldrecords. McMechan and Yedlin (1981) show that an imageof a dispersion curve is obtained directly by a slant stack(the p-r domain) followed by a one-dimensional Fouriertransform over r (the p-u domain), where r is the time in-tercept, p is the horizontal slowness, and u is the fre-quency. The loci of maximum amplitudes in the p-u do-main define the phase-velocity dispersion curves for dif-ferent modes. Gabriels et al. (1987) used f-k (frequency-wavenumber) transformation to achieve separation of thefundamental and higher mode Rayleigh waves. As in thecase of the p-u technique, the loci of maximum amplitudesin the f-k domain define the phase-velocity dispersioncurves for the different modes; the corresponding phase ve-locity for any point on a locus is given by the f/k ratio.

Inversion: General concepts

The inversion of geophysical data typically beginswith a discrete parameterization of the subsurface in termsof a finite-length vector p of discrete parameters. For agiven discrete parameterization, an infinite number of dif-ferent realizations of p exists, one realization for each setof physically reasonable numerical values that can be as-signed to the elements of p. The complete set of possiblerealizations of p is termed parameter space. The primarypurpose of inversion is to select a specific parameter vec-tor pa from parameter space as representative of the actualproperties of the subsurface.

A necessary tool for the selection of pa is some meas-ure of consistency (known as the objective function) be-tween the observed geophysical data and a set of corre-sponding theoretical predictions called the theoreticaldata; the theoretical data are computed from a trial pa-rameter vector ptrial and a satisfactory theory of the rele-vant phenomenon called the forward model or forwardproblem. The objective function for a succession of trialparameter vectors is evaluated as a means of converging ona satisfactory choice for pa.

Additional criteria are often used to reduce nonunique-ness in the selection of pa, including the minimization (ormaximization) of certain global characteristics such as themagnitude or spatial variation of the parameter vector;these additional criteria are often incorporated into the ob-jective function.

Given this general description of geophysical inver-sion, the basic components of an inversion procedure forsurface-wave data may be listed as follows:



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• A finite number of points on an observed dispersioncurve

• A discrete parameterization of the subsurface, typicallyas a horizontally layered medium

• A solution to the problem of computing theoretical dis-persion data for a given layered earth model (i.e., the so-lution to the forward problem)

• An objective function that decreases with increasinglydesirable characteristics of the layered earth model

• A search process that considers a succession of trial lay-ered earth models and selects a model that is optimum inthe sense of minimizing the objective function

• A process to appraise the uniqueness, resolution, andvariance of the optimum layer parameters

General references for geophysical inversion theory in-clude the compilation edited by Lines (1988), and the text-books by Tarantola (1987), Menke (1989), Parker (1994),and Scales and Smith (1994).

Inversion of surface wave dispersion curves

A stack of L horizontal layers over a half space (Fig-ure 20) is the most common discrete parameterization forinversion of surface wave dispersion curves. Each layer isassumed to be a homogenous and isotropic linearly elasticmedium. The parameters for layer j are typically chosen tobe the thickness hj, S-wave velocity VSj, P-wave velocityVPj, and density pj. Equivalent parameters in each layer canbe defined based on the general relationships between theP-wave and S-wave velocities, the elastic constants, andthe density (e.g., an equivalent set of layer parameters isthickness hj, Lamé modulus lj, shear modulus 2j, and den-sity pj). If Love waves are under consideration, then it isunnecessary to include the P-wave velocity or the Lamémodulus. A parameter vector p with M = 4(L + 1) parame-ters for Rayleigh waves, or M = 3(L + 1) parameters forLove waves, is used to represent the complete set of all pa-rameters.

The observed data consist of N > M phase velocitiesc(ui) measured for a particular surface-wave type(Rayleigh or Love) and mode, and at a given set of fre-quencies ui:

. (90)

These data are to be compared with N theoretical phase ve-locities ct(ui) computed for the same surface-wave type,mode, and frequencies ui:

, (91)

where trial values are used for the elements of the parame-ter vector p.

Computation of theoretical phase velocities for a lay-ered linearly elastic subsurface is the forward problem inthis case. It is typically a process of finding the roots of adispersion equation or period equation which representsthe constraints imposed on surface wave propagation in thelayered model:

. (92)

Given a frequency u and parameter vector p, the dis-persion equation defines the wavenumbers that can exist.These wavenumbers are denoted here by kn(u,p) for inte-ger n, and are ordered so that k0(u,p) > k1(u,p) > k2(u,p)and so on. The fundamental mode has wavenumberk0(u,p), and the higher modes are associated with the suc-cessively smaller wavenumbers. The theoretical phase ve-locity at frequency u for mode n is computed by the ratioof frequency to wavenumber:


+x

+z

Free surface (tractions zero)

VPj VSj pj hj l j 2j pj hj

VP1 VS1 p1 h1 l1 21 p1 h1

VP(L+1), VS(L+1), p(L+1) l (L+1), 2(L+1), p(L+1)

Layer 1

Layer j

Half-space

VPL VSL pL hL lL 2L pL hL Layer L

Figure 20. Discrete parameterization of the subsurface interms of L horizontal layers underlain by a half-space. Eachlayer is a homogeneous and isotropic linearly elasticmedium. Parameters may be P-wave velocity VP, S-wave ve-locity VS, density p, and layer thickness h, or the elasticLamé modulus l, the shear modulus 2, density p, and layerthickness h.


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. (93)

Thus, by finding the roots of the dispersion equation (92)and computing the phase velocity using equation (93), aphase-velocity dispersion curve for each mode can be con-structed.

Equations (92) and (93) represent an overview of theforward problem for a surface-wave inversion. Numerousspecific methods exist for computing theoretical dispersioncurves for surface waves for a layered elastic half space.These include the Thomson-Haskell matrix method(Thomson, 1950; Haskell, 1953), and the approaches cred-ited to Knopoff and colleagues (Knopoff, 1964; Schwaband Knopoff, 1970, 1972). The Thomson-Haskell matrixmethod is a special case of the more general formulation ofelastic wave propagation in a vertically heterogeneousmedium introduced by Gilbert and Backus (1966) andknown as the propagator matrix method. Other methodsinclude the method of reflection and transmission coeffi-cients (Kennett, 1983), the stiffness matrix method (Kauseland Roesset, 1981), and the numerical integration method(Takeuchi and Saito, 1972).

Given a discrete parameterization and the solution tothe forward problem, the inversion is carried out by search-ing parameter space for one parameter vector pa that min-imizes an objective function. The most basic objectivefunction Φ(p) is the cumulative squared discrepancy be-tween the observed and theoretical data:

, (94)

where the superscript T indicates transpose. The search forpa may proceed iteratively through a limited portion of pa-rameter space from an initial guess p0 (e.g., by means ofsolving a sequence of local linear discrete inverse prob-lems), or it may be a global search which is conducted overthe entire parameter space.

Regardless of the search strategy, the inversion of sur-face-wave data generally suffers from nonuniqueness inthe sense that more than one parameter vector can be re-garded as acceptably minimizing the objective function.Nonuniqueness may be addressed by adding a priori infor-mation (e.g., it is common to fix the values of the P-wavevelocity and density in an inversion of Rayleigh wave data

because the inversion is relatively less sensitive to these pa-rameters), and by adding a reasonable global constraint(e.g., requiring the S-wave velocities in pa to be within acertain range). Questions of uniqueness are tied closely tothe concepts of parameter resolution (the degree to whichsmall features can be distinguished) and parameter vari-ance (expected statistical variability). An understanding ofparameter resolution and variance is obtained by referenceto one of the previously cited general sources.

The literature describing the inversion of surface wavedata is extensive if consideration is given to all scales of ap-plication. Key concepts for discrete linear inversion areidentified and thoroughly discussed by Wiggins (1972); thiswork has influenced many later investigations. Recent pa-pers that focus on various aspects of the inversion of sur-face-wave data for near-surface properties include Rix andLeipski (1991), Addo and Robertson (1992), Yuan andNazarian (1993), Ganji et al. (1998), and Xia et al. (1999).Inversion based on neural network theory is developed byMichaels and Smith (1997) and by Gucunski et al. (1998).The neural network papers and the work by Ganji et al.(1998) address the problem of including multiple modes.

