NBSIR 74-565

Acoustic Emission:

Some Applications of Lamb's Problem

Franklin R. Breckenridge, Carl E. Tschiegg and Martin Greenspan

Sound Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington. D. C. 20234

September 1974

Final

Report to Department of the Navy

Office of Naval Research

Arlington, Virginia 22217

Government Order NAonr 7-75

NBSIR 74-565

ACOUSTIC EMISSION:

SOME APPLICATIONS OF LAMB'S PROBLEM

Franklin R. Breckenridge, Carl E. Tschiegg and Martin Greenspan

Sound Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

September 1974

Final

Report to Department of the Navy

Office of Naval Research

Arlington, Virginia 22217

Government Order NAonr 7-75

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Roberts. Director

ACOUSTIC EMISSION: SOME APPLICATIONS OF LAMB'S PROBLEM

Franklin R. Breckenridge, Carl E. Tschiegg and Martin Greenspan

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

ABSTRACT

A method for obtaining the signatures (waveforms) of certain

acoustic emission events has been developed. The waveform is that

at the source, free of contamination by ringing of the specimen,

apparatus and transducer. The technique is based on the comparison

of two signals at the transducer, one from the event in question and

one from an artificial event of known waveform. The apparatus is

also adapted to the calibration of transducers in a certain sense.

The configurations of source (real or simulated acoustic-emission

event) and receiving transducer correspond to those of some special

cases of Lamb's problem. As a byproduct, the results may be of some

interest to seismologists.

Key Words: Acoustic emission; calibration of transducers; electrostatic

transducers; Lamb's problem; seismic pulses; ultrasonic

transducers

.

ACOUSTIC EMISSION: SOME APPLICATIONS OF LAMB'S PROBLEM

Franklin R. Breckenridge , Carl E. Tschiegg and Martin Greenspan

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

INTRODUCTION

It is widely thought, or at least hoped, that the waveform (or

the spectrum) of an acoustic emission signal is characteristic of

the process which produces it (the source event) , and considerable

effort has been expended in attempts to obtain such in the

12 3 laboratory. * ' So far, no really satisfactory waveforms have been

acquired. There are two main difficulties. The first, which is the

requirement for a wide-band transducer, with a consequent loss of

sensitivity, can be set aside for the present if attention is

directed only to sufficiently energetic events. The second is more

troublesome. The source event excites the test specimen, and

frequently the testing apparatus, into vibration (ringing), masking

the desired signal. That is, the spectrum of the signal for the

most part reflects merely the normal modes of vibration of the

specimen and apparatus.

We describe some apparatus which is expected to circumvent the

above difficulty, at least in considerable part. However, it

develops that the same apparatus, with only minor modifications, can

be used in the calibration of acoustic-emission transducers, and we

now report on this phase of the work. We also present some results

of interest to seismologists.
PRINCIPLE OF THE METHOD

Figure 1 is a schematic of the basic apparatus. The "transfer

block", A, is a thick slab of aluminum alloy, steel, glass or other

material having low attenuation for sound in the megahertz range.

The test specimen, B, coupled to the transfer block sometimes

through a liquid or a grease, should be no larger than a few tenths

of a millimetre in any dimension. When the sample is deformed by

the threaded indenter, C, acoustic emissions take place, usually one

at a time because of the samll volume of the sample. The signal

from each event is picked up by a transducer, D, directly opposite

the specimen. The transverse dimensions of the transfer block are

large enough so that the first reflections from the lateral walls

arrive at the transducer too late to interfere with the reception of

the important part of the signal. The effects of ringing of the

block are thus avoided. The specimen is small, and it therefore

rings only at frequencies above the range of interest. Thus it

appears possible, in a research situation, to obtain a signal from a

source event uncontaminated by ringing of the specimen. Of course,

in practice, the event usually occurs somewhere in the interior of a

solid, rather than on a surface, but we shall later present some

evidence that this point is not too important.

If we knew the response of the transducer, and the transfer

function of the block, we could calculate from the received signal

the signature of the source event at its point of origin. Here it

is well to digress and consider what is meant by the response of the

2
FIG. 1. Schematic of set-up for recording of acoustic-emission signatures uncontaminated by ringing of specimen: A, transfer

block; B, test sample; C, indenter; D, transducer; E, lead

zi rconate-ti tanate disc; F, charge amplifier; G, high-speed

storage oscilloscope; H, trigger-signal pickup.

transducer. In acoustic emission work, the transducer is usually

thought of as measuring stress, but it is placed on a free surface

where there is no traction when the transducer is absent . Whatever the

transducer is supposed to measure, stress, displacement or velocity,

its output depends on the impedance it presents to the specimen, and

this depends on frequency, usually in a complicated way. Transducers

which are not in contact with the specimen, and perforce measure

displacement or velocity, are exceptions, and we will discuss them

later. However, they have in general relatively low sensitivity.

