TID-4500, UC-35Peaceful Applications

of Explosions

TECHNICAL REPORT E-73-4SEISMIC REFRACTION EXPLORATION FOR

ENGINEERING SITE INVESTIGATIONS

BRUCE B. REDPATH

U. S. ARMY ENGINEER WATERWAYS EXPERIMENT STATIONEXPLOSIVE EXCAVATION RESEARCH LABORATORY

Livermore, California

MS. date: May 1973

ForewordThis report was prepared by the U. S. Army Engineer Waterways Experiment Station

(USAEWES) Explosive Excavation Research Laboratory (EERL), formerly the ExplosiveExcavation Research Office (EERO) from 1 August 1971 until 21 April 1972. Prior to 1August 1971 the organization was known as the USAE Nuclear Cratering Group.

The report was sponsored and funded under RDT&E 21X2040 P562G by theDirectorate of Military Construction, Office of the Chief of Engineers (DAEN-MCE-D).

The Director of the Waterways Experiment Station during the preparation of this reportwas COL Ernest D. Peixotto; the Directors of EERL were LTC Robert L. LaFrenz and LTCRobert R. Mills, Jr.

AbstractThis report is a summary of the theory and practice of using the refraction seismograph

for shallow, subsurface investigations. It is intended to be a guide to the application of thetechnique and not a comprehensive analysis of every aspect of the method. The reportbegins with the fundamentals and then progresses from time-intercept calculations tointerpretations using delay times. The limitations of this exploration tool are discussed, andother applications of the equipment, such as uphole surveys, are described. The reportalso recommends field procedures for carrying out refraction surveys.

AcknowledgmentsMessrs. Bruce Hall and Vincent Gottschalk monitored the project for the Directorate of Military Construction,

Office of the Chief of Engineers (DAEN-MCE-D), and the author is grateful for their helpful suggestions and theirpatience. The author also wishes to thank Messrs. Paul Fisher and Wayne McIntosh of the Geology Branch,Engineering Division, Office of the Chief of Engineers, and Messrs. Sigmund Schwarz and Boyd Bush ofShannon & Wilson, Inc., Seattle, for all of their valuable comments and constructive criticism of the report.

Conversion factorsBritish units of measurement used in this report can be converted to metric units as follows:

Contents

FOREWORD . . . . . . . . . . . iiABSTRACT . . . . . . . . . . iiiACKNOWLEDGMENTS . . . . . . . . . ivCONVERSION FACTORS . . . . . . . . . . ivINTRODUCTION . . . . . . . . . 1

Purpose . . . . . . . . . . 1Background . . . . . . . . . . 1Scope . . . . . . . . . . 2

THEORY . . . . . . . . . . . 2Fundamentals . . . . . . . . . . 2Intercept Times . . . . . . . . . 5Critical Distance . . . . . . . . . 7Dipping Layers . . . . . . . . . 8Delay Times . . . . . . . . . 9

PROBLEMS, LIMITATIONS, AND ADDITIONAL APPLICATIONS . . . . 19The Blind Zone and Velocity Reversals . . . . . . . 19Other Problems and Limitations . . . . . . . 25Additional Techniques . . . . . . . . . 28

FIELD PROCEDURES . . . . . . . . . 32CONCLUSIONS . . . . . . . . . . 35REFERENCES . . . . . . . . . . 37BIBLIOGRAPHY . . . . . . . . . . 38APPENDIX A. MATERIAL VELOCITIES . . . . . . . 39APPENDIX B. EXAMPLE PROBLEM . . . . . . . . 43

FIGURES1 Schematic of seismic refraction survey . . . . . . 32a Snell's Law and refraction of ray transmitted across

boundary between two media with different velocities(V2 = 2V1) . . . . . . . . . 4

2b Amplitudes of reflected and refracted compressionalwaves relative to incident waves as a function of angleof incidence . . . . . . . . . 4

3 Simple two-layer case with plane, parallel boundariesand corresponding time-distance curve . . . . . 5

4 Schematic of multiple-layer case and correspondingtime-distance curve . . . . . . . . 6

5 Plot of ratio of critical distance to depth of first layeras a function of velocity contrast . . . . . . 8

6 Example of dipping interface and concepts of "reverseshooting" and “apparent velocity" . . . . . . 8

7 Definition of delay time . . . . . . . 108 Schematic of reversed seismic line and delay-time

method of depth determination . . . . . . 119a Reversed seismic profile in which refracted arrivals

from both ends are recorded at only three detectors . . . . 139b Increasing overlap of refracted arrivals for situation in

Fig. 9a by firing shot beyond end of line and plotting"phantom” arrivals . . . . . . . . 13

10 Three-layer case showing travel paths of first arrivalsand corresponding time-distance curves . . . . . 15

FIGURES (continued)

11 Same time-distance curves as shown in Fig. 10 but withaddition of shot at center of seismic line . . . . . 16

12 Same time-distance curves as shown in Fig. 10 but withaddition of beyond end shot (center shot has beenomitted for sake of clarity) . . . . . . . 17

13 Method of determining true velocity of refractor by plottingdifferences of arrival times . . . . . . . 20

14 Wave-front diagram and maximum "undetectable" thicknessof "blind zone" . . . . . . . . 21

15 Nomograph to be used in determining maximum thicknessof possible hidden layer 23

16 Velocity reversal and corresponding time-distance curve . . . 2417 Schematic of ray-paths and time-distance curve for continuous

increase of velocity with depth . . . . . . 2518 Schematic of shallow, irregular refractor surface producing

different first-layer travel times at same geophonefrom shots on either side of it . . . . . . 26

19 Schematic of refraction survey across body of water . . . . 2820 Example of uphole survey and corresponding plot of

arrival times . . . . . . . . 3021a Meissner wave-front diagram showing high-velocity

layer at depth of 5 to 16 m . . . . . . . 3121b Meissner wave-front diagram showing thin high- and low-

velocity layers . . . . . . . . 3122 Recommended shot layout for seismic line . . . . . 3323 Example of seismic record on Polaroid film obtained with

portable engineering seismograph . . . . . 34B1 Travel times observed in hypothetical exploration

program . . . . . . . . 45B2 Identifying layers by velocity and determining half-intercept

times and delay times for first layer . . . . . 47B3 Determination of true value of V3 and delay times ∆T12

(intermediate shots not shown for sake of clarity) . . . . 49B4 Original profile compared with that derived by interpreting

synthesized time-distance data . . . . . . 51

TABLESA1 Speed of propagation of seismic 'waves in subsurface

materials . . . . . . . . . 40A2 Approximate range of velocities of longitudinal waves

for representative materials found in the earth's crust . . . . 41A3 Velocities of seismic waves in rocks . . . . . . 42B1 Observed travel times . . . . . . . 45B2 Velocities, cosines, times, and thicknesses . . . . . 51

SEISMIC REFRACTION EXPLORATION FORENGINEERING SITE INVESTIGATIONS

Introduction

PURPOSE

This report is intended as a guide to theapplication of seismic refraction techniquesto shallow, subsurface exploration ofengineering sites. Many civil engineers andgeologists have some acquaintance withthis basic geophysical tool, but few apply itfrequently. The primary purpose of thereport is to provide the reader with aworking knowledge of the method, with aconvenient reference, and further, with abasis to judge the applicability of themethod and the results to his particularexploration problem.

BACKGROUND

Refraction seismic surveying was thefirst major geophysical method to beapplied in the search for oil bearingstructures. Today, however, oil explorationrelies almost exclusively on some variety ofthe modern reflection seismograph. Recentprogress in geophysical exploration for oilhas stemmed from refinements toinstrumentation and from the computer-assisted processing and enhancement ofthe data. Refraction surveys are still usedoccasionally in oil exploration, particularlywhere they can assist in resolvingcomplicated problems in structural geology.

Although its application in the oilindustry has diminished over the years, themethod has found increasing use for siteinvestigations for civil engineering. It is avaluable investigative tool well-suited forshallow surveys, particularly when used inconjunction with the exploratory drill.

Significant advances in refraction-seismograph instrumentation have notoccurred to the same extent that they havein the development of the sophisticatedreflection equipment used for oilexploration. Solid state electronics haveimproved the portability of engineering typerefraction instruments, but they operatefundamentally in the same way they did 40years ago. The basic field practices andmethods of interpreting the data have notchanged with time, although specializedinterpretational techniques have beenproposed and developed for some difficultcases.

The conduct of refraction surveys andthe interpretation of the data are well-established and reasonably straight-forward, although they are not invariant.The user can change the field layout of hisequipment and apply judgment andimagination in his handling of the raw data.In common with other indirect methods ofsubsurface exploration, there

are no rigid, inflexible approaches tomaking sense of the data, nor are thereany handbooks that infallibly direct theengineer, geologist, or geophysicist to thecorrect answer. The general case willrequire thought and care; ambiguities anduncertainties are not uncommon. Someforeknowledge of site conditions and anunderstanding of what is geologically .plausible will always assist in resolving theraw data into meaningful information.

SCOPE

This report addresses the elements ofrefraction theory, the basic methods ofinterpretation, a variety of applications, andsome of the limitations. In discussing thetheory of the method, it is the intention ofthis report to progress from the simple tothe more realistic, deriving the formulasand procedures for interpretation as we goalong. The treatment is far fromexhaustive, but suitable references to theliterature are included for those who wishto pursue a specific aspect of the method.