A recent contribution by Forbriger (2003a, b) uses aFourier-Bessel expansion to implement full-wavefield in-version; this method accounts for higher modes and leakymodes without identification of dispersion curves. The as-sumption of a horizontally layered subsurface model to ac-count for dispersion has been called into question by vanWijk and Levshin (2004), who show that near-surface het-erogeneity can give rise to dispersion without layering. Ad-ditional papers on surface-wave inversion are listed in theselected references at the end of this chapter.

AcknowledgmentsI thank Don Steeples for his review of a preliminary

draft, Dwain Butler for his extraordinary patience withmissed deadlines, and Daryl Jones and Sona Andrews, whogave me permission to work on this project. I also thankLee Liberty, who contributed the data for some of the fig-ures in the section on reflection methods and brought to myattention several recent innovations in instrumentation.This chapter is Contribution Number 127 of the Center forGeophysical Investigation of the Shallow Subsurface atBoise State University.



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Appendix A

Crosscorrelation and autocorrelation

The crosscorrelation of two real functions h1(t) andh1(t) gives the crosscorrelation function h12(t) defined asfollows:

, (A-1)

where the symbol ⊗ indicates the operation of crosscorre-lation. The crosscorrelation function is a measure of thesimilarity of the two functions at different shifts or lagsrepresented by the variable t. The crosscorrelation of twodifferent functions is not commutative, but the followingrelationship holds:

. (A-2)

A change of variables demonstrates that the crosscor-relation of functions h1(t) and h2(t) can be computed byconvolution:

. (A-3)

The autocorrelation of a real function h(t) is the cross-correlation of h(t) with itself and results in an even func-tion.

Cross spectrum and crosscorrelation theorem

The cross spectrum~h12(u) is the Fourier integral trans-

form of the crosscorrelation function h12(u):

. (A-4)

Given the following Fourier integral transform pairs:

(A-5)

the crosscorrelation theorem may be stated as follows:

(A-6)

where the asterisk indicates the complex conjugate.

Appendix BThis appendix is devoted to a detailed development of

the geophone equation which is given in the text as equa-tion (10). Although the design and fabrication of a moving-coil electrodynamic geophone varies with the manufac-turer, it is reasonable to represent any geophone of thistype as a damped harmonic oscillator. The geophonemodel shown in Figure B-1 is adopted here as a fairly re-alistic representation. The following development is stimu-lated by an approach to geophone analysis described byPieuchot (1984).

The source of the magnetic field is a ring-shaped mag-net of high permanent magnetization. A coil of fine wire issuspended by a spring in the annular gap between a ring-shaped pole piece and a central cylindrical pole piece, bothpole pieces being made of material of high magnetic sus-ceptibility. The magnetic induction B is radial in the annu-lar gap but axial within the central pole piece; the overallshape of the magnetic flux lines is torroidal. Motion of thecase is coupled to motion of the coil through the spring, butbecause the coupling is not rigid, the coil can move relativeto the case. In an ideal geophone, the relative motion is re-stricted to be in a direction that is parallel to the axis of thegeophone. The axis is taken to be vertical in the followinganalysis but the development for a geophone with a hori-zontal axis is essentially the same.

Several measures of vertical displacement are neededin order to derive the equation of motion for the coil. Thereference frame shown in Figure B-1 with origin O is fixedwith respect to an undisturbed portion of the earth. The topof the coil (point A) is chosen as a reference point indicat-ing the vertical position of the coil. When the spring is un-deformed (i.e., in an unextended and uncompressed posi-tion), point A is aligned with the origin O on the vertical z-axis of the reference frame, and the reference point on thecase (point B) is also aligned with origin O. Under staticconditions in the earth’s gravitational field, the weight ofthe coil causes the spring to sag so that point A is locatedat position ∆, whereas point B remains aligned with originO. During ground motion, the vertical displacement of thecase uB(t) is measured by the position of point B along thez-axis, and similarly the vertical displacement of the coiluA(t) is measured by the position of point A along the z-axis.

Of course, if the geophone is rigidly attached to theearth, then uB(t) is also the particle displacement. The iner-tia of the coil and the nonrigid coupling between coil andcase means that, in general, uA(t) will differ from uB(t).That difference between them is the vertical displacementof point A (i.e., the coil) relative to point B (i.e., the case),and is represented here by the symbol u(t):

, (B-1)



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where u(t) is called the relative coil displacement. Consid-eration of the definitions of points A and B indicates thatu(t) is also the extension of the spring. It will prove con-venient to define one additional vertical displacementfunction:

, (B-2)

where y(t) is the spring extension in excess of its static ex-tension under the weight of the coil.

According to Newton’s second law, the sum of theforces acting on the coil must equal the mass of the coil mtimes its acceleration in the chosen reference frame:

. (B-3)

The forces acting on the coil are summarized as fol-lows:

• a constant gravitational force directed vertically downand of magnitude mg where g is a positive number giv-ing the gravitational acceleration

• the spring force, which is directed opposite to u(t) withmagnitude K⏐u(t)⏐ where K is a positive number calledthe spring constant

• a mechanical damping force directed opposite to the ve-locity du(t)/dt and of magnitude D⏐du(t)/dt⏐ where D isa positive number called the mechanical damping coeffi-cient

• an electromagnetic damping force of magnitude23rn⏐B⏐I(t) that opposes the motion of the coil, whereI(t) is a positive number giving the current induced in thecoil by its motion relative to the magnetic field, r is theradius of the coil, and n is an integer giving the numberof turns in the coil

The mechanical damping force represents all viscous ef-fects as the spring/coil system moves in the air-filled annu-lar gap. The electromagnetic damping force is the force ex-erted on the electrical current I(t), and is computed by in-tegrating dF = (dl × B)I(t), where dl is a differential lengthelement along the coil in the direction of the current. As aconsequence of Lenz’s law, the current direction will besuch that the magnetic force instantaneously opposes thecoil motion. In this case, the vector cross product d l × Bgives a force that is vertical (up or down depending on thecurrent direction) at every point of the coil.

All of the time-dependent forces acting on the coil aregiven above in terms of the relative coil displacement u(t)except the electromagnetic damping force. It is thereforenecessary to express the current I(t) in terms of u(t) . Thisis accomplished by first computing the magnitude of theinduced electromotive force e(t) in the coil using Faraday’slaw:

, (B-4)

where Φ(t) is the total magnetic flux through the coil ande(t) is such that it produces a current that counteracts theflux change. Because the flux can change only by movingthe coil relative to the case, the flux must be a function ofu(t):

. (B-5)

Substituting the flux in equation (B-5) into equation (B-4),and applying the chain rule for derivatives, gives the elec-tromotive force in terms of the relative coil displacement:

, (B-6)

where Φ(u) is assumed to be linear for small enough u(t)that ⏐dΦ(u)/du⏐ can be approximated by a positive trans-duction constant C0 with SI units of V per m/s.


S N S

O A B

RA

RL

RS

Reference frame

+z Soil

∆

Surface

Figure B-1. Vertical moving-coil electrodynamic geophoneattached to the earth with a spike. The vertical axis of thereference frame is fixed with respect to an undisturbed por-tion of the earth. Reference point A at the top of coil andreference point B on the case both align with origin O whenthe spring is in undeformed state. Position ∆ is static posi-tion of A when spring deforms under the weight of the coil.Resistances RA, RL, and RS are the input resistance (amplifierimpedance) of the seismograph, resistance of the line be-tween the geophone and the seismograph, and the geophoneshunt resistance, respectively.


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The current generated by e(t) depends on the resist-ance Rc and inductance Lc of the coil, and the external cir-cuit attached to the geophone terminals. Analysis of the ex-ternal circuit shown in Figure B-1 gives the following re-sult:

. (B-7)

The resistance RE is the equivalent resistance of the ex-ternal circuit:

, (B-8)

where RS is the geophone shunt resistance, RA is the inputresistance (amplifier impedance) of the seismograph, andRL is the resistance of the line between the geophone andthe seismograph. If the inductance term in equation (B-7)is small relative to the resistance terms, then equations (B-6) and (B-7) can be combined to give the desired expres-sion for the current I(t) in terms of the relative displace-ment u(t):

. (B-9)

Neglecting the inductance of the coil, and representing theexternal circuit as a pure resistance RE, are simplificationsthat do not undermine the fundamental results of the analy-sis.