Thus, in trying to implement the above scheme, we are faced with

two difficulties. For one, we do not know under what conditions to

calibrate the transducer, and for the other, we do not know the

transfer function of the block. It seems desirable to bypass these

problems and take a different approach. Suppose that we produce, at

the point on the surface of the transfer block at which the specimen

normally is put, a stress pulse having a known waveform and therefore a

known spectrum. We create thus a "standard source event" and record at

the transducer output a "standard signal", different for different

transducers. Then from the spectrum of the test signal and that of the

standard signal as measured on the same transducer, and the known

spectrum of the standard source event, the spectrum of the test source

event at its point of origin can be calculated.

3
STANDARD SOURCE EVENT AND STANDARD RECEIVER

We have chosen for the standard source event a step function of

stress. To realize It, a short length of thin-walled glass

capillary, of diameter about 0.15 mm, is substituted for the

specimen, B, in Fig. 1 and slowly compressed by means of the

threaded indenter, C, until it breaks. Upon fracture, the load is

released suddenly; we shall see that the rise time (10-90 percent)

is less than 0.1 ys. A disc of lead zirconate-titanate , E,

connected to a charge amplifier, F, can be used to measure the total

load released (of the order of 10 N) ; it is calibrated with dead

weights.

In order to establish an upper limit on the rise time of the

step-function load produced by breaking a capillary, we need an

elastic system, having a known transfer function, of which the

step-function is the input, and a transducer, which does not load

the system, for an output. For the latter we have chosen a

D.C. -biased electrostatic transducer. Such transducers have been

used as transmitters and receivers for high-frequency sound in

solids for many years, beginning perhaps with Bordoni and Nuovo

(who, however, tuned them by means of inductors to produce a small

bandwidth and high sensitivity) , and continuing up to recent work by

5 2 Legros, et. al. and by Graham and Alers. In these cases, and all

others we know about, except for some work by Sherwood,^ solid

dielectrics (thin plastic films) were employed, metallized on one

side to provide the outer electrode. We find these to have

4
undesirable resonances. A massive outer electrode, with either solid

or air dielectric is much better. In many ways, air-dielectric

transducers are more satisfactory; although use of solid dielectric

increases the sensitivity it usually introduces anomalous frequency

effects and instabilities associated with humidity and perhaps other

variables.

A little reflection will show that in the ideal case, an airdielectric transducer should be flat with frequency as a force

transmitter or as a displacement receiver. (The differentiated

output should be flat with velocity.) In a practical case the

resonant properties of the air gap must be considered. The

acoustical impedance of the air gap as seen at the surface of the

transfer block will be high near zero frequency and near frequencies

for which the gap is a multiple of a half wavelength. In our case a

typical thickness of air gap is about 4 pm (set by small shims of

polycarbonate film) for which the lowest antiresonant frequency is

about 40 MHz. A simple calculation shows that the impedance of the

air gap will be less than 5 percent of the characteristic impedance

of a typical solid for frequencies ranging from about 6 kHz to just

below 40 MHz. This calculation ignores the attenuation in the air

and air pumping at low frequencies, but it is clear that we can

expect our transducers to have a very large bandwidth, and experiment

bears this out. We also find that an increase in the mass of the

outer electrode lowers the lower cutoff frequency, so it is likely

that this cutoff is set by resonance of the mass of the electrode

5
with the compliance of the shims. To use an air gap as small as A ym

with a polarization of some 250 V successfully requires that the

opposing surfaces be scraped flat and smooth, and that scrupulous

cleanliness be observed during assembly.

A SEISMIC SURFACE PULSE EXPERIMENT

To check on these ideas, we examine the following problem,

borrowed from seismology. A step-function of force, ZU(t), is

applied at a point on, and normal to the plane surface of a

semi-infinite isotropic solid for which the speed of the shear wave

is c and the shear modulus is p. The vertical displacement of the

surface, w, is measured at a distance r. This problem was first

studied by Lamb^ and since then by many others. We use explicit

g expressions given by Pekeris. It turns out that wTiyr/Z is a

function only of t = ct/r. Pekeris presents the result for Poisson's

ratio, u, equal to 1/A, numerically the simplest case. The result is

shown in Fig. 2, to which we may compare an oscillogram, Fig. 3,

taken on a glass plate for which the measured value of u was 0.226.