Theory

FUNDAMENTALS

This section will review the principles ofseismic refraction theory and will developthose methods of interpretation that havethe widest use. There are many textbookson geophysics that discuss the principlesand applications of refraction surveys;however, most of them are oriented towardsexploration for oil and give only passingattention to detailed shallow investigations.Numerous journal articles treat the solutionof specific interpretation problems but only afew of these articles have broad application.Much of the following material will befamiliar to engineers and geologists whohave taken a first course in geophysics orwho have acquired first-hand experiencewith refraction surveys. The elements arepresented for those who have had noprevious exposure or who desire a review ofbackground material.

Before going into detail, it is appropriateto present a synopsis of refraction

exploration so that the factors discussedlater can be viewed with some sense ofperspective.

The refraction method consists ofmeasuring (at known points along thesurface of the ground) the travel times ofcompressional waves generated by animpulsive energy source. The energysource is usually a small explosive chargeand the energy is detected, amplified, andrecorded by special equipment designed forthis purpose. The instant of the explosion,or "zero-time,” is recorded on the record ofarriving pulses. The raw data, therefore,consists of travel times and distances, andthis time-distance information is thenmanipulated to convert it into the format ofvelocity variations with depth. Theinterpretation of this raw data will bedeveloped as we go along.

The process is schematically illustratedin Fig. 1. All measurements are made at thesurface of the ground, and the subsurfacestructure is inferred from

Fig. 1. Schematic of seismic refraction survey.

interpretation methods based on the laws ofenergy propagation.

The propagation of seismic energythrough subsurface layers is described byessentially the same rules that govern thepropagation of light rays through transparentmedia. The refraction or angular deviationthat a light ray or seismic pulse undergoeswhen passing from one material to anotherdepends upon the ratio of the transmissionvelocities of the two materials. Thefundamental law that describes therefraction of light rays is Snell's Law, andthis, together with the phenomenon of“critical incidence,” is the physical foundationof seismic refraction surveys.

Snell's Law and critical incidence areillustrated in Fig. 2a, which shows a mediumwith a velocity V1, underlain by a medium

with a higher velocity V2. Figure 2b is a plotof the relative amplitudes of the pulsestransmitted into, and reflected from, thehigher speed material.* Until the criticalangle of incidence is reached, almost all ofthe compressional energy is transmitted(refracted) into the higher velocity medium.When the critical angle is exceeded, theenergy is almost totally reflected and noenergy is refracted into the high-speed layer.Note

*It may seem anomalous in Fig. 2b that the sum ofthe amplitudes of the reflected and refracted pulses isgreater than that of the incident wave (i.e., greaterthan 1.0). However, the energy of a pulse isproportional to the square of its amplitude, and thesum of the energies of the reflected and refractedwaves is equal to the energy of the incident wave.

Fig. 2a. Snell's Law and refraction of raytransmitted across boundary betweentwo media with different velocities (V2 =2V1).

Fig. 2b. Amplitudes of reflected and refractedcompressional waves relative to incidentwaves as a function of angle ofincidence.

that we are dealing only with compressionalwaves and ignoring shear energy and thetransformation of a portion of thecompressional wave into a shear wave thatcan occur at boundaries.

The particular case of the critical angle ofincidence is fundamental to the derivation ofthe formulas for refraction exploration.Although the exact mathematical andphysical description of what occurs when aray is incident at the critical angle iscomplex, it is entirely adequate to assumethat the critically refracted ray travels alongthe boundary between the two media at thehigher of the two velocities. Further, as thecritically refracted ray travels along theboundary, it continually generates seismicwaves in the lower-velocity (upper) layer thatdepart from the boundary at the angle ofcritical incidence. In the literature thesewaves are frequently referred to as headwaves. If the velocities of the layers increasewith depth, a portion of the energy willeventually be refracted back to the surfacewhere it can be detected.

The following derivations of the refractionequations assume that the subsurface layerspossess certain characteristics: each layerwithin a stratigraphic sequence is isotropicwith regard to its propagation velocity, raypaths are made up of straight-line segments,and each layer has a higher velocity than theoverlying one. These are entirely reasonableassumptions and relatively few actual caseswill depart from these assumptions. Thespecial case of a velocity reversal (i.e., alayer having a lower velocity than the onewhich overlies it) will be discussed later. Thespecial situation in which velocity increasescontinuously (vs incrementally) with depthwill also be discussed briefly later in thereport.

We begin with the simplest of all cases:two layers with plane and parallelboundaries as illustrated in Fig. 3. A smallexplosive charge is detonated in a shallowhole at A and the energy is

detected by a set of detectors laid out in astraight line along the surface. The arrivaltimes of the impulses are plotted againstthe corresponding shot-to-detectordistances as shown in Fig. 3. The first fewarrival times are those of direct arrivalsthrough the first layer, and the slope of theline through these points, ∆T/∆X, is simplythe reciprocal of the velocity of that layer;i.e., 1/V1. At some distance from the shot,a distance called the critical distance, ittakes less time for the energy to traveldown to the top of the second layer,refract along the interface at the highervelocity V2 and travel back up to thesurface, than it does for the energy totravel directly through the top layer. Theenergy that arrives at the detectorsbeyond the critical distance will plot alonga line with a slope of 1/V2. The linethrough these refracted arrivals will notpass through the origin, but rather willproject back to the time axis to intersect itat a time called the intercept time.Because both the intercept time and thecritical distance are directly dependentupon the velocities of the two materialsand the thickness of the top layer, theycan be used to determine the depth to thetop of the second layer.

INTERCEPT TIMES

Referring to Fig. 3, let us compute thearrival time of the refracted impulse at adetector. Consider the travel path ABCD:

Fig. 3. Simple two-layer case with plane,parallel boundaries and correspondingtime-distance curve.

where Z1 is the thickness of the top layer,and a is the critical angle of incidence.The travel time is therefore given by:

Snell's law defines the critical angle ofincidence, a, by:

and selectively substituting Eq. (1) intothe previous equation:

If we now let X = 0, then T becomes theintercept time, Ti, and we can rewrite thelast expression as:

For the situation we have assumed in Fig.3, everything on the right-hand side of Eq.(2) can be determined from the time-distance plot; therefore, the depth to thesecond layer can be computed. The depthof the shot has been ignored in thederivation above, and the true depth to thesecond layer is determined simply

*An alternative version of this equation is:

by adding one-half the shot depth to thevalue of Z1 computed by Eq. (2).

In the particular example of Fig. 3, thedepth computed by Eq. (2) is the depthalong the entire seismic line because westipulated that the layers were plane andparallel.

A very important point to bring out at thistime is that all depths determined inrefraction surveys are measured normal tothe boundary between layers and are notnecessarily vertical depths beneath theground surface.

The intercept-time analysis can beextended to the case of multiple layers;however, only the resulting formulas will begiven here because their derivations areredundant and may be found in a number ofreferences. 1,2 Figure 4 schematicallyillustrates the multiple layer case

Fig. 4. Schematic of multiple-layer case andcorresponding time-distance curve.

and corresponding time-distance plot. NoteMat the intercept times and layerthicknesses have been identified by asubscript corresponding to the number ofthe layer:

If the velocity contrasts between layers arehigh enough; say 2 to 1, and onlyapproximate depths are required, then thefollowing formulas can be used:

where ∆T2 and ∆T3; are as indicated in Fig.4. Equations (6) and (7) will give

thicknesses that are greater than actual,and it is suggested that thicknesses initiallybe computed both ways to learn whetherthe error is significant in a particularsituation.

CRITICAL DISTANCE

The critical-distance method fordetermining depth will receive only briefattention here because it is analagous tothe intercept-time method, and offers noadvantages significant enough to warrantfurther detail. Its primary application is tocompute the depth of the first layer and toestimate the length of the seismic linerequired for a particular exploration task.

The critical distance is the distance fromthe shot point to the point at which therefracted energy arrives at the same timeas the energy traveling directly through thetop layer. The critical distance (Xc) isillustrated in Fig. 3; it is the breakpoint inthe graph of arrival times.*

By an approach similar to the one usedin deriving the intercept-time formulas, itcan be shown that the depth of the firstlayer is given by:

where Xc is the critical distance.

*There is, of course, a critical distance forrefractions from each layer in a multilayer case; weare concerned here only with the first breakpoint.

Equation (8) can be used to construct agraph showing the length of a seismic line(relative to the depth of the first layer)required to detect refractions from theunderlying layer, as a function of velocityratios. Figure 5 is a graph of Eq. (8), whichcan be of use in planning a seismic surveyif velocity ratios are assumed. The graphalso assists in giving a sense of perspectiveto the effect of velocity contrasts. Forexample, assume that there is about 15 ft ofoverburden with a velocity of 2, 500 ft/sec,and that it is underlain by a shale with avelocity of about 5,500 ft/sec. How longshould the seismic line be to insureadequate coverage for mapping theoverburden thickness? The velocity ratio,V2/V1 , is 2.2 so that Xc/Z1 is approximately3.25, which means that the critical distancewill be about 50 ft. The seismic spreadshould be at least three times this distance;

Fig. 5. Plot of ratio of critical distance to depth offirst layer as a function of velocity contrast.

therefore, a seismic line 150 to 200 ft longwould be satisfactory.

DIPPING LAYERS

We will now briefly consider theexistence of a dipping interface, theconcept of apparent velocities, and theireffect on depth computations.