The equation of motion of the coil is obtained accord-ing to equation (B-3) by summing the four forces listedabove and equating the sum to the product of the coil massand acceleration

(B-10)

where equation (B-9) is used for I(t) in the electromagneticdamping force. Because mg = K∆ and the time derivativesof u(t) and y(t) are identical, the equation of motion (B-10)can be written in terms of the spring extension y(t),

(B-11)

where definition (B-1) has been used to substitute for uA(t).The dependent variable in equation of motion (B-11) canbe converted from y(t) to the voltage V(t) across the seis-mograph input by multiplying the input resistance RA bythe current I(t) to obtain the following relation:

, (B-12)

where the current I(t) is from equation (B-9). The voltagesign convention is chosen in equation (B-12) so that a pos-itive voltage corresponds to an upward motion of the coil(downward motion of the case). Differentiating equation ofmotion (B-11) once with respect to t and applying equation(B-12) gives the geophone equation:

(B-13)

where vB(t) and aB(t) are the velocity and acceleration ofthe case, respectively:

and. (B-14)

The constants u0, h, and C are called the natural frequency,total damping constant, and total transduction constant,respectively, and are defined as follows:

and

(B-15)

As mentioned in the main text, the geophone equation(B-13) is important because it relates the voltage observedat the seismograph input to the motion of the case. The mo-tion of the case is a proxy for particle motion if the geo-phone is firmly attached to the earth.



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Spitzer, R., F. O. Nitsche, A. G. Green, and H. Horstmeyer,2003, Efficient aquisition, processing, and interpreta-tion strategy for shallow 3D seismic surveying; A casestudy: Geophysics, 68, 1792–1806.

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Steeples, D. W., A. G. Green, T. V. McEvilly, R. D. Miller,W. E. Doll, and J. W. Rector, 1997, A workshop ex-amination of shallow seismic reflection surveying: TheLeading Edge, 16, 1641–1647.

Steeples, D. W., R. W. Knapp, and C. D. McElwee, 1986,Seismic reflection investigations of sinkholes beneathInterstate Highway 70 in Kansas: Geophysics, 51, 295–301.

Steeples, D. W., and R. D. Miller, 1990, Seismic reflectionmethods applied to engineering, environmental, andgroundwater problems, in S. H. Ward, ed., Geotechni-cal and environmental geophysics: Society of Explo-ration Geophysicists, 1, 1–30.

———1998, Avoiding pitfalls in shallow seismic reflec-tion surveys: Geophysics, 63, 1213–1224.

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Journal of Environmental and Engineering Geophys-ics, 0, 15–24.

Stokoe, K. H., II, S. G. Wright, J. A. Bay, and J. M. Roes-set, 1994, Characterization of geotechnical sites by theSASW method, in R. D. Woods, ed., Geophysicalcharacterization of sites: International Science, 15–25.

Takeuchi, H., and M. Saito, 1972, Seismic surface waves,in B. A. Bolt, ed., Seismology: Surface waves andearth oscillations: Methods in Computational Physics,11, Academic Press, 217–295.

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Tokimatsu, K., S. Tamura, and H. Kojima, 1992, Effects ofmultiple modes on Rayleigh wave dispersion charac-teristics: Journal of Geotechnical Engineering, 118,1529–1543.

van der Veen, M., H. A. Buness, F. Büker, and A. G. Green,2000, Field comparison of high- frequency seismicsources for imaging shallow (10-250 m) structures:Journal of Environmental and Engineering Geophys-ics, 5, 3956.

van der Veen, M., and A. G. Green, 1998, Land streamerfor shallow seismic data acquisition: Evaluation ofgimbal-mounted geophones: Geophysics, 63, 1408-1413.

van der Veen, M., R. Spitzer, A. G. Green, and P. Wild,2001, Design and application of a towed land-streamersystem for cost-effective 2-D and pseudo-3-D shallowseismic data acquisition: Geophysics, 66, 482–500.

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Vrettos, C., 1991, Time-harmonic Boussinesq problem fora continuously non-homogeneous soil: Earthquake En-gineering and Structural Dynamics, 20, 961-977.

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Wiggins, R. A., 1972, The general linear inverse problem:Implication of surface waves and free oscillations forearth structure: Reviews of Geophysics, 10, 251–285.

Xia, J., R. D. Miller, and C. B. Park, 1999, Estimation ofnear-surface shear-wave velocity by inversion of Ray-leigh waves: Geophysics, 64, 691–700.

Xia, J., R. D. Miller, C. B. Park, J. A. Hunter, and J. B. Har-ris, 2000, Comparing shear-wave velocity profilesfrom MASW with borehole measurements in uncon-solidated sediments, Fraser River Delta, B.C., Canada:Journal of Environmental and Engineering Geophys-ics, 5, 1–3.



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Yilmaz, O., 2001, Seismic data processing: Society of Ex-ploration Geophysicists.

Yuan, D., and S. Nazarian, 1993, Automated surface wavemethod: Inversion technique: Journal of GeotechnicalEngineering, 119, 1112–126.

Zelt, C. A., and R. B. Smith, 1992, Seismic traveltime in-version for 2-D crustal velocity structure: GeophysicalJournal International, 108, 16–4.

Supplementary ReferencesThe literature describing the applications and method-

ology of near-surface seismology has grown considerablysince the original SEG publication on geotechnical and en-vironmental geophysics (Ward, 1990). The following cate-gorized list of references is for the interval 1990–2004 in-clusive, and serves as a supplement to the references citedin the main text. With very few exceptions, the supplemen-tary references are limited to refereed journal articles pub-lished in English that address seismic methods in which thesources and receivers are deployed at the surface on land.Together with the references cited in the main text, thesupplementary references serve as an introduction to theliterature, and are by no means a comprehensive compila-tion of relevant papers. Each reference is placed under onecategory but many of them apply equally well to other cat-egories.

Archaeological and forensic studies

Benjumea, B., T. Teixido, and J. A. Pena, 2001, Applica-tion of the CMP refraction method to an archaeologi-cal study (Los Millares, Almeria, Spain): Journal ofApplied Geophysics, 46, 77–84.

Karastathis, V. K., and S. P. Papamarinopoulos, 1997, Thedetection of King Xerxes’ Canal by the use of shallowreflection and refraction seismics; preliminary results:Geophysical Prospecting, 45, 389–401.

Rabell, W., H. Stuempel, and S. Woelz, 2004, Archaeolog-ical prospecting with magnetic and shear-wave sur-veys at the ancient city of Miletos (western Turkey):The Leading Edge, 23, 69–693, 703.

Tsokas, G. N., et al., 1995, The detection of monumentaltombs buried in tumuli by seismic refraction: Geo-physics, 60, 1735–1742.

Vafidis, A., et al., 2003, Mapping the ancient port at the ar-chaeological site of Itanos (Greece) using shallowseismic methods: Archaeological Prospection, 10,163–173.

Witten, A., D. D. Gillette, J. Sypniewski, and W. C. King,1992, Geophysical diffraction tomography at a dino-saur site: Geophysics, 57, 187–195.

Environmental problems

Choudhury, K., D. K. Saha, and P. Chakraborty, 2001,Geophysical study for saline water intrusion in acoastal alluvial terrain: Journal of Applied Geophys-ics, 46, 189–200.

de Iaco, R., A. G. Green, H. R. Maurer, and H. Horstmeyer,2003, A combined seismic reflection and refractionstudy of a landfill and its host sediments: Journal ofApplied Geophysics, 52, 139–156.

Haegeman, W., and W. F. Van Impe, 1999, Characterizationof disposal sites from surface wave measurements:Journal of Environmental and Engineering Geophys-ics, 4, 27–33.

Juhlin, C., 1995, Imaging of fracture zones in the Finnsjönarea, central Sweden, using the seismic reflectionmethod: Geophysics, 60, 66–75.

Juhlin, C., and H. Palm, 1999, 3-D structure below Avro Is-land from high-resolution reflection seismic studies,southeastern Sweden: Geophysics, 64, 662–667.

Miller, R, D., and D. W. Steeples, 1994, Applications ofshallow high-resolution seismic reflection to variousenvironmental problems: Journal of Applied Geophys-ics, 31, 65–72.

Musil, M., et al., 2002, Shallow seismic surveying of analpine rock glacier: Geophysics, 67, 1701–1710.

Pugin, A. J. M., et al., 2004, Near-surface mapping usingSH-wave and P-wave seismic land-streamer data ac-quisition in Illinois, U.S.: The Leading Edge, 23, 677–682.

Sharp, M. K., D. K. Butler, and K. J. Sjostrom, 1999, Inte-grated geophysical methods approach to subsurfacegeologic mapping utilizing high-resolution transientelectromagnetic surveys: Journal of Environmental &Engineering Geophysics, 4, 57–70.