9 Figure 4 shows the result of a calculation we have made for the case

V = 1/3, and Fig. 5 is an oscillogram taken on an aluminum-alloy

block for which the measured value of u was 0.343. The

differentiated output, proportional to velocity, is shown on the

oscillogram. Fig. 6. The apparatus (aluminum block) is shown in the

photograph. Fig. 7. In these experiments the loads were applied

using breaking glass capillaries as described, and the displacements

6
S 0

-.2--

-.4--

.5 .6 1.2 1.3

R

T = ct/r

FIG. 2. Vertical displacement for seismic surface pulse calculated

o from an expression of Pekeris for v = 1/4. P, S, and R

show arrivals of the longitudinal, shear, and Rayleigh

waves, respectively. See text for meaning of symbols.
r- '

I —

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, au '

' '

'

f 1 M

\ 1

^ i ~

. i

1 1 1

1

1 1 1

1

(

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1 1 1 1 1 1 1 i -H- 1 1 1 1 1 1 1 1 1 1 1

1

1

1

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1

;

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/

FIG. 3. Oscillogram showing result of a seismic surface pulse ex- periment on a glass block, v = 0.226. The block was 3.3 cm thick and all lateral dimensions exceeded 9 cm. Source,

breaking of glass capillary 0.15 mm in diameter. Receiver:

cylindrical brass electrode 6.3 mm in diameter and 6.3 mm

long; air gap, 2 /xm; polarization, 20 V. Source to receiver,

2.54 cm. Each division on the abscissa equals 1 /xs. Compare

with Fig. 2.
FIG. 4. Same as Fig. 2 but recalculated for v= 1/3.
FIG. 5. Same as Fig. 3 but for aluminum-anoy block, v= 0.343, 6.3

cm thick and 17.8 cm in diameter. Source, breaking of glass

capillary 0.15 mm in diameter. Receiver: cylindrical brass

electrode 1.27 cm in diameter and 1.27 cm long; air gap, 3.6

/xm; polarization, 200 V. Source to receiver, 5.08 cm. Each

division on the abscissa equals 2 /us. Compare with Fig. 4.
r

^

1

\\

lUU

1 90—- - : r

V

— - MM MM

T » MM MM MM MM -H- -h MM MM MM

10 —Q-/.- • • •

• • 1

iv am^L. J

FIG. 6. Oscillogram obtained in experiment similar to that of Fig.

5, but witfi ordinate proportional to velocity, rather than

displacement. Obtained by insertion of true differentiator

in amplifier chain. Each division on the abscissa equals

2 fJLS.
FIG. 7. Photograph of set-up which yielded oscillogram, Fig. 5. The

pickup near the indenter provides a signal which triggers a high-speed storage oscilloscope.
were measured using an electrostatic transducer having a cylindrical

electrode with axis parallel to the surface of the block and normal

to the line from the point of application of the load. Relevant

parameters are given in the captions to the figures. The jog near

the end of the trace in each of the oscillograms, Figs. 3, 5 and 6,

marks the arrival of the first reflection from the back of the block.

Of course, it is difficult to make a quantitative comparison

between calculation and experiment when the former leads to an

infinite displacement. Nevertheless, the similarity between the two

is remarkable. Also we note that the fall time (10 to 90 percent) of

the drop corresponding to the arrival of the R-wave, which is zero in

the ideal case, is actually only about 0.15 us. The factors

contributing to a finite fall time are (1) finite rise-time of the

input (this is the point in question), (2) finite area of application

of the load, (3) attenuation in the block, "'"^ (4) finite size of the

receiving transducer, and (5) frequency response of the receiving

circuits. Part of (A) above, namely the finite width of the

receiver, alone accounts for 0.06 ps in case of the glass and 0.13 ys

in case of the aluminum. Thus the rise-time of the step produced by

the breaking capillary does not exceed 0.1 ps; it is probably much

smaller

.

It thus appears that we have at our disposal a standard source

(i.e., the breaking glass capillary) the signal from which, as

received by the transducer, G (see Fig. 1), can be compared with that

gotten on the same transducer from an actual source event in the

sample, B.

7
A QUASI-BURIED PULSE EXPERIMENT

We now have to examine the effect of having the source event located on a surface of a solid instead of within it, as is usually the

case. For this purpose we have recourse to another seismological

problem, that of the "buried seismic pulse". In this problem,

treated first by Lamb'' and later by others, we have a step-function

load source, ZU(t), at a point in the interior of a semi-infinite

solid at a distance H below the free plane surface. We can compare

the analytical solution of this problem to the experimental results

obtained with the transfer block. Pekeris and Lifson^"*^ give an exact

solution for the following case. The free surface is horizontal and

the step function of force, vertical. The displacement is calculated

for all points (except the epicentral one) on the surface for u =

1/4. From this solution we have calculated the displacement at the

epicentral point (i.e., directly above the load point) for u = 1/3.

The result is shown in Fig. 8. Except for H, the symbols have the

same meaning as before. This is to be compared with the oscillogram.