The equations derived above requireknowledge of the "true" velocities of thelayers. If the boundaries between interfacesare nonparallel (i.e., if there are dippinginterfaces), a plot of arrival times vsdistance will give only apparent velocitiesfor the refracting layers, and the use ofthese apparent velocities will result inerroneous depths: The case of a dippingboundary and its effect on travel-time plotsis illustrated in Fig. 6. Figure 6 alsointroduces the idea of

Fig. 6. Example of dipping interface and conceptsof reverse shooting and "apparent velocity:'

"reverse shooting” of which should alwaysbe applied in refraction surveys. Reverseshooting simply means firing a shot at bothends of the seismic line so that arrival timesat each detector are measured from bothdirections.

It is evident from Fig. 6 that the apparentvelocity of the refracting layer, asdetermined from the time-distance plot,depends upon whether the shot is fired atthe up-dip or the down-dip end of theseismic line, and that a depth determined onthe basis of only one shot will be valid onlyat one point along the line. Unless the dipangle is known, reverse shooting is requiredto determine the true value of V2.

If the apparent velocity of the refractor asobserved from the down-dip shot is V2D,then from Snell's Law:

V2D = V1 / sin (αααα + γγγγ),

where γγγγ is the dip angle of the interfacerelative to the surface and αααα is the criticalangle of incidence. Similarly, the apparentvelocity, V2U, observed for the shot in the up-dip direction is given by:

V2U = V1 / sin (αααα - γγγγ).

We can rearrange the two relationshipsabove to obtain:

from which the dip angle can be determined:

The true value of V2 is not the arithmeticaverage of V2U and V2D, but is instead theharmonic mean multiplied by the cosine ofthe dip angle:

Other methods of determining true velocitieswill be discussed later.

As an example of the degree to which adipping interface can affect observedvelocities on a time-distance plot, considerthe case of a 2,000-ft/sec material overlyinga 5,000-ft/sec material with their interfacedipping 10 deg relative to the surface. Thefollowing refractor velocities would beobserved:

Up-dip (V2U): 8,515 ft/secDown-dip (V2D): 3,615 ft/secArithmetic average: 6,065 ft/secHarmonic mean: 5,075 ft/secHarmonic meanX Cos γγγγ: 5,000 ft/sec

= true velocity

The harmonic mean is generally accurateenough for computations; i.e., it is notusually necessary to compute the dip angleunless it is of interest in itself.

Depths are always computed using truevelocities. The use of apparent velocitiesmay result in significant errors.

DELAY TIMES

Previously, it was pointed out that truerefractor velocities cannot be determined byfiring a shot at only one end of

a seismic line, but that such velocities canbe determined if arrival times are recordedfrom both ends. Further, a depth computedfrom an intercept time actually representsthe depth of the refracting surfaceprojected back to the shot point. Thereversed profile, however, offers asignificant advantage in that the truevelocities and the thicknesses of layers canbe computed on a much more detailedbasis by means of delay times. Under idealcircumstances, depths can be determinedbeneath each geophone to allow mappingof irregular and dipping boundaries.

The meaning of the term "delay time" isillustrated by reference to Fig. 7 in whichthe delay time is defined at the shot pointand at the detector.* The delay time is thedifference between the time actually spentby the pulse traveling on its upward ordownward path through the upper layer,and the time it would have spent traveling,at the refractor velocity, along the normalprojection of this path on the interface.Although the definition of the delay timemay at first appear to be cumbersome, itsmeaning and application will becomeclearer as we progress. Consider the pulsetraveling up to the detector in Fig. 7 forwhich the delay time has been defined as:

* Although the distinction is not important inthe context of this report, the delay time" isreferred to as the timedepth, in some of theliterature. Strictly speaking, the term delay timeimplies that the refractor surface is horizontal;in this report depths are measured normal tothe refractor surface, regardless of itsdisposition.

Fig. 7. Definition of delay time.

The equivalence between a delay time andan intercept time is apparent when Eq. (12)is compared to the intercept-time

formula, Eq. (2). A delay time can bethought of as being analagous to the timetaken by a pulse to travel upward ordownward through a layer. from oneinterface to the next. It is evident that if thevalue of the delay time, ∆TD, at a particulardetector can be determined, then the depthbeneath the detector can be computed.

Before discussing the method by whichdelay times are determined, we willconsider the path of the refracted pulse,from shot to detector, which is shown inFig. 7. The total delay time is, by definition:

where Tt is the observed total travel timefrom shot to detector. It can be shown thatthe total delay time is the sum of the delaytimes at the shot and at the detector; i.e.,

∆TSD = ∆TS + ∆TD,

and by combining these two expressionswe obtain the following equation for thedelay time beneath the detector:

Consequently, if the delay time at the shot(∆TS) were known, ∆TD and the depthbeneath the geophone could be calculated.

If the depth of the refractor beneath theshot and the velocities of the layers areknown beforehand, then ∆TS can becalculated, and the arrival time from onlyone end of the line would be sufficient todetermine the delay time and depthbeneath the geophone. Although the depthbeneath the shot and the velocities are notgenerally known beforehand, the delaytime beneath the geophone can

nevertheless be determined by firing shotsat both ends of the line.

The reversed seismic line shown inFigure 8 will be used to illustrate themethod of delay times. Figure 8 shows thearrival times at the geophones from shotsat both ends of a seismic line. The totaltravel time from one end of the line to theother (sometimes called the "reciprocal"time)3 has been designated Tt and shouldbe the same for both shots.* The arrivaltimes at one of the (arbitrarily selected)geophones from the two shots, SP1 andSP2, have been designated TD1

* If the shot depths are equal.

Fig. 8. Schematic of reversed seismic lineand delay-time method of depthdetermination.

and TD2, respectively. Remembering thatthe objective is to find the delay time, ∆TD,at the geophone, consider the following.From Eq. (13) we can write each arrivaltime in terms of the component delay times:

therefore, TD1 + TD2 = ∆TS1 + ∆TS2 + 2∆TD +S/V2, where ∆TS is the delay time at a shotpoint. Similarly the total time can beexpressed in terms of delay times:

Note that the delay time beneath thegeophone is determined by subtracting thetotal time from the sum of the two arrivaltimes, and taking half the result. The depthbeneath the geophone to the top of therefractor is then calculated by Eq. (12):

It is important to keep in mind that TV thetotal time that is subtracted from the sum ofthe two arrival times in Eq. (14), must bethe arrival time of a pulse refracted from thesame layer from which the two otherarrivals were refracted. The total time

cannot be the arrival time of a pulserefracted from a deeper layer.

In the event that the derivation of Eq.(14) by means of something called a delaytime appears circuitous and indirect, thefollowing analysis, also based on Fig. 8, ispresented as an alternative:

Fig. 9a. Reversed seismic profile in whichrefracted arrivals from both endsare recorded at only threedetectors.

The first derivation, which explicitly usesa delay time, is the one commonly foundin the literature.

Before extending the delay-timemethod to a case in which there are morethan two layers, it is important to notethat the method can be applied onlywhere there is “overlap" between arrivalsrefracted from the same layer. In otherwords, the actual length of the seismicline should be sufficient to insureoverlapping of the refracted arrivals. Thispoint is illustrated in Fig. 9a, which

Fig. 9b. Increasing overlap of refractedarrivals for situation in Fig. 9a byfiring shot beyond end of line andplotting phantom arrivals.

shows the reversed time-distance curvessynthesized for a two-layer case. Althoughnot immediately obvious from a look at thetime-distances curves, only three of thedetectors near the center of the linerecorded refractions from both directions.Consequently, delay times can bedetermined only for these three detectors. Ifthe seismic line had been longer more of therefracted arrivals would have overlapped,and more delay times could be determined.

If the lack of overlap is noted in the fieldby reducing and plotting the dataimmediately after the shots. it is oftenpossible to partially remedy the situation byfiring additional shots off one or both ends ofthe line (i.e., beyond the end of the seismiccable) in line with the detector array. Thearrival times from a beyond-the-end shot areused to extrapolate the first set of refractedarrivals back towards the shot point.* Thistechnique is referred to as "phantoming" andis illustrated in Fig. 9b, which shows thesame data as Fig. 9a but with the addition ofa beyond-the-end shot.

If the plot of arrival times from thebeyond-the-end shot parallels the arrivaltimes from the end shot, they representrefractions from the same layer. This is thecase in Fig. 9b, in which the difference inarrival times between refracted arrivals fromboth the end and the beyond-the-end shotsis a constant, AT. Figure 9b shows how therefracted arrivals from the end shot areextrapolated back

* We are assuming, of course, that thearrivals from the beyond-the-end shot havebeen refracted from the layer from which the firstset of arrivals was refracted.

towards the shot point by reducing thebeyond-the-end arrival times by ∆T toproduce the phantom arrivals at distancesless than the critical distance. Thesephantom arrivals can then be used todetermine delay times over the regionshown in Fig. 9b. An additional shot couldalso be fired beyond the other end of theline to allow delay times to be determinedover the entire spread, permitting the depthto the refractor to be computed beneathevery detector. If there is a shot at thecenter of a seismic line, the shots placed atthe ends of the cable are, in effect, beyond-the-end shots for the opposite half of theline. If the arrival times from a beyond-the-end shot do not parallel the times from theend shot, there is a third, deeper layerpresent; this situation is discussed below.

In general, the interpreter is cautioned totry to assure himself that the two arrivaltimes that he is using to compute a delaytime represent refractions from the samelayer; otherwise he will be “Mixing applesand oranges.” Verifying the stratigraphicorigin of an arrival is not always easy.