Temples, T. J., M. G. Waddell, W. J. Domoracki, and J.Eyer, 2001, Noninavasive determination of the loca-tion and distribution of DNAPL using advanced seis-mic reflection techniques: Ground Water, 39, 465–474.

Wyatt, D. E., M. G. Waddell, and G. B. Sexton, 1996, Geo-physics and shallow faults in unconsolidated sedi-ments: Ground Water, 34, 326–334.

Xia, J., C. Chen, P. H. Li, and M. J. Lewis, 2004, Delin-eation of a collapse feature in a noisy environmentusing a multichannel surface wave technique: Geo-technique, 54, 17–27.

Zinni, E. V., 1995, Subsurface fault detection using seismicdata for hazardous-waste-injection well permitting: Anexample from St. John the Baptist Parish, Louisiana:Geophysics, 60, 468–475.



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Geotechnical engineering and mining

Al-Rawahy, S. Y. S., and N. R. Goulty, 1995, Effect of min-ing subsidence on seismic velocity monitored by a re-peated reflection profile: Geophysical Prospecting, 43,191–201.

Anderson, N., M. Roark, M. Shoemaker, and J. Baker,1998, Reflection seismic mapping of an abandonedcoal mine, Belleville, Illinois: Journal of Environmen-tal and Engineering Geophysics, 2, 81-88.

Andrus, R. D., and K. H. Stokoe, 2000, Liquefaction re-sistance of soils from shear-wave velocity: Journal ofGeotechnical and Geoenvironmental Engineering, 126,1015–1025.

Cardarelli, E., C. Marrone, and L. Orlando, 2003, Evalua-tion of tunnel stability using integrated geophysicalmethods: Journal of Applied Geophysics, 52, 93–102.

Davies, E. B., E. J. Mercado, M. W. O’Neill, and J. A. Mc-Donald, 1998, Physical model studies of a real timeriverbed scour measurement system: Journal of Envi-ronmental and Engineering Geophysics, 3, 111-120.

———2001, Field experimental studies of a riverbedscour measurement system: Journal of Environmentaland Engineering Geophysics, 6, 57–70.

———2002, Studies of a riverbed scour monitor systemusing a pier-interior cased borehole: Journal of Envi-ronmental and Engineering Geophysics, 7, 151–160.

Ferguson, I. J., J. P. Ristau, V. G. Maris, and I. Hosain,1999, Geophysical imaging of a kaolinite deposit atSylvan, Manitoba, Canada: Journal of Applied Geo-physics, 41, 105–129.

Ferrucci, F., M. Amelio, M. Sorriso-Valvo, and C. Tansi,2000, Seismic prospecting of a slope affected by deep-seated gravitational slope deformation; The LagoSackung, Calabria, Italy: Engineering Geology, 57, 53–64.

Frappa, M., and C. Molinier, 1993, Shallow seismic reflec-tion in a mine gallery: Engineering Geology, 33,201–208.

Gendzwill, D. J., and R. Brehm, 1993, High-resolutionseismic reflections in a potash mine: Geophysics, 58,741–748.

Goforth, T., and C. Hayward, 1992, Seismic reflection in-vestigations of a bedrock surface buried under allu-vium: Geophysics, 57, 121–1227.

Guy, E. D., R. C. Nolen-Hoeksema, J. J. Daniels, and T.Lefchik, 2003, High-resolution SH-wave seismic re-flection investigations near a coal mine-related road-way collapse feature: Journal of Applied Geophysics,54, 51–70.

Hammer, P. T. C., R. M. Clowes, and K. Ramachandran,2004, High-resolution seismic reflection imaging of athin, diamondiferous kimberlite dike: Geophysics, 69,1143–1154.

Imran, I., S. Nazarian, and M. Picornell, 1995, Crack de-tection using time-domain wave propagation tech-nique: Journal of Geotechnical Engineering, 121, 198–207.

Jeng, Y., 1995, Shallow seismic investigation of a site withpoor reflection quality: Geophysics, 60, 1715–1726.

Johnston, M. A., and P. J. Carpenter, 1998, Use of seismicrefraction surveys to identify mine subsidence frac-tures in glacial drift and bedrock: Journal of Environ-mental and Engineering Geophysics, 2, 213–221.

Kalinski, M. E., A. Ata, K. H. Stokoe II, and M. W.O’Neill, 2001, Use of SASW measurements to evalu-ate the effect of lime slurry conditioning in drilledshafts: Journal of Environmental and EngineeringGeophysics, 6, 147–156.

Kim, J. S., W. M. Moon, G. Lodha, M. Serza, and N. Soon-awala, 1994, Imaging of reflection seismic energy formapping shallow fracture zones in crystalline rocks:Geophysics, 59, 753–765.

Kovin, O. N., 2000, Some results of acoustic reflectiontesting in russian potash mines: Journal of Environ-mental and Engineering Geophysics, 5, 39–45.

Kwasnicka, B., and H. Marcak, 1998, The thickness of al-tered zones in tunnels determined from seismic inter-ference waves: Journal of Environmental and Engi-neering Geophysics, 3, 89–96.

Lesmes, D., and F. D. Morgan, 2001, Seismic measure-ments of ground displacements caused by trains andquarry blasts at the superconducting super collider sitein Texas: Journal of Environmental and EngineeringGeophysics, 6, 133–143.

Louis, J., T. Papadopoulos, G. Drakatos, and P. Pantzartzis,1995, Conventional and modern seismic investigationsfor rock quality determination at a dam site; A casehistory: Geophysical Prospecting, 43, 779–792.

Nichol, D., and J. M. Reynolds, 2002, Application of re-flection seismology to foundation investigations at A5Pont Melin Rug, North Wales: Quarterly Journal ofEngineering Geology and Hydrogeology, 35, 247–256.

Nyquist, J. E., W. E. Doll, R. K. Davis, and R. A. Hopkins,1996, Cokriging surface topography and seismic re-fraction data for bedrock topography: Journal of Envi-ronmental and Engineering Geophysics, 1, 67–74.

Okko, O., 1994, Vertical increase in seismic velocity withdepth in shallow crystalline bedrock: Journal of Ap-plied Geophysics, 32, 335–345.

Perron, G., and A. J. Calvert, 1998, Shallow, high-resolu-tion seismic imaging at the Ansil mining camp in theAbitibi greenstone belt: Geophysics, 63, 379–391.

Pietsch, K., and R. Slusarczyk, 1992, The application ofhigh-resolution seismics in Polish coal mining: Geo-physics, 57, 171–180.



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Qingdong, Z., et al., 2004, Geophysical exploration for in-terlayer slip breccia gold deposits; Example fromPengjiakuang gold deposit, Shandong Province, China:Geophysical Prospecting, 52, 97–108.

Radzevicius, S. J., and G. L. Pavlis, 1999, High-frequencyreflections in granite? Delineation of the weatheringfront in granodiorite at Piñon Flat, California: Geo-physics, 64, 1828–1835.

Ramos Martinez, J., et al., 1997, Site effects in MexicoCity; constraints from surface wave inversion of shal-low refraction data: Journal of Applied Geophysics,36, 157-165.

Robertson, P. K., S. Sasitharan, J. C. Cunning, and D. C.Sego, 1995, Shear-wave velocity to evaluate in-situstate of ottawa sand: Journal of Geotechnical Engi-neering, 121, 262–273.

Ryden, N., C. B. Park, P. Ulriksen, and R. D. Miller, 2004,Multimodal approach to seismic pavement testing:Journal of Geotechnical and Geoenvironmental Engi-neering, 130, 636–645.

Shoemaker, M. L., et al., 1999, Reflection seismic andground-penetrating radar study of previously mined(lead/zinc) ground, Joplin, Missouri: Journal of Envi-ronmental and Engineering Geophysics, 4, 105–112.

Urosevic, M., B. Evans, and L. Vella, 2002, Shallow high-resolution seismic imaging of the Three Springs talcmine, Western Australia: The Leading Edge, 21, 923–926.

Woolery, E. W., 2002, SH-wave seismic reflection imagesof anomalous foundation conditions at the Mis-sissinewa dam, Indiana: Journal of Environmental andEngineering Geophysics, 7, 161–168.

Wright, C., J. A. Wright, and J. Hall, 1994, Seismic reflec-tion techniques for base metal exploration in EasternCanada: Examples from Buchans, Newfoundland: Jour-nal of Applied Geophysics, 32, 105–116.