Fig. 9, gotten under the conditions given in the caption. The

agreement in the general features is altogether remarkable. Two

quantitative comparisons are noteworthy. First, the measured rise

time is something over 0.1 ys of which some 0.03 ps is owing to the

finite diameter of the receiver. Second, the calculated ratio of the

displacement at t = 1.0 to that at t = 0.5 is 4.38; the experimental

value, as nearly as can be read from the oscillogram, is 4.4. It

thus appears that there is no important difference between the

8
I .5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 1.4

T-Ct/H

8. Vertical displacement for seismic buried pulse calculated

from expressions of Pekeris and Lifson'''^ for v = 1/3. P and

S show the arrivals of the longitudinal and shear waves, respectively. See text for meaning of symbols.
FIG. 9. Oscillogram showing the vertical displacement at a point on one surface of a block resulting from a step of load applied

to the other surface directly opposite. The block is the

, same aluminum-alloy block as in Fig. 5. Source, breaking of

glass capillary 0.1 mm in diameter. Receiver: tungsten car- bide backplate 9.6 mm in diameter and 2.5 cm long, flat end

' to; air gap, 4.1 fim; polarization, 200 V. Each division on the abscissa equals 2 /xs. Compare with Fig. 8.
vertical displacement at the eplcentral point produced by a source

event on the surface and that produced by an event in the interior.

The oscillogram. Fig. 10, is the same as Fig. 9, except the ordinate

is velocity, obtained by differentiation.

CALIBRATION OF TRANSDUCERS

A convenient set-up for the purpose of calibrating a transducer

is that of Fig. 1, with the test-sample B replaced by a standard

source. The output of the test transducer is then compared with that

of a standard transducer. In our work, the latter is an

electrostatic one, as already described. The standard source can be

any that is reproducible, but the calibration can be obtained only

for those frequencies at which the source has adequate output - hence

our emphasis on sources of short rise-time. If the source is a

one-shot affair, the transducer outputs could be acquired on a

transient recorder or the waveforms digitized some other way - in

either case the data would be processed off line. We have used a

breaking glass capillary for such a source; its output has a

reproducible spectrum and the amplitude can be normalized from

measured values.

A repetitive source allows the transducer outputs to be

processed on line with a conventional spectrum analyzer, the received

signal being gated to eliminate reflections. As already indicated,

an air-dielectric electrostatic transducer is flat with frequency as

a force transmitter. We have constructed one of these using, as an

9
[ 1

i

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Y

1

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100 •• •

1 90 —

1 1 1

1

1 1 1

1 -1-4 4-1- 1 1 1

1 1 1 1 1

1 1 1

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1 1 1 Mil 1 V

1 1 1

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10 —0%- • •

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V

FIG. 10. Oscillogram obtained in an experiment similar to that of

Fig. 9, but with ordinate proportional to velocity, rather

than displacement. Obtained by insertion of a quasi -differentiator, having a time constant of 0.1 /xs, in amplifier

chain. Each division on the abscissa equals 2 fxs.
outer electrode, a tungsten cylinder of diameter 1 cm and length 0.5

cm having its flat end spaced 4 \im from the surface of the transfer

block. This was energized with a 200-V step having a rise time of

about 10 ns gotten from an ordinary mercury-wetted relay. As one

example, a calibration was run on a 1-MHz wide-band transducer of the

type commonly sold for flaw detection. With a pulse repetition rate

of 10 to 20 per second, a spectrum covering the range 0-10 MHz was

obtained in about 100 seconds. The peaks near (but below) 1, 3 and 5

MHz were rather pronounced. On the other hand, a similar test of a

5-MHz transducer by the same manufacturer revealed a much less

pronounced resonance, showing it to be more highly damped than the

1-MHz transducer. For accurate work, these spectra should be

compared to that of a standard transducer, because the standard

source used applies the force over a large area and the result is not

calculable.

12 13 Another repetitive source is due to Bell ' who has developed

an interesting method for calibration of acoustic-emission

transducers based on a spark source. A spark is struck between a

needle or ball electrode and the surface of a test block and a signal

is picked up by the test transducer at a remote point on the surface

of a long bar. The point of view is different from that discussed

here. Bell assumes that the mechanical load impressed by the spark

is the same as that of an acoustic emission source event; the

signature obtained from the transducer is then considered to

represent its response to a source event in a typical application. A

10
repetitive spark is easily got from a simple relaxation oscillator

and the output can be processed on line as just described. With our

apparatus the time history of the load impressed by such a spark is

easily determined. It resembles a step-function deficient in low

frequencies - the smaller the spark, the greater the deficiency. The

rise is rather fast, but in some cases there is some overshoot. In a 14

later development the spark is drawn between two electrodes near,

but not touching, the specimen. In this case, there is again great

variability, depending on the parameters. For instance, for a 3 mm

gap 3 mm from the surface the rise time is about 5 ys, but for a 1.5

mm gap 1.5 mm from the surface it is about 1 ps. In no case did the

spark appear to be either a step- or 6-f unction source. All of the

spark sources we tried had the desirable feature that the results

were repeatable once the parameters