The delay-time method is not limited tothe simple two-layer case. Ideally. a delaytime would be computed beneath eachgeophone for each layer in a sequence, butthis is almost never possible. Figure 10illustrates a very common situation inrefraction investigations. Note that there arethree layers and that the travel paths of thefirst arrivals are shown on the drawing.Examination of Fig. 10 will show that onlytwo of the detectors (at Stations 250 and300) recorded refractions from the thirdlayer from both of the end shots. There isobviously

Fig. 10. Three-layer case showing travelpaths of first arrivals andcorresponding time-distance curves.

no overlap of refractions from the secondlayer. The two delay times that can bedetermined at Stations, 250 and 300 willbe the sum of the delay times for the firstand second layers. The delay time in thefirst (top) layer must be subtracted fromthe total delay time before the thickness ofthe second layer can be computed.However, with only the information shownin Fig. 10, we have no way of determiningthe actual delay time for the first layer.

If we had only the arrival times from thetwo end shots as shown in Fig. 10, ouronly recourse would be to compute thethickness of the first layer at each end ofthe line by using the intercept-timeformula, and to interpolate linearly thesetwo values of depth across the length ofthe line. The interpolated depths of the firstlayer could be converted to delay times atStations 250 and 300 by Eq. (11). and

then subtracted from the total delay timesdetermined at these two detectors. Theresult would be values of delay times forthe second layer at these two stations, andthe thickness of the second layer would beinterpreted as:

where ∆T12 is the combined delay time forthe first and second layers, and ∆T1 is thedelay time for the first layer computed frominterpolated values of depth and Eq. (11).

Inspection of Fig. 10 will show that theabove procedure will lead to some verywrong answers. The first layer thickensappreciably in the middle of the spread,but there is no way of knowing this if shotsare fired only at the ends of the spread.The thickness of the second layer wouldbe considerably overestimated becausethe thickness of the first layer wasunderestimated; i.e., an insufficientamount of time would be subtracted fromthe total delay times at Stations 250 and300. Computing depths on the basis of theintercept times of the third-layer refractionswould result in the same errors.

The situation described above anddepicted in Fig. 10 was chosen to illustratethe merit of firing intermediate shots alongthe length of a seismic line. Intermediateshot points will result in better control offirst-layer depths and velocities; fewerassumptions are required to interpret theraw data.

Figure 11 is the same as Fig. 10, exceptthat a shot in the middle of the spread hasbeen added. An intercept

Fig. 11. Same time-distance curves asshown in Fig. 10 but with addition ofshot at center of seismic line.

time can now be obtained at the center aswell as the ends of the line, and we alsohave a check on the first-layer velocity atthe center.

It would be apparent from the intercepttimes in Fig. 11 that the 2,700-ft/sec first-layer is thicker near the center of the linethan at the ends; consequently, a muchmore accurate appraisal of the secondlayer's thickness could now be made.Additional intermediate shots would helpresolve the first layer in greater detail, andeventually permit more detailed mappingof the second layer.

The apparent velocities of the secondlayer shown in Fig. 11 may appear to varyconsiderably. The velocities on the right-hand portion are up-dip and down-dip dipvelocities with a harmonic mean of about5,650 ft/sec. The overall average for V2 isabout 5,450 ft/sec, very close to thenominal value of 5,500 ft/sec. The scatterof values about the nominal value is

typical of the accuracy that can beexpected in refraction surveys.

In the hypothetical case beingconsidered (Fig. 11) we can obtainenough detail about the top layer bymeans of intermediate shots. In thisparticular example there is not enoughoverlap of refractions from the top of thesecond layer to compute first-layerthicknesses by the delay-time method.This will generally be the case formultilayer situations. If this were a typicalengineering survey our interest wouldprobably be directed toward mapping thetop of the high-speed layer (10,500 ft/sec).How do we obtain more information? Withthe data in Fig. 11 we could compute thedepth to the top of the third layer at threelocations; i.e., at the center and ends ofthe line. A beyond-the-end shot is requiredfor more detail.

The arrival times from a shot locatedbeyond the end of the line are shown inFig. 12. These times were used togenerate phantom refracted arrivals by thetechnique demonstrated in Fig. 9, anddelay times were then computed from theoverlap of actual and phantom arrivaltimes from Station 250 to Station 550.These delay times are the sum of thedelay times in the first and second layer.We now introduce a new technique forusing these delay times to extract moreinformation from the data.

If the delay times in Fig. 12 aresubtracted from the corresponding arrivaltimes and the differences plotted, wehave, in effect, a new time-distance curvethat is equivalent to placing the shot anddetectors at the top of the third layer. Thereduced arrival times should plot with areciprocal slope equal to the

Fig. 12. Same time-distance curves as shown in Fig. 10 but with addition of beyond-the-end shot(center shot has been omitted for sake of clarity).

true velocity of the refracting horizon; i.e.,the third layer. This operation has beenperformed for the detectors at Stations 250to 550 in Fig. 12, and we see that thereciprocal slope is 10,000 ft/sec, inreasonable agreement with the nominalvelocity of 10,500 ft/sec shown in the crosssection in Fig. 10. This is a very usefulmethod of determining true refractorvelocities. Further, we can draw a line withthis same slope through the two reducedarrival times (at Stations 250 and 300) forthe reverse shot. Delay times for thedetectors at Stations 0 to 200 are then readdirectly as the difference between the arrivaltimes and the extrapolated line having areciprocal slope of 10,000 ft/sec. Thisoperation is also illustrated in Fig. 12.

At this point we have total delay times forthe first and second layers at each detectoron the line. We can determine . thethickness of the first layer by means ofintermediate shots and the intercept-timemethod, interpolate these depths over thefull spread to obtain corresponding first-layer delay times at each detector,* andsubtract these first-layer times from the totalto give us second-layer delay times at eachdetector.

As a consequence of firing a fewintermediate shots along the line and a shotbeyond the end, we have been able toarrive at a reasonably detailed interpretationof the subsurface structure. This is incontrast to the very erroneous picture of thesubsurface that would result from aninterpretation based only on the

* If the shot depths are relatively shallow,say a few feet, half intercept times will be nearlyequal to the delay times, and can beinterpolated directly.

shots at the ends of the seismic line.Further, we have a reasonable value for thetrue velocity of the refractor.

The techniques outlined above call beextended to more than three layers, but thedifficulties increase, and there is a loss ofaccuracy and resolution as the number ofdiscrete layers increases.

The foregoing example demonstratedthat true velocities could be determined bysubtracting delay times from arrival timesand plotting the reduced arrival times. Thereis another method of determining truevelocities that is frequently of great value,particularly for determining whether lateralvariations of velocity exist along a refractinghorizon. This method will be discussed next.

In the alternate derivation of the delay-time formula given earlier, the arrival time ofa refraction at a given detector from a shotat the end of the line was:

and the arrival time at the same geophonefrom a shot at the opposite end of theseismic line was:

where Z1 and Z2 are depths to the refractinghorizon beneath the shot points and ZD isthe depth beneath the detector. Thedifference in arrival times will be:

For a given seismic line, the only variableterm on the right-hand side of the aboveequation is the second one; therefore:

It follows that differences in arrival timesplotted against distance, X, will form a linethe reciprocal slope of which is half thevelocity of the refractor. The method isillustrated in Fig. 13 where arrival-timedifferences for a three-layer case have beenplotted above and below an arbitraryreference line. The arrival times beingdifferenced must represent arrivals from thesame refractor. The method is frequentlyuseful for determining whether the arrivalshave been refracted from the same layer. Adeviation of the points from a straight linemay indicate either that there exists a lateralvariation of the refractor velocity, or that thetimes being differenced represent arrivalsrefracted from two different layers. Thelatter is the case in Fig. 13.

Problems, Limitations, and Additional Applications

THE BLIND ZONE AND VELOCITYREVERSALS

The following material will be concernedwith problems that constitute importantlimitations to the method, particularly froman engineering geology standpoint. The twomajor potential problem areas in refractionsurveys are the phenomenon of a “blindzone” and the effect of a velocity reversal.

The term blind zone refers to thepossible existence of a hidden layer, i.e.,the inability of the refraction seismograph todiscern the existence of certain beds orlayers because of insufficient velocitycontrast or thickness. This inability cannotbe remedied by any change in the layout ofthe geophones, and it is probably thegreatest drawback of the seismic refractionmethod. In most cases the blind zone will liebetween the surface and a high-speedlayer.

An example of this type of problem istaken directly from Soske.4 Figure 14 fromSoske4 depicts an example of a three-layercase with the layers having good velocitycontrasts. However, Fig. 14 shows theminimum thickness of the intermediate8,500-ft/sec layer that would have to existbefore its presence could be detected byfirst arrivals, regardless of the geophonelayout. It will be noted that there is noindication of the 8,500-ft/sec layer on thetime-distance curve in Fig. 14.

It would be necessary that theintermediate 8, 500-ft/sec layer in Fig. 14 beat least 70 ft thick in order that refractionsfrom it be recorded as first arrivals. It mayseem puzzling that the

Fig. 13. Method of determining true velocity of refractor by plotting differences of arrival times.

Fig. 14. Wave-front diagram and maximum "undetectable" thickness of "blind zone" (taken from Fig.4, p. 326 of Soske4 - used with permission).

8, 500-ft/sec layer be as thick as 70 ft beforearrivals refracting from its top surface couldbe detected. The velocity contrasts betweensuccessive layers in Fig. 14 are high, and atfirst sight this example might seem to be anideal case for refraction mapping. Reference4 uses a wave-front analysis to show howthis apparent anomaly occurs.