Glacial, sedimentological, or structural geology

Baker, G. S., et al., 2003, Near-surface seismic reflectionprofiling of the Matanuska Glacier, Alaska: Geo-physics, 68, 147–156.

Barnes, M. K., and R. F. Mereu, 1996, An application ofthe 3-D seismic technique for mapping near-surfacestratigraphy near London, Ontario: Journal of Envi-ronmental and Engineering Geophysics, 1, 171–177.

Benjumea, B., and T. Teixido, 2001, Seismic reflectionconstraints on the glacial dynamics of Johnsons Glac-ier, Antarctica: Journal of Applied Geophysics, 46,31–44.

Büker, F., A. G. Green, and H. Horstmeyer, 1998, Shallowseismic reflection study of a glaciated valley: Geo-physics, 63, 1395–1407.

Carr, B. J., Z. Hajnal, and A. Prugger, 1998, Shear-wavestudies in glacial till: Geophysics, 63, 1273–1284.

Chroston, P. N., R. Jones, and B. Makin, 1999, Geometryof Quaternary sediments along the north Norfolkcoast, UK; A shallow seismic study: Geological Mag-azine, 136, 465–474.

Hawman, R. B., and H. O. Ahmed, 1995, Shallow seismicreflection profiling over a mylonitic shear zone, RubyMountains-East Humboldt Range metamorphic corecomplex, NE Nevada: Geophysical Research Letters,22, 1545–1548.

Hawman, R. B., C. L. Prosser, and J. E. Clippard, 2000,Shallow seismic reflection profiling over the Brevardzone, South Carolina: Geophysics, 65, 1388-1401.

Miller, R. D., and J. Xia, 1997, Delineating paleochannelsusing shallow seismic reflection: The Leading Edge,16, 1671–1674.

Pugin, A., S. E. Pullan, and D. R. Sharpe, 1996, Observa-tion of tunnel channels in glacial sediments with shal-low land-based seismic reflection: Annals of Glaciol-ogy, 22, 176–180.

Roberts, M. C., S. E. Pullan, and J. A. Hunter, 1992, Ap-plications of land-based high resolution seismic reflec-tion analysis to Quaternary and geomorphic research:Quaternary Science Review, 11, 557–568.

Sharpe, D., A. Pugin, S. Pullan, and J. Shaw, 2004, Re-gional unconformities and the sedimentary architec-ture of the Oak Ridges Moraine area, southern On-tario: Canadian Journal of Earth Sciences, 41, 183–198.

Wiederhold, H., H. A. Buness, and K. Bram, 1998, Glacialstructures in northern Germany revealed by a high-res-olution reflection seismic survey: Geophysics, 63,1265–1272.

Groundwater resources

Ayers, J. F., 1990, Shallow seismic refraction used to mapthe hydrostratigraphy of Nukuoro Atoll, Micronesia:Journal of Hydrology, 113, 123-133.

Baker, G. S., D. W. Steeples, C. Schmeissner, and K. T.Spikes, 2000, Ultrashallow seismic reflection monitor-ing of seasonal fluctuations in the water table: Envi-ronmental and Engineering Geoscience, 6, 271–277.

Clow, D. W., et al., 2003, Ground water occurrence andcontributions to streamflow in an alpine catchment,Colorado Front Range: Ground Water, 41, 937–950.

Davies, K. J., R. D. Barker, and R. F. King, 1992, Applica-tion of shallow reflection techniques in hydrogeology:The Quarterly Journal of Engineering Geology, 25,207–216.

Eddy-Dilek, C. A., et al., 1997, Definition of a critical con-fining zone using surface geophysical methods:Ground Water, 35, 451–462.



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Gburek, W. J., G. J. Folmar, and J. B. Urban, 1999, Fielddata and ground water modeling in a layered fracturedaquifer: Ground Water, 37, 175–184.

Holman, I. P., K. M. Hiscock, and P. N. Chroston, 1999,Crag aquifer characteristics and water balance for theThurne catchment, Northeast Norfolk: The QuarterlyJournal of Engineering Geology, 32, 365–380.

Holzschuh, J., 2002, Low-cost geophysical investigationsof a paleochannel aquifer in the Eastern Goldfields,Western Australia: Geophysics, 67, 690–700.

Jarvis, K. D., and R. J. Knight, 2002, Aquifer heterogene-ity from SH-wave seismic impedance inversion: Geo-physics, 67, 1548–1557.

MacDonald, A. M., D. F. Ball, and D. M. McCann, 2000,Groundwater exploration in rural Scotland using geo-physical techniques, in N. S. Robinson, and B. D. R.Misstear, eds., Groundwater in the Celtic regions;Studies in hard rock and Quaternary hydrogeology:Geological Society of London Special Publications,182, 205–217.

Meekes, J. A. C., B. C. Scheffers, and J. Ridder, 1990, Op-timization of high-resolution seismic reflection param-eters for hydrogeological investigations in The Nether-lands: First Break, 8, 263–270.

Meekes, J. A. C., and M. F. P. van Will, 1991, Comparisonof seismic reflection and combined TEM/VES meth-ods for hydrogeological mapping: First Break, 9, 543–551.

Miller, P. T., S. McGeary, and J. A. Madsen, 1996, Highresolution seismic reflection images of New Jerseycoastal aquifers: Journal of Environmental and Engi-neering Geophysics, 1, 55–66.

Odum, J. K., et al., 1999, Shallow high-resolution seismic-reflection imaging of karst structures within the Flori-dan aquifer system, Northeastern, Florida: Journal ofEnvironmental and Engineering Geophysics, 4, 251–261.

Olsen, H., C. Ploug, U. Nielsen, and K. Sorensen, 1993,Reservoir characterization applying high-resolution seis-mic profiling, Rabis Creek, Denmark: Ground Water,31, 84–90.

Paillet, F., 1995, Integrating surface geophysics, well logsand hydraulic test data in the characterization of het-erogeneous aquifers: Journal of Environmental andEngineering Geophysics, 0, 1–13.

Palmer, S. P., et al., 1995, Application of reflection seis-mology to the hydrogeology of the Spokane Aquifer:Washington Geology, 23, 27–30.

Sharpe, D. R., A. Pugin, S. E. Pullan, and G. Gorrell, 2003,Application of seismic stratigraphy and sedimentologyto regional hydrogeological investigations; An exam-ple from Oak Ridges Moraine, southern Ontario,Canada: Canadian Geotechnical Journal, 40, 711–730.

Shtivelman, V., and M. Goldman, 2000, Integration of shal-low reflection seismics and time domain electromag-netics for detailed study of the coastal aquifer in theNitzanim area of Israel: Journal of Applied Geophys-ics, 44, 197–215.

Sumanovac, F., and M. Weisser, Evaluation of resistivityand seismic methods for hydrogeological mapping inkarst terrains: Journal of Applied Geophysics, 47, 13–28.

Taucher, P., and B. N. Fuller, 1994, A refraction staticsmethod for mapping bedrock: Groundwater, 32, 895–904.

Whitely, R. J., J. A. Hunter, S. E. Pullan, and P. Nutalaya,1998, “Optimum offset” seismic reflection mapping ofshallow aquifers near Bangkok, Thailand: Geophysics,63, 1385–1394.

Wolfe, P. J., and B. H. Richard, 1996, Integrated geophys-ical studies of buried valley aquifers: Journal of Envi-ronmental and Engineering Geophysics, 1, 75–84.

Woodward, D., 1994, Contributions to a shallow aquiferstudy by reprocessed seismic sections from petroleumexploration surveys, eastern Abu Dhabi, United ArabEmirates: Journal of Applied Geophysics, 31, 271–289.

Seismic and volcanic hazards

Benjumea, B., J. A. Hunter, J. M. Aylsworth, and S. E. Pul-lan, 2003, Application of high-resolution seismic tech-niques in the evaluation of earthquake site response,Ottawa Valley, Canada: Tectonophysics, 368, 193–209.

Benson, A. K., and N. B. Mustoe, 1995, Analyzing shallowfaulting at a site in the Wasatch fault zone, Utah, USA,by integrating seismic, gravity, magnetic, and trenchdata: Engineering Geology, 40, 139–156.

Bruner, I., and E. Landa, 1991, Fault interpretation fromhigh-resolution seismic data in the northern Negev, Is-rael: Geophysics, 56, 1064–1070.

Catchings, R. D., and W. H. K. Lee, 1996, Shallow veloc-ity structure and Poisson’s ratio at Tarzana, California,strong-motion accelerometer site: Bulletin of the Seis-mological Society of America, 86, 1704–1713.

Cox, R. T., et al., 2000, Quaternary faulting in the southernMississippi Embayment and implications for tectonicsand seismicity in an intraplate setting: Geological So-ciety of America Bulletin, 112, 1724–1735.

Dolan, J. F., and T. L. Pratt, 1997, High-resolution seismicreflection profiling of the Santa Monica fault zone,West Los Angeles, California: Geophysical ResearchLetters, 24, 2051-2054.

Dutta, U., et al., 2000, Delineation of spatial variation ofshear wave velocity with high-frequency Rayleigh



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waves in Anchorage, Alaska: Geophysical Journal In-ternational, 143, 365–375.

Gomberg, J. S., et. al., 2003, Lithology and shear-wave ve-locity in Memphis, Tennessee: Bulletin of the Seismo-logical Society of America, 93, 986–997.

Gosar, A., 1998, Seismic reflection surveys of the KrskoBasin structure; implications for earthquake hazard atthe Krsko nuclear power plant, southeast Slovenia:Journal of Applied Geophysics, 39, 131–153.

Harris, J. B., and R. L. Street, 1997, Seismic investigationof near-surface geological structure in the Paducah,Kentucky, area, application to earthquake hazard eval-uation, in R. B. Van Arsdale, ed., Neotectonics andearthquakes in the central Mississippi Valley: Engi-neering Geology, 46, 369-383.

Havenith, H. B., et al., 2002, Site effect analysis around theseismically induced Ananevo Rockslide, Kyrgyzstan:Bulletin of the Seismological Society of America, 92,3190–3209.

Lee, T. C., S. Biehler, S. K. Park, and W. J. Stephenson,1996, A seismic refraction and reflection study acrossthe central San Jacinto Basin, Southern California:Geophysics, 61, 1258–1268.

McBride, J. H., et al., 2003, Variable post-Paleozoic defor-mation detected by seismic reflection profiling acrossthe northwestern “prong” of New Madrid seismiczone: Tectonophysics, 368, 171–191.

Morey, D., and G. T. Schuster, 1999, Palaeoseismicity ofthe Oquirrh Fault, Utah from shallow seismic tomog-raphy: Geophysical Journal International, 138, 25–35.

Odum, J. K., et al., 1995, High- resolution, shallow, seis-mic reflection surveys of the Northwest Reelfoot Riftboundary near Marston, Missouri: U. S. GeologicalSurvey Professional Paper, P1–P18.

Odum, J. K., W. J. Stephenson, K. M. Shedlock, and T. L.Pratt, 1998, Near-surface structural model for defor-mation associated with the February 7, 1812, NewMadrid, Missouri, earthquake: Geological Society ofAmerica Bulletin, 110, 149–162.

Odum, J. K., W. J. Stephenson, and R. A. Williams, 2003,Variable near-surface deformation along the Com-merce segment of the Commerce geophysical linea-ment, southeast Missouri to southern Illinois, USA:Tectonophysics, 368, 155-170.

Odum, J. K., et al., 2001, High resolution seismic-reflec-tion imaging of shallow deformation beneath thenortheast margin of the Manila High at Big Lake,Arkansas: Engineering Geology, 62, 91–103.

Palmer, J. R., et al., 1997, Shallow seismic reflection pro-files and geological structure in the Benton Hills,Southeast Missouri, in R. B. Van Arsdale, ed., Neotec-tonics and earthquakes in the central Mississippi Val-ley: Engineering Geology, 46, 217–233.

Pratt, T. L., et. al., 1998, Multiscale seismic imaging of ac-tive fault zones for hazard assessment; A case study ofthe Santa Monica fault zone, Los Angeles, California:Geophysics, 63, 479–489.

Pratt, T. L., et al., 2001, Late Pleistocene and Holocene tec-tonics of the Portland Basin, Oregon and Washington,from high-resolution seismic profiling: Bulletin of theSeismological Society of America, 91, 637–650.

Pratt, T. L., et al., 2002, Shallow seismic imaging of foldsabove the Puente Hills blind-thrust fault, Los Angeles,California: Geophysical Research Letters, 29, doi:10.1029/2001GL014313.

Rashed, M., et al. , 2003, Acquisition, processing and in-terpretation of shallow seismic reflection profileacross Uemachi Fault, along Yamato River, Osaka,Japan: Journal of Geosciences, Osaka City University,46, 193–206.

Rashed, M., et al., 2002, Weighted stack of shallow seismicreflection line acquired in downtown Osaka City,Japan: Journal of Applied Geophysics, 50, 231–246.

Rotstein, Y., G. Shaliv, and M. Rybakov, 2004, Active tec-tonics of the Yizre’el Valley, Israel, using high-resolu-tion seismic reflection data: Tectonophysics, 382, 31–50.

Saccorotti, G., B. Chouet, and P. Dawson, 2003, Shallow-velocity models at the Kilauea Volcano, Hawaii, deter-mined from array analyses of tremor wavefields: Geo-physical Journal International, 152, 633–648.

Scott, J. B., et al., 2004, A shallow shear-wave velocitytransect across the Reno, Nevada, area basin: Bulletinof the Seismological Society of America, 94, 2222–2228.

Shedlock, K. M., T. M. Brocher, and S. T. Harding, 1990,Shallow structure and deformation along the San An-dreas Fault in Cholame Valley, California, based onhigh-resolution reflection profiling: Journal of Geophys-ical Research, B, Solid Earth and Planets, 95, 5003–5020.

Sheley, D., et al., 2003, 2-D seismic trenching of colluvialwedges and faults: Tectonophysics, 368, 51–69.

Shields, G., et al., 1998, Shallow geophysical survey acrossthe Pahrump Valley fault zone, California-Nevada bor-der: Bulletin of the Seismological Society of America,88, 270–275.

Shtivelman, V., U. Frieslander, E. Zilberman, and R. Amit,1998, Mapping shallow faults at the Evrona playa siteusing high-resolution reflection method: Geophysics,63, 1257–1264.

Stephenson, W. J., and J. H. McBride, 2003, Contributionsto neotectonics and seismic hazard from shallow geo-physical imaging: Tectonophysics, 368, 1–5.

Stephenson, W. J., K. M. Shedlock, and J. K. Odum, 1995,Characterization of the Cottonwood Grove and Ridge-ly faults near Reelfoot Lake, Tennessee, from high-res-



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olution seismic reflection data: U. S. Geological Sur-vey Professional Paper, I1–I10.

Stephenson, W. J., R. A. Williams, J. K.Odum, and D. M.Worley, 2000, High-resolution seismic reflection sur-veys and modeling across an area of high damage fromthe 1994 Northridge earthquake, Sherman Oaks, Cali-fornia: Bulletin of the Seismological Society of Amer-ica, 90, 643–654.

Sun, R., Q.-C., Sung, and T.-K. Liu, 1998, Near-surface ev-idence of Recent Taiwan Orogeny detected by a shal-low seismic method: Earth and Planetary Science Let-ters, 163, 291–300.

Van Arsdale, R., J. Purser, W. J. Stephenson, and J. K.Odum, 1998, Faulting along the southern margin ofReelfoot Lake, Tennessee: Bulletin of the Seismologi-cal Society of America, 88, 131–139.

Wang, C. Y., 2002, Detection of a recent earthquake faultby the shallow reflection seismic method: Geophysics,67, 1465–1473.

Wang, C. Y., J. D. Chiu, and L. A. Lin, 2001, The detectionof three active faults on the Taoyuan Terrace, north-western Taiwan by shallow reflection seismic: Terres-trial, Atmospheric and Oceanic Sciences, 12, 599–614.

Wang, C. Y., S. Y. Kuo, and J. W. Hsiao, 2003, Investigat-ing near-surface structures under the Changhua Fault,west-central Taiwan, by the reflection seismic method:Terrestrial, Atmospheric and Oceanic Sciences, 14,343–367.

Wang, Z., I. P. Madin, and E. W. Woolery, 2003, ShallowSH-wave seismic investigation of the Mt. Angel Fault,Northwest Oregon, USA: Tectonophysics, 368, 105–117.

Williams, R. A., et al., 1995, Seismic surveys assess earth-quake hazard in the New Madrid area: The LeadingEdge, 14, 30–34.