Soske indicates that the problem can beovercome by firing a shot in a deep holesuch that arrivals from the intermediatelayer are recorded at the surface. Of course,it would be necessary that the existence ofthe intermediate layer be known beforehandbecause of some other source ofinformation, such as a drill hole, before thiswould normally be attempted. If a time-

distance curve shows a very large velocitycontrast between the first and secondlayers, the existence of a blind zone mightbe suspected. The error that results fromnot knowing the existence of a blind zone isthat the computed-depth to the refractinglayer is too shallow. However, even in theworst case, it is doubtful whether the errorwould approach 50%.

If the presence of a blind zone issuspected, the following procedure can beused to determine the maximum thicknessof such a layer (Z2) that could exist and stillnot be manifested by first arrivals on thetime-distance curve.

Let us assume that a straightforwardinterpretation of a time-distance curve

results in some value for Z1. This is themaximum value of Z1, and it is obtained byignoring the possibility that an intermediatelayer exists. If there is a blind zone,however, there will be an infinite number ofcombinations of Z1 and Z2, with Z2 rangingup to its maximum, undetectable thickness,at which value Z1 will be a minimum. Thecombined thickness of the first two layers(Z12) can lie anywhere between the limits:

Z12(min) = Z1(max) + 0,

and

Z12(max) = Z1(min) + Z2(max),

where Z2(max) is the maximum,undetectable thickness of the second layerand Z1(max) is the value of Z1 obtained fromthe time-distance curve. Based on thematerial in Refs. 5 and 6, the followingstatements can be made:

and is obtained from the chart in Fig. 15,and

where: α23 = sin-1 V2 / V3,

α13 = sin-1 V1 / V3.

As an illustration of the procedure fordetermining Z2(max), consider the followingexample: A time-distance plot shows twovelocities, 2,300 and 14,000 ft/sec, and it issuspected that there is a hidden layerbetween the low-velocity (2,300 ft/ sec)surface layer and the 14,000-ft/sec refractor.A value for Z1 of 37 ft is obtained from thetime-distance curve. If we assume that aprobable velocity for the suspected blindzone is 7,500 ft/sec, how thick could it beand still not be detected by first arrivals?From the available information and theassumed value of V2, we can write:

Z1(max) = 37 ft (determined from thetime-distance curve by anintercept time)

On Fig. 15, we determine the value of R bylocating the intersection of α12 = 17.9 degand α23 = 32.5 deg, and interpolatingbetween the R-lines; R is seen to beapproximately 0.62. To find the value of S:

so that from Eq. (17):

Fig. 15. Nomograph to be used in determining maximum thickness of possible hidden layer (takenfrom Fig. 90(b), p. 148, of Leet5 - based on Maillet and Bazerque, "La Prospectionseismique du sons-sol” Annales des Mines, XX, Douzieme Serie, p. 314, 1931).

Therefore, the maximum undetectablethickness of the hidden layer is 20 ft, andthe combined thickness of the first twolayers can range from a minimum of 37 ft

(no intermediate layer) up to a maximum of52 ft; i.e., Z1(min) + Z2(max).

The hidden layer problem can be aserious drawback to shallow surveys withthe refraction seismograph. The possibilityof such a layer's existence emphasizes thedesirability of using an exploratory drill inconjunction with seismic surveys wheneverpossible.

Another functional problem than canoccur in refraction surveys is the existenceof a velocity reversal that will result inerroneous computations of depths

to underlying beds. A velocity reversalcan exist because of a low-velocity layeror because of a high-speed layer. Ineither case velocities do not increaseprogressively with depth, and at somepoint in the stratigraphy there isdownward transition to a relatively lowervelocity. This has the effect of refractingthe seismic ray downwards towards thevertical as shown in Fig. 16. Refractionsfrom such a low-velocity layer cannot bedetected at the surface, and theexistence of this layer cannot bedetermined from the time-distance curve.In fact, the ray will not return to thesurface until it encounters a layer with avelocity higher than any layer previouslyencountered in its downward travel.

In certain unusual circumstances inwhich the velocity of the bed immediatelyoverlying the low-velocity layerincreases. with depth, a "shadow zone"may result at the surface where no firstarrivals at all

Fig. 16.Velocity reversal andcorresponding time-distancecurve.

are detected, and in similarcircumstances the time-distance curvemay show a sudden jump in time at aspecific distance.5,7

The effect of a low-velocity layer is tomake the computed depths larger thanactual depths. If the presence andvelocity of a low-velocity layer areknown, the layer can be compensatedfor in the computations, but its existencemust be determined by means of a moredirect method, such as an upholevelocity survey. Fortunately, velocityreversals are seldom encountered inshallow surveys.

There is a third type of velocity-depthsituation, a continuous increase ofvelocity with depth that rarely occurs butstill warrants a brief discussion. This typeof situation can exist because of a finelystratified geology or because of aprogressive decrease of weathering withdepth. A continuous increase of velocitywith depth will manifest itself in a time-distance curve similar to the one shownin Fig. 17.

This type of curve can be transformedinto a curve of velocity vs depth bymeans of the following equation8:

where:

ZS = depth at which velocity is VS

VS = velocity (from time-distance curve)corresponding to distance S fromshot point.

*This is the "Herglotz-Weichert-Bateman" equation.

Fig. 17. Schematic of ray-paths and time-distance curve for continuousincrease of velocity with depth.

VX = velocity (from time-distance curve)corresponding to any distance X < Sfrom shot point.

X = distance from shot point.

The integral is evaluated graphically bychoosing a particular distance S and thecorresponding velocity VS, obtained fromthe tangent to the time-distance curve at S,and plotting values of cosh-1(VS/VX)against X, where X is any distance lessthan S. The area under the resulting curve(obtained with a planimeter) is multipliedby 1/π to determine the depth, ZS, at whichthe velocity is VS. The integration isrepeated for decreasing values of S, andthe graph can then be constructed of the

variation of velocity with depth. Themethod is tedious and should only be usedwhen there is a smooth, continuousincrease of velocity with depth. Often,gradual increases of velocity can beinterpreted by assuming that the curvedtime-distance plot is made up of a fewstraight-line segments.

OTHER PROBLEMS ANDLIMITATIONS

This section of the report outlines someof the drawbacks and difficulties that canaffect seismic refraction investigations.The following discussion is not intended toleave the reader with an unfavorableimpression of the refraction method, butmerely to alert him to some possibleproblems that can influence the results of asurvey. The refraction seismograph is avery powerful exploration tool, and itsvalue will be enhanced by a realistic andknowledgeable operator. Reference 9 is anexcellent summary of the problems ofseismic investigations at shallow depthsand will be of interest to engineers orgeologists who routinely use refractionsurveys; much of the following material isbased on this reference.

Generally, as the depth of theinvestigation becomes shallower the limitsof method are approached, and theproblems inherent in the method increase.A large proportion of refraction surveys forengineering purposes are concerned withdepths of the order of 50 to 75 ft and totaltimes of 50 to 100 msec. It is apparentthen that a millisecond is a large unit oftime, and arrival times must be picked withan accuracy of a millisecond or less. Thismeans that the charge weight, itssurrounding medium and coupling, the

amplifier gains, and the placement of thegeophones are all important factors inobtaining the sharp breaks required foraccurate timing of first arrivals. An error of 1msec corresponds to only 1 ft of depth witha first-layer velocity of 2,000 ft/sec, but theerror would be 5 ft for a first-layer materialwith a velocity of 10,000 ft/sec.

it is necessary to maintain close controlof overburden velocities and depths,particularly to distinguish travel time spentin the overburden from time spent inunderlying, higher velocity layers. This isparticularly so when there are more thantwo layers. Unconsolidated overburdendeposits frequently show lateral changes invelocity over relatively short distances, andit is almost always desirable to fire at leastone intermediate shot between the ends ofthe line.

Generally, when one is working withshort lines, say 500 ft or less, obtainingsharp breaks will not be a problem, unlessthere is difficulty in burying sufficientexplosive deep enough. Because of theattenuation of the explosive impulse . withincreasing distance, and particularlybecause of the relatively greaterattenuation of the high-frequencycomponents, the arrivals tend to becomeless distinct and more rounded withincreasing distance from the shot. Theobjective is to nick arrival times to within 1msec or less, and to pick what appears tobe the onset of the pulse. The presence ofbackground noise, such as that generatedby vehicle traffic, or weak arrivals causedby poor charge coupling, can makeaccurate determinations difficult.

Irregularities in a shallow bedrocksurface have a more pronounced effect onaccuracy than irregularities in a deeper

horizon. A highly irregular refractor surfacewill tend to make delay-time methodssomewhat inaccurate because the timesbeing compared represent different depths,depending on the direction of the shot. Thissituation is depicted in Fig. 18. The effect ofusing delay times to compute depths will beto "smooth" a highly irregular surface. Thesituation is aggravated if the velocitycontrasts are not large; i.e., if the horizontaloffsets between the geophone and thepoint at which the ray emerges from therefractor (≅≅≅≅ Z tan αααα) are large.

Further complications arise if the rocksurface is not only eroded and irregular, butalso weathered. In this case the rocksurface will not be a well-defined boundarybut rather a zone of transition. In the caseof layered rock, some of the layers may bebetter media for the transmission of seismicenergy and the refractions may notnecessarily be from the top of the rock.Also, as distance from the shot increasesthe higher frequency (i.e., shorterwavelength) energy is progressivelyabsorbed and because of the signal'sincreasing wavelength, the energy

Fig. 18. Schematic of shallow, irregularrefractor surface producing differentfirst-layer travel times at samegeophone from shots on either sideof it.

may refract from progressively thicker beds.It is necessary to bear in mind that thewavelength becomes a significant factorwhen the refractor is of a limited thickness.Long wavelength seismic signals do not"see" thin beds.

Some materials may be anisotropic, i. e.,there may be differences between horizontaland vertical velocities, or even betweenhorizontal velocities in different directions.These differences may be as large as 40%in some materials. Rocks with finely beddedstructure, such as sandstones and shales,generally exhibit some degree of anisotropy.

There is no hard and fast guidance for asequence of steps to be followed wheninterpreting or reducing travel-time curves.Straightforward two- or three-layer plots withwell-defined straight-line segmentsrepresenting each layer will probably be theexception rather than the rule. Overburdenvelocities may change along the length ofthe line, there may be relief in the refractinghorizons, layers may pinch out, andbreakover points (i.e., critical distances) inthe plots may not be readily apparent.

The first step is to attempt to identify thelayers present according to their velocities,and then to determine which arrival timescorrespond to the various layers. Where thearrivals do not line up in straight lines,identification can be attempted by plottingdifferences in overlapping arrival times forthose believed to be from the samerefractor. Also, delay times can be computedand plotted below the arrival times, and thelineups, or lack thereof, of the reduced timeswill assist in assigning velocities to thevarious layers and sorting the arrival times.

In the same context that there does not exista standard sequence of interpretationalsteps, the interpreter should not feelconstrained by a rigid format, but shouldrather attempt a number of methodsaccording to his judgment. Some knowledgeof geology is helpful in reconciling theinterpretation with what is reasonable from astructural geology standpoint.

Some refraction data obtained in complexgeology will be very puzzling to theinterpreter. There is always a reason whythe arrival times are as they are, although itis not always apparent. Some cases aresimply not amenable to straightforwardinterpretation using the methods alreadydescribed. There are other techniques,generally involving the construction ofwavefront diagrams,10,11 that are availablefor analyzing complex cases; however, theyare time-consuming and tedious to apply,and are beyond the scope of this report.

Domalski9 states: “The basic difficulty inthe interpretation of a shallow refractionsurvey consists not so much on the choiceof a suitable method, on which to base theinterpretation, as on the correct decisionregarding the various aspects of the results.In other words, the information which isnormally obtained from the examination ofthe time-distance curves cannot be acceptedentirely at its face value.” He concludes hispaper on a more positive note by saying:“Results obtained from shallowinvestigations are useful because theyprovide rapidly a picture of the bedrockconfiguration, and guide a subsequentdrilling programme.”

As stated at the beginning of this section,this discussion of potential problems wasintended to alert the reader to possibledifficulties and not to discourage theapplication of the technique. In fact, it isbelieved that the method is not used widelyenough in exploration programs. When therefraction seismograph is used wisely, andparticularly when allied with the exploratorydrill, it will invariably speed the recovery ofsubsurface information and reduce siteinvestigation costs.

ADDITIONAL TECHNIQUES

The refraction seismograph isfundamentally an accurate timing deviceand can be applied to explorationsituations other than routine refractionsurveys along the ground. The method canbe modified for use over water, and theequipment can be used for measuringvelocities in drill holes. This section willdiscuss some of these techniques.

The first problem for consideration isthat of running a refraction survey across ariver. Normal procedure would require thata line of detectors be laid across thebottom of the river or ,floated on the watersurface. Both these procedures requirespecial cables and detectors and they are,therefore, often impractical. However,because shot and detector are theoreticallyinterchangeable in refraction work, thenormal arrangement of having detectorsalong a line across the river with shots onthe banks can be reversed so that thedetectors are on the banks and the shotsare in the river. This arrangement isillustrated in Fig. 19.

A series of small charges are detonatedon the river bottom along a line across theriver. It is required that the detector on thefar bank from the seismograph beconnected to the recording instrument bymeans of a cable running across the river.It is required, further, that the distance ofthe shot from the

Fig. 19. Schematic of refraction survey across body of water.

detectors be surveyed and known, and thatthe shot instant be transmitted to theseismograph. The latter can be done eitherby hard wire or, if the equipment is available,by radio transmission. The usual practice isto fire the shots from a small boat and tolocate its position by transit triangulation. It isnot necessary that the shots be fired at evenincrements of distance across the river. Insome cases the distance from shot todetector has been determined by recordingthe direct arrival of the explosive impulsethrough the water. If the detectors are placedvery close to the water's edge, the shockarrival through the water can often be seenon the record as a high-frequency signal.With the water velocity known (4,800ft/sec±), the distance to the shot is easilydetermined. The arrival times and distancesare plotted and interpreted in the normalfashion. This method is an expedienttechnique for dam site exploration whenknowledge of the thickness of river bottomdeposits is needed.

In some cases of overwater surveys itmay not be possible to place detectors onthe ground simply because the body of wateris too large, as in the case of a bay or a lake.In these cases it will be necessary to employeither a floating or submerged cable withhydrophones instead of geophones. Thefloating cable has the advantage that it canbe towed along the line of exploration. Eitherway two boats will be required, onecontaining the recording instruments andtowing cable and the other being used as ashot-firing boat. A radio-transmitted timebreak is a necessity for this type of work.

It is possible for loose, unconsolidatedbottom sediments in bays and estuaries tohave a lower velocity than that of sound in

water. 12 and in such a case the directarrival through the water will obscure thearrival of energy through the sediments. Aspecial low-pass filter to block the high-frequency arrival through the water is thenrequired.

The refraction seismograph can be usedto measure vertical velocities in boreholes.Such uphole surveys are a valuable adjunctto conventional refraction explorationbecause they provide a vertical velocityprofile and will indicate the presence of alow-velocity layer, if one exists. The termuphole refers to placing shots in a drill holeand recording arrival times at the surface.The reverse of this procedure is called adownhole survey, and is conducted by firingshots at the surface and recording arrivalsdown the hole, usually by means of amultidetector cable. Downhole surveysrequire that the hole be filled with fluid, orthat a geophone capable of being coupled tothe wall of the hole be available. Theprinciples are the same in both cases, but anuphole survey, which has the advantage ofrequiring no special equipment, usuallydestroys the borehole.

In practice, a string of small explosivecharges is preassembled so that the chargesare spaced at the desired intervals. Eachcharge has a separate firing line and theentire assembly is suspended in the holeand fully stemmed to prevent the explosivesbeing blown out of the hole. The intervalbetween charges will depend on the depth ofthe hole and the amount of detail desired.Charge spacings of 5 to 10 ft are typical forholes 50 to 100 ft deep, and it is evident thatthe charges must be detonated one by onein a sequence

starting at the bottom - otherwise the firinglines will be cut. Charge weights of theorder of 1 /4 lb. or less are typical. Severalgeophones are placed near the hole collar,say 5 to 10 ft from it, and the averagearrival time is used. The arrangement for.an uphole survey is shown in Fig. 20together with the plot of arrival timesmeasured at the surface. The slantdistance from shot to geophones must beused for the shots near the top of the hole.

It will be noted that the velocities derivedfrom the arrival times in Fig. 20 do notalways correspond exactly to the nominalvelocities of the various layers. Thedifferences between the actual velocitiesand those based on the arrival times shownin Fig. 20 are representative of theprecision to be expected in the typical

Fig. 20. Example of uphole survey and corresponding plot of arrival times.

borehole survey. Further, it is notuncommon for a discrepancy to existbetween the velocities obtained from aborehole velocity survey and thoseobserved in refraction surveys. There areseveral reasons for such a discrepancy. Aspreviously indicated, some materials showanisotropy in their seismic velocities,particularly finely bedded sediments. Also, alow-velocity layer will not be apparent on arefraction time-distance curve, but it will bedetected in a borehole survey. If adiscrepancy does exist, it is not generallylarge and, unless it is due to a low-velocity

layer, there is usually no need to correctrefraction surveys on the basis of theborehole velocity data.

An interesting variation of the upholesurvey is developed by Meissner13 in whicha conventional seismic line is laid outradially away from the hole collar so thatarrival times from each uphole shot arerecorded along the entire seismic cable.Wave fronts of the seismic energy areconstructed by connecting points of equaltravel times. The assumption is

Fig. 21b. Meissner wave-front diagram showing thin high and low-velocity layers (taken fromFig. 6, p. 537, of Meissner13 - used with permission).

made that the travel time from a shot atdepth Z to a geophone on the surface at adistance X from the hole is the same as thatfrom a (fictitious) shot at the top of the holeto a (fictitious) geophone at a distance Xand a depth Z. Unless the beds arereasonably flat lying and the terrain is level,this assumption will lead to errors.

A separate travel-time curve isgenerated by each uphole shot. The wavefronts are constructed by plotting the arrivaltimes at each geophone at a depth beneaththat geophone location equal to the depthof the shot in the hole. Points of equal traveltimes are then contoured to give a wave-front diagram. Two examples of the resultsof this technique are shown in Fig. 21. The

method provides a qualitative picture ofsubsurface conditions as an adjunct to thestandard uphole information. Meissnerpresents examples of wave-front diagramsfor other geological conditions in hispaper.13

The main sources of error in thistechnique are small, local inhomogeneitieswithin the near-surface layer and thepresence of dipping high-velocity layers.Also, an elevation change along the seismicline imposes a delay or an advance on allwave-front times below the line; therefore,this type of survey should be carried out onflat ground if possible.