Williams, R. A., et al., 2000, Correlation of 1- to 10-Hzearthquake resonances with surface measurements ofS-wave reflections and refractions in the upper 50 m:Bulletin of the Seismological Society of America, 90,1323–1331.

Williams, R. A., W. J. Stephenson, and J. K. Odum, 2003,Comparison of P- and S-wave velocity profiles ob-tained from surface seismic refraction/reflection anddownhole data: Tectonophysics, 368, 71-88.

Wise, D. J., J. Cassidy, and C. A. Locke, 2003, Geophysi-cal imaging of the Quaternary Wairoa North Fault,New Zealand; A case study: Journal of Applied Geo-physics, 53, 1–16.

Woolery, E. W., J. A. Schaefer, and Z. Wang, 2003, Ele-vated lateral stress in unlithified sediment, Midconti-nent, United States—Geotechnical and geophysical in-dicators for a tectonic origin: Tectonophysics, 368,139–153.

Woolery, E. W., and R. Street, 2002, Quaternary fault reac-tivation in the fluorspar area fault complex of westernKentucky; Evidence from shallow SH-wave reflectionprofiles, in R. L. Wheeler, and D. Ravat, eds., The Illi-nois Basin, seismicity, Quaternary faulting, and seis-mic hazard: Seismological Research Letters, 73, 628–639.

Woolery, E. W., R. L. Street, Z. Wang, and J. B. Harris,1993, Near-surface deformation in the New Madridseismic zone as imaged by high resolution SH-waveseismic methods: Geophysical Research Letters, 20,1615–1618.

Reflection method

Ayers, J. F., 1996, Synthetic seismogram generation for de-signing shallow seismic surveys: Journal of Environ-mental and Engineering Geophysics, 1, 109–118.

Baker, G. S., D. W. Steeples, and M. Drake, 1998, Mutingthe noise cone in near-surface reflection data: An exam-ple from southeastern Kansas: Geophysics, 63, 1332–1338.

Baker, G. S., D. W. Steeples, and C. Schmeissner, 2002,The effect of seasonal soil-moisture conditions on near-surface seismic reflection data quality: First Break, 20,35–41.

Brokesova, J., J. Zahradnik, and P. Paraskevopoulos, 2000,Ray and finite-difference modelling of CDP seismicsections for shallow lignite deposits: Journal of Ap-plied Geophysics, 45, 261–272.

Dasios, A., et al., 1999, Seismic imaging of the shallowsubsurface; Shear-wave case histories: GeophysicalProspecting, 47, 565–591.

Deidda, G. P., and R. Balia, 2001, An ultrashallow SH-wave seismic reflection experiment on a subsurfaceground model: Geophysics, 66, 1097–1104.

Feroci, M., et al., 2000, Some considerations on shallowseismic reflection surveys: Journal of Applied Geo-physics, 45, 127–139.

Karastathis, V. K., and I. F. Louis, 2004, Comparison testof seismic sources in shallow reflection seismics: An-nales Geologiques des Pays Helleniques, 40A, 159–173.

Liu, Z.-M., and R. A. Young, 2001, Dispersive and non-dis-persive noise removal by local, slant sum, adaptive fil-tering:Journal of Environmental and Engineering Geo-physics, 6, 157–163.

Malinowski, M. S., and G. S. Baker, 2003, Energy and soil-moisture effects on nonlinear deformation associatedwith near-surface seismic reflection sources: Journalof Environmental and Engineering Geophysics, 8, 221–226.

McMechan, G. A., and R. Sun, 1991, Depth filtering offirst breaks and ground roll: Geophysics, 56, 390–396.



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Miller, K. C., S. H. Harder, D. C. Adams, and T. O’Don-nell, Jr., 1998, Integrating high-resolution refractiondata into near-surface seismic reflection data process-ing and interpretation: Geophysics, 63, 1339-1347.

Miller, R. D., and D. W. Steeples, 1990, A shallow seismicreflection survey in basalts of the Snake River Plain,Idaho: Geophysics, 55, 761–768.

Miller, R. D., N. L. Anderson, H. R. Feldman, and E. K.Franseen, 1995, Vertical resolution of a seismic surveyin stratigraphic sequences less than 100 m deep insoutheastern Kansas: Geophysics, 60, 423–430.

Paine, J. G., R. A. Morton., and L. E. Garner, 1997, Site de-pendency of shallow seismic data quality in saturated,unconsolidated coastal sediments: Journal of CoastalResearch, 13, 564–574.

Pugin, A., and S. E. Pullan, 2000, First-arrival alignmentstatic corrections applied to shallow seismic reflectiondata: Journal of Environmental and Engineering Geo-physics, 5, 7–15.

Pullan, S. E., 1990, Recommended standard for seismic(/radar) data files in the personal computer environ-ment: Geophysics, 55, 1260–1271.

Richwalski, S., K. Roy-Chowdhury, and J. C. Mondt,2001, Multi-component wavefield separation appliedto high-resolution surface seismic data: Journal of Ap-plied Geophysics, 46, 101–114.

Robertsson, J. O., et al., 1996, Effects of near-surfacewaveguides on shallow high-resolution seismic refrac-tion and reflection data: Geophysical Research Letters,23, 495–498.

Roth, M., and K. Holliger, 1999, Inversion of source-gen-erated noise in high-resolution seismic data: The Lead-ing Edge, 18, 1402–1406.

——— 2000, The non-geometric PS wave in high-resolu-tion seismic data; Observations and modelling: Geo-physical Journal International, 140, F5–F11.

Roth, M., K. Holliger, and A. G. Green, 1998, Guidedwaves in near-surface seismic surveys: GeophysicalResearch Letters, 25, 1071–1074.

Spitzer, R., F. O. Nitsche, and A. G. Green, 2001, Reduc-ing source-generated noise in shallow seismic datausing linear and hyperbolic transformations: Geophys-ics, 66, 1612–1621.

Sun, R., and A. Wang, 1998, Removing bad traces in shal-low seismic exploration: Terrestrial, Atmospheric andOceanic Sciences, 9, 183–196.

Wilson, T. H., 1990, Model studies of shallow common-offset seismic data: Geophysics, 55, 394–401.

Xia, J., and R. D. Miller, 2000, Fast estimation of parame-ters of a layered-dipping earth model by inverting re-flected waves: Journal of Environmental and Engi-neering Geophysics, 5, 21–29.

———2000, Design of a hum filter for suppressing power-line noise in seismic data: Journal of Environmentaland Engineering Geophysics, 5, 31–38.

Refraction method and surface-based tomography

Aldridge, D. F., and D. W. Oldenburg, 1992, Refractor im-aging using an automated wavefront reconstructionmethod: Geophysics, 57, 378–385.

Ayers, J. F., 2000, Seismic refraction analysis of multipledipping interfaces—Revisited: Journal of Environ-mental and Engineering Geophysics, 5, 1–5.

Belfer, I., et al., 1998, Detection of shallow objects usingrefracted and diffracted seismic waves: Journal of Ap-plied Geophysics, 38, 155–168.

Belfer, I., and E. Landa, 1996, Shallow velocity depthmodel imaging by refraction tomography: Geophysi-cal Prospecting, 44, 859–870.

Bloor, R., 1996, Near-surface layer traveltime inversion; Asynthetic example: Geophysical Prospecting, 44, 197–213.

Brzostowski, M. A., and G. A. McMechan, 1992, 3-D to-mographic imaging of near-surface seismic velocityand attenuation: Geophysics, 57, 396–403.

Chang, X., et al., 2002, 3-D tomographic static correction:Geophysics, 67, 1275–1285.

Ditmar, P., J. Penopp, R. Kasig, and J. Makris, 1999, Inter-pretation of shallow refraction seismic data by reflec-tion/refraction tomography: Geophysical Prospecting,47, 871–901.

Improta, L., et al. , 2003, High-resolution seismic tomog-raphy across the 1980 (Ms 6.9) southern Italy earth-quake fault scarp: Geophysical Research Letters, 30,doi:10.1029/2003GL017077.

Landa, E., S. Keydar, and A. Kravtsov, 1995, Determina-tion of a shallow velocity-depth model from seismicrefraction data by coherence inversion: GeophysicalProspecting, 43, 177–190.

Lecomte, I., H. Gjoystdal, A. Dahle, and O. C. Pedersen,2000, Improving modelling and inversion in refractionseismics with a first-order Eikonal solver: GeophysicalProspecting, 48, 437–454.