Field Procedures

This section recommends general fieldprocedures for conducting refractionsurveys. The first consideration in arefraction survey is the interval between thegeophones. The spacing will depend on thedepth of exploration and the subsurfacedetail desired. As a rule of thumb, the totalspread length should be three to five timesthe maximum depth anticipated. Changesin geophone spacing can be made inresponse to the data observed in the field;i.e., by picking and plotting records as theyare obtained. The total spread length willobviously determine the geophone intervalto some extent; however, there is norequirement to have a constant spacingover the length of the line. It is sometimesdesirable to shorten the spacing betweengeophones at each end of the line, at leastfor the first few lines run in a new area. Thispractice will provide more complete data onoverburden velocities.

Seismic cables are manufactured withfixed spacings; i.e., the "take-out" orpolarized connector for each detector ismolded into the cable. It is desirable tohave several cables available with differentspacings, such as 25, 50, and 100 ft. The25-ft spacing is most applicable to the bulkof engineering surveys, which are seldomdirected towards explorations deeper than50 or 100 ft.

The cable is laid out along the ground ina straight line. If the terrain along the linehas any relief, surveys will be required sothat layer thicknesses can later be plotted intrue elevation.

The shots at the ends of the cableshould be offset at a right angle to the cableand not beyond the end in line with thecable. This arrangement is illustrated

in Fig. 22. The purpose of the right-angledoffset is to allow determination of the totaltimes; i.e., the travel time from each shot tothe far geophone. The travel time from ashot beyond the end of the cable, in linewith it, will be greater than the total time.The offset distance, usually 5 to 15 ft,normally provides a direct arrival throughthe surface layer and allows a determinationof its velocity. The slant distances from shotto geophone must be computed for plottingarrival times at the first two or threegeophones.

As discussed in the section oninterpretation, it is always advisable to firesupplementary shots along the length of theline in order to provide as much informationas possible about the depth of theoverburden and possible variations of itsvelocity. The necessity for these shots canbe determined as the survey programprogresses; however, it should be standardprocedure to fire at least one shot at thecenter of the seismic cable, even for shortlines with a 25-ft spacing.

There is no fixed rule for the distance abeyond-the-end shot should be from theend of the cable. In most cases the distanceneed not even be measured because weare usually interested only in the relativetimes obtained from such a shot. Theobjective of a beyond-the-end shot is to

record refracted arrivals from the layer weare trying to map, and to record thoserefractions at as many geophones aspossible. A distance somewhere betweenhalf the cable length and the whole cablelength is usually adequate. If a number ofrefraction lines are to be surveyed end toend, it is advisable to locate the beyond-the-end shots at exactly half the cable length ora whole cable length from the end; i.e., sothat they will coincide with the middle or endshot of the adjacent geophone array.

The data points should be plotted on aconvenient scale; it is generally best if thetime and distance scales are approximatelythe same length. It is helpful if differentsymbols are used to designate arrival timesfor each shot; this particularly helps to avoidconfusion where the time-distance curvescross each other. It is suggested that faint,dashed lines be used to connect all thearrival times for each shot. The straight lineportions of the plots, if any, can be joined byheavier lines, projected back for timeintercepts, and labeled with theircorresponding velocities.

Charge weights adequate to producesharp first arrivals will vary with geology,length of line, and amount of backgroundnoise. Weights may vary from only ablasting cap for a 100-ft line to

Fig. 22. Recommended shot layout pattern for seismic line.

several pounds for long lines under adverseconditions. Generally a few ounces in ashallow 1- or 2-ft hole will be adequate for a275-ft line. Coupling of explosive energycan be improved by burying charges deeperand saturating the shot hole with water. Anemplacement hole can often be formed witha heavy steel bar driven into the ground.Figure 23 shows a seismograph record froma 275-ft line in which adequate first arrivalshave been obtained at each geophone.Note the rounding of the breaks withincreasing distance from the shot.

Special blasting caps are made forseismic work; e.g., Dupont SSSSeismograph or Atlas Staticmaster. The useof if instantaneous" standard caps shouldbe avoided because they can have a delayof up to 15 msec between application ofcurrent and detonation, and further, this

delay is not constant. Almost allseismographs indicate zero-time when thecurrent is applied to the cap. The specialseismograph caps will detonate in less than1 msec after application of current.

The geophones must be firmly coupledto the ground. There are a variety ofgeophone bases, such as a spike or atripod, to suit the type of ground surface.The spike-type of base is probably the mostcommon; the spike is pushed into the soil toprovide a rigid coupling with the groundsurface.

A 12-channel seismograph that producesa visual record of the waveforms arriving ateach geophone is preferred over the single-channel seismographs that are available forshallow investigations. These small, single-channel

Fig. 23. Example of seismic record on Polaroid film obtained with portableengineering seismograph.

instruments indicate arrival times bydifferent methods, such as neon lamps,glow tubes, dashes on paper, oroscilloscope displays. Although light andcompact, they are suited only for veryshallow work and suffer from thedisadvantage of not simultaneouslydisplaying the complete set of arrivals at allgeophones. There is often some judgmentrequired in picking first arrivals from aseismograph record, particularly if noise ispresent, and a machine that records thecomplete set of waveforms allows theexercising of this judgment.

There are several 12-channelinstruments commercially available,generally as a complete package includingcable and geophones. They all employlight-beam galvanometers and record thesignals either on Polaroid film or on a

continuous roll of photo-sensitive paper.These instruments are well-suited forengineering use.

A valuable accessory in the conduct ofrefraction surveys is a blasting machine thatcan transmit the zero-time to the recorderby means of radio. This capa-bility allowsmuch greater flexibility in field operationsand means that beyond-the-end shots canbe made without the need to manipulatelarge quantities of wire. Such a device isparticularly desirable for overwater surveys.It is a fairly straightforward task to buildsuch a blasting machine and to useordinary Citizens Band radios to transmitand to receive the zero-time. One approachis to transmit a tone and have thedetonation of the cap interrupt the tone.

Conclusions

This report has covered thefundamentals of seismic refraction theoryand interpretation. It is recognized that itmay be difficult to arrive at anunderstanding of refraction surveying onlyby reading about it. However, it is hopedthat this document, when combined withactual field experience, will assist thereader in acquiring a working familiarity withthe technique. For those who have beenusing the refraction seismograph, and whomay have learned something new from thisreport, it is suggested that they considerreevaluating some of their previoussurveys.

The methods of interpretation describedin this report are not the only methodsavailable, but it is believed that they are themost applicable ones for the majority of

engineering surveys, and they are also thesimplest. In those cases where the strataare reasonably flat lying, depths computedby time-intercepts will generally beadequate. Wherever the time-distance plotsreveal, by their undulations or irregularities,the existence of something more complex,the delay-time method should be attempted.

Recommendations have been madeabout the desirability of using refractionsurveys in conjunction with a drillingprogram. This point cannot beoveremphasized. Exploratory drilling isalmost always done in a site investigation;its value, in terms of the quality ofinformation gathered, will be enhanced ifrefraction surveys are carried out first andthe

results used to guide the drilling operations.Even if some of the refraction data appearscomplex, ambiguous, or just plain peculiar,this in itself is information, and thoserefraction surveys will have designatedareas in which drilling will provide moreuseful information. Conversely, stratigraphyobtained from a drill hole is very oftenhelpful in interpreting a refraction profile.Because the velocity of geologic material is

in itself a useful index, borehole surveys(e.g.. uphole) warrant serious considerationas a follow-up investigation for selectedareas, particularly if a hidden layer issuspected.

The refraction seismograph offers arapid, inexpensive, and accurate method ofsubsurface exploration. Its application tosite investigations should be the routinerather than the exception.

References

1. M. B. Dobrin, Introduction to Geophysical Prospecting (McGraw-Hill, New York, 1960).

2. J. J. Jakosky, Exploration Geophysics (Trija Publishing Co., Newport Beach, Calif., 1957 ).

3. L. V. Hawkins, “The Reciprocal Method of Routine Shallow Seismic Refraction

Investigations,” Geophysics 26, 806-819 (1961).

4. J. L. Soske, “The Blind Zone Problem in Engineering Geophysics”, Geophysics 24, 359-365

(1959).

5. D. L. Leet, Practical Seismology and Seismic Prospecting (D. Appleton-Century Co., New

York, 1938).

6. R. Green, “The Hidden Layer Problem”. Geophys. Prospect. 10, 166-177 (1962).

7. L. B. Slichter, “The Theory of the Interpretation of Seismic Travel-Time Curves in Horizontal

Structures,” Phys. 3, 273-295 (1932).

8. B. B. Redpath, “Seismic Investigations of Glaciers on Axel Heiberg Island;” in Axel

Heiberg Island Research Reports, Geophysics No. 1, McGill University, Montreal,

Quebec, 1965.

9. W. Domalski, “Some Problems of Shallow Refraction Investigations;” Geophys. Prospect.

4, 140-166 (1956).

10. H. R. Thornburgh, “Wave-front Diagrams in Seismic Interpretation;” Bull. Am. Assoc:

Petroleum Geologists 14, No. 2 (1930).

11. J. G. Hagedoorn, “The Plus-Minus Method of Interpreting Seismic Refraction Sections,”

Geophys. Prospect. 7, 158-182 (1959).

12. C. B. Officer, “A Deep-Sea Seismic Reflection Profile;” Geophysics 20, 270-282 (1955).

13. R. Meissner, “Wave-front Diagrams from Uphole Shooting,” Geophys. Prospect. _9, 533-543

(1961).

14. Subsurface Investigation-Geophysical Explorations, U. S. Army Corps of Engineers,

Washington, D. C., Engineering Manual EM-1110-2-1802 (1948).

Bibliography

Black, R. A., F . C. Frisehknecht, R. M. Hazlewood, and W. H. Jackson, Geophysical Methods of Exploringfor Buried Channels in the Monument Valley Area, Arizona and Utah, U. S. Geological Survey,Bulletin 1083-F, 1962.

Burke, K. B. S., "A Review of Some Problems of Seismic Prospecting for Groundwater in Surficial Deposits,"in Mining and Groundwater Geophysics, 1967, Geological Survey of Canada, Economic Report No.26, Ottawa. Canada, 1970.

Bush, B. O., and S. D. Schwarz, Seismic Refraction and Electrical Resistivity Measurements over FrozenGround, National Research Council of Canada. Associate Committee on Soil and Snow Mechanics,Technical Memorandum No. 86, Ottawa, Ontario, 1965.

Grant, F. S., and G. F. West, Interpretation Theory in Applied Geophysics (McGraw-Hill, New York,1965).

Griffiths, D.H., and R. F. King, Applied Geophysics for Engineers and Geologists (PergammonPress, Inc., New York, 1965).

Hales, F. W.; “An Accurate Graphical Method for Interpreting Seismic Refraction Lines,” Geophys.Prospect. 6, 285-294, 1958.

Hawkins, L. V., and D. Maggs, "Nomograms for Determining Maximum Errors and Limiting Conditionsin Seismic Refraction Surveys with a Blind Zone Problem, Geophys. Prospect. 6, 526-532,1961.

Heiland, C: A., Geophysical Exploration Hafner Publishing Co.. New York, 1963).Hobson, G. D., "Seismic Methods in Mining and Groundwater Exploration," in Mining and Groundwater

Geophysics, 1967, Geological Survey of Canada, Economic Report No. 26, Ottawa, Canada,1970.

Linehan, D., and V. J. Murphy, "Engineering Seismology Applications in Metropolitan Areas," Geophysics27, 213-220, 1962.

Musgrave, A. W., Ed., Seismic Refraction Prospecting, Society of Exploration Geophysicists, Tulsa,Okla., 1967.

Schwarz, S. D., Site Evaluation-Geophysical Exploration, Fifth Chicago Soil Mechanics Lecture Series,1970.

Scott, J. H., B. L. Tibbetts, and R. G. Burdick. Computer Analysis of Seismic Refraction Data, U. S. Dept.of Interior, Bureau of Mines, Washington, D. C., RI 7595, 197 2.

Slotnick, M. M., Lessons in Seismic Computing, Society of Exploration Geophysicists, Tulsa, Oklahoma,1959.

Tarrant, L. H., "A Rapid Method of Determining the Form of a Seismic Refractor from Line Profile Results,"Geophys. Prospect. 4, 131-139, 1956.

Wyrobeck, S. M„ "Application of Delay and Intercept-Times in the Interpretation of Multilayer RefractionTime Distance Curves;' Geophys. Prospect. 4, 112-130, 1956.

Zirbel, N. N., “Comparison of Break-Point and Time-Intercept Methods in Refraction,

Appendix A

Material Velocities

Tables A1, A2, and A3, which list thelongitudinal wave velocities of variousmaterials, have been selected from anumber of publications1,2,14 They arepresented here as a series of separate

tables, and no attempt has been made toconstruct a "universal" table of velocities.The tables are included to give some ideaof what velocities mean in terms ofgeologic media.

Table A1. Speed of propagation of seismic waves in subsurface materials.14

Table A2. Approximate range of velocities of longitudinal waves for representative materialsfound in the earth's crust.a

Table A3. Velocities of seismic waves in rocks. *a

Appendix BExample Problem

This appendix contains a hypothetical setof time-distance curves which are intendedto illustrate some of the points in this report.The travel times were synthesized from aknown geologic profile, and the interpretationof the time-distance curves can therefore becompared with the original profile.

Assume the following circumstances: Weare exploring the foundation conditions for alarge dike, and our primary interest is depthto rock, although the thicknesses andvelocities of any intermediate layers

are also of interest. Similar exploratory workin a nearby area indicates that we canexpect sandstone overlain by a glacial tillwith a sandy overburden. A refraction linewith 50-ft geophone spacing has beensurveyed, with shots fired at the ends (15-ftoffset), at the middle, and at oneintermediate point. Shot depths were about 2ft and can be considered negligible. There isno drilling information anywhere on the line.

The travel times we observed aretabulated in Table B1 and are plotted in Fig.B1.

Table B1. Observed travel times.

Fig. B1. Travel times observed in hypothetical exploration program.

The first step is to try to identify thevarious layers according to theirvelocities. In Fig. B2 straight lines havebeen drawn through those arrival timesthat are initially believed to be refractionsfrom the same layer. . The apparentvelocities that result from this procedurewould indicate that we have a three-layersituation: a; first layer with a velocity of2,500 to 2,700 ft/sec, an intermediatelayer with apparent velocities of 4,100 to6,400 ft/sec, and a bottom layer (rock)with a velocity that lies somewherebetween 8,900 and 10,000 ft/sec.

Although an intermediate layer isclearly indicated on the western half ofthe line, the situation is not asstraightforward towards the east; the endshot at Station 550 shows a 6,000-ft/secline-up of points, but the middle shot doesnot indicate the presence of anintermediate layer towards the east. Anintermediate shot at Station 425 wouldhave helped resolve this, but, for the sakeof our illustration, we are assuming thatwe did not fire one. For the present, wecan pass over this point and go on torefine our velocity values.

The first layer velocities show littlevariation along the line and a simpleaverage will be adequate; i.e.,

V1 ≅≅≅≅ 2,558, say 2,550 ft/sec.

On the western half of the line we cancompute two values of V2 by takingharmonic means; i.e.,

and averaging these values with the6,000 ft/sec on the eastern half, weobtain:

V2 ≅≅≅≅ 5,408, say 5,400 ft/sec.

The value of V3 will be determined inthe next diagram, but first we proceed tocompute delay times or half intercepttimes for the first layer wherever we can.(Remember that half intercept times anddelay times are equivalent if the shotdepths are negligible.) Half intercepttimes are available at Stations 0, 125,275, and 550. We can compute delaytimes at Stations 50, 200, and, for thepresent, at Station 400. All of these timesare shown in Fig. B2. For theintermediate stations we will have tointerpolate between the values above.

Fig. B2. Identifying layers by velocity and determining half-intercept times anddelay times for first layer.

Our next step is to plot the differences inarrival times for the two end shots. Thisprocedure should tell us which timesrepresent refractions from the rock, andwhat the rock velocity is.

The plot of differences in Fig. B3 resultsin a value for V3 of 9,000 ft/sec andsuggests that Stations 200 through 450recorded refractions from the rock from bothend shots. Points that do not fall on the linemean that they are differences of arrivaltimes from different layers (assuming nolateral velocity variations in the rock).

Feeling reasonably confident that thearrivals from both directions at Stations 200through 450 are refractions from the top ofthe rock, we can proceed to compute delaytimes at these stations. The computationsare shown in Fig. B3. Remember that thesetimes are the combined delay times for thefirst and second layers (i.e., ∆T12).

As was done in Fig. 12, we reduce thearrival times by the corresponding delaytimes, obtaining reduced arrival times thatnow line up at the true refractor

velocity. Extending these lines allows us toread off delay times for the remaininggeophones. The fact that the line throughone set of reduced arrivals has a reciprocalslope of 9,200 ft/sec and the other 9, 000ft/sec is because of normal scatter, we willuse 9, 000 ft/sec for V3 which was obtainedfrom the difference plots.

We are ready to compute layerthicknesses, but first refer back to Fig. B2where we computed a first-layer delay timeat Station 400. We have just demonstratedthat the arrival at Station 400 from the shotat Station 550 is really a refraction from thetop of the rock; therefore; this first-layerdelay time is not valid and we will have tointerpolate between the half intercept timesat Stations 275 and 550. Also, the 6,000ft/sec that we attributed to the second layerat the east end of the line is really anapparent velocity for the rock; however, thearrival at Station 500 from the end shot atStation 550 is a legitimate refraction fromthe second layer and the 6,000 ft/ sec is stillvalid.

Fig. B3. Determination of true value of V3 and delay times ∆T12 (intermediate shots notshown for sake of clarity).

Let us now assemble all of ourinformation in Table B2.

Figure B4 is a comparison of theforegoing interpretation with the originalmodel from which the travel times .werederived. A number of significant pointsare apparent. The velocity values of

V1 = 2,500, V2 = 5,400, V3 = 9,000ft/sec determined in the interpretation arein good agreement with the actual valuesused in the synthesis. Agreementbetween actual depths and thosecomputed in the interpretation is verygood over the western half of the line, butit is not as good on the eastern half. Thereason for firing intermediate shotsshould now be apparent; only because of

the shots at Stations 125 and 275 werewe able to follow variations in the depth ofthe over-burden along the western half.The delay times in the overburden are asignificant proportion of the total delaytime, and any errors in these times arecompounded when the difference∆T12 - ∆T1 is multiplied by the highervelocity of the underlying layer. Withoutan intermediate shot between Stations275 and 500, we had no choice but tointerpolate linearly the half intercept timesbetween these points, and consequentlythere was no way of knowing that theoverburden thickened appreciably nearStations 300 and 350.

Table B2. Velocities, cosines, times, and thicknesses.

Fig. B4. Original profile compared with and that derived by interpreting synthesized time-distance data.