Liu, C., and J. M. Stock, 1993, Quantitative determinationof uncertainties in seismic refraction prospecting: Geo-physics, 58, 553–563.

Macrides, C. G., and L. P. Dennis, 1994, 2D and 3D re-fraction statics via tomographic inversion with under-relaxation: First Break, 12, 523–537.

Orlowsky, D., H. Rueter, and L. Dresen, 1998, Combina-tion of common-midpoint-refraction seismics with thegeneralized reciprocal method: Journal of Applied Geo-physics, 39, 221–235.



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Seisa, H. H., and M. S. El Shafey, 1999, A two-dimen-sional ray-tracing program for shallow seismic refrac-tion data: Egyptian Journal of Geology, 42, 347–362.

Shtivelman, V., 1996, Kinematic inversion of first arrivalsof refracted waves—A combined approach: Geophys-ics, 61, 509–519.

Stefani, J. P., 1995, Turning-ray tomography: Geophysics,60, 1917–1929.

Whiteley, R. J., 2004, Shallow seismic refraction interpre-tation with visual interactive ray trace (VIRT) model-ing: Exploration Geophysics, 35, 116–123.

Xia, J., Miller, et al., A pitfall in shallow shear-wave re-fraction surveying: Journal of Applied Geophysics, 51,1–9.

Surface wave method

Beaty, K. S., and D. R. Schmitt, 2003, Repeatability ofmultimode Rayleigh-wave dispersion studies: Geophys-ics, 68, 782–790.

Gucunski, N., and R. D. Woods, 1991, Instrumentation forSASW testing, in S. K. Bhatia and G. W. Blaney, eds.,Recent advances in instrumentation, data acquisitionand testing in soil dynamics: American Society ofCivil Engineers, Geotechnical Special Publication 29,1–16.

———1992, Numerical simulation of the SASW test: SoilDynamics and Earthquake Engineering, 11, 213–227.

Hering, A., et al., 1995, A joint inversion algorithm toprocess geoelectric and surface wave seismic data;Part I, Basic ideas: Geophysical Prospecting, 43, 135–156.

Herman, G. C., P. A. Milligan, R. J. Huggins, and J. W.Rector, 2000, Imaging shallow objects and hetero-geneities with scattered guided waves: Geophysics,65, 247–252.

Kalinski, M. E., and K. H. Stokoe II, 2003, In situ estimateof shear wave velocity using borehole spectral analy-sis of surface waves tool: Journal of Geotechnical andGeoenvironmental Engineering, 129, 529–535.

Li, X.-P., 1997, Elimination of higher modes in dispersivein-seam multimode Love waves: Geophysical Pros-pecting, 45, 945–961.

Long, L. T., and A. H. Kocaoglu, 2001, Surface-wavegroup-velocity tomography for shallow structures:Journal of Environmental and Engineering Geo-physics, 6, 71–81.

Marosi, K. T., and D. R. Hiltunen, 2004, Characterizationof spectral analysis of surface waves shear wave ve-locity measurement uncertainty: Journal of Geotechni-cal and Geoenvironmental Engineering, 130, 1034–1041.

Misiek, R., et al., 1997, A joint inversion algorithm toprocess geoelectric and surface wave seismic data;

Part II, Applications: Geophysical Prospecting, 45,65–85.

Ohori, M., A.. Nobata, and K. Wakamatsu, 2002, A com-parison of ESAC and FK methods of estimating phasevelocity using arbitrarily shaped microtremor arrays:Bulletin of the Seismological Society of America, 92,2323–2332.

O’Neill, A., M. Dentith, and R. List, 2003, Full-waveformP-SV reflectivity inversion of surface waves for shal-low engineering applications: Exploration Geo-physics, 34, 158–173.

Pedersen, H. A., J. I. Mars, and P.-O. Amblard, 2003, Im-proving surface-wave group velocity measurements byenergy reassignment: Geophysics, 68, 677–684.

Scherbaum, F., K. G. Hinzen, and M. Ohrnberger, 2003,Determination of shallow shear wave velocity profilesin the Cologne, Germany area using ambient vibra-tions: Geophysical Journal International, 152, 597–612.

Tian, G., D. W. Steeples, J. Xia, and K. T. Spikes, 2003,Useful resorting in surface-wave method with the au-tojuggie: Geophysics, 68, 1906–1908.

Tokimatsu, K., S. Kuwayama, S. Tamura, and Y. Miyadera,1991, VS determination from steady state Rayleighwave method: Soils and Foundations, 31, 153–163.

Tokimatsu, K., K. Shinzawa, and S. Kuwayama, 1992, Useof short-period microtremors for VS profiling: Journalof Geotechnical Engineering, 118, 1544–1558.

Tokimatsu, K., S. Tamura, and H. Kojima, 1992, Effects ofmultiple modes on Rayleigh wave dispersion charac-teristics: Journal of Geotechnical Engineering, 118,1529–1543.

Xia, J., et al., 2004, Utilization of high-frequency Rayleighwaves in near-surface geophysics: The Leading Edge,23, 753–759.

Zerwer, A., G. Cascante, and J. Hutchinson, 2002, Parame-ter estimation in finite element simulations of Ray-leigh waves: Journal of Geotechnical and Geoenviron-mental Engineering, 128, 250–261.

Zhang, S. X., and L. S. Chan, 2003, Possible effects ofmisidentified mode number on Rayleigh wave inver-sion: Journal of Applied Geophysics, 53, 17–29.

Other applications or methods

Al-Ali, M., R. Hastings-James, M. Makkawi, and G. Ko-rvin, 2003, Vibrator attribute leading velocity estima-tion: The Leading Edge, 22, 400–405.

Bachrach, R., and A. Nur, 1998, High resolution shallow-seismic experiments in sand, Part I: Water table, fluidflow, and saturation: Geophysics, 63, 1225–1233.

Bachrach, R., J. Dvorkin, and A. Nur, 1998, High resolu-tion shallow-seismic experiments in sand, Part II: Ve-locities in shallow unconsolidated sand: Geophysics,63, 1225–1233.



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Baker, G. S., C. Schmeissner, D. W. Steeples, and R. G.Plumb, 1999, Seismic reflections from depths of lessthan two meters: Geophysical Research Letters, 26,279–282.

Baker, G. S., D. W. Steeples, and C. Schmeissner, 1999, In-situ, high-frequency P-wave velocity measurementswithin 1 m of the earth’s surface: Geophysics, 64,323–325.

Bergman, B., A. Tryggvason, and C. Juhlin, 2004, High-resolution seismic traveltime tomography incorporat-ing static corrections applied to a till-covered bedrockenvironment: Geophysics, 69, 1082–1090.

Butler, K. E., R. D. Russell, A. W. Kepic, and M. Maxwell,1996, Measurement of the seismoelectric responsefrom a shallow boundary: Geophysics, 61, 1769–1778.

Gallardo, L. A., and M. A. Meju, 2003, Characterization ofheterogeneous near-surface materials by joint 2D in-version of dc resistivity and seismic data: GeophysicalResearch Letters, 30, doi:10.1029/2003GL017370.

Greenhalgh, S. A., and B. Zhou, 2003, Surface seismic im-aging by multi-frequency amplitude inversion: Explo-ration Geophysics, 34, 217–224.

Jefferson, R. D., D. W. Steeples, R. A. Black and T. Carr,1998, Effects of soil-moisture content on shallow-seis-mic data: Geophysics, 63, 1357–1362.

Jeng, Y., J. Tsai, and S. Chen, 1999, An improved methodof determining near surface Q: Geophysics, 64,1608–1617.

Landa, E., and S. Keydar, 1998, Seismic monitoring of dif-fraction images for detection of local heterogeneities:Geophysics, 63, 1093–1100.

Meju, M. A., L. A. Gallardo, and A. K. Mohamed, 2003,Evidence for correlation of electrical resistivity andseismic velocity in heterogeneous near-surface materi-als: Geophysical Research Letters, 30, doi:10.1029/2002GL016048.

Michaels, P., 2002, Identification of subsonic P-waves:Geophysics, 67, 909–920.

Mikhailov, O. V., M. W. Haartsen, and M. N. Toksoz, 1997,Electroseismic investigation of the shallow subsurface;Field measurements and numerical modeling: Geo-physics, 62, 97–105.

Moret, G. J. M., W. P. Clement, M. D. Knoll, and W. Bar-rash, 2004, VSP traveltime inversion: Near-surface is-sues: Geophysics, 69, 345–351.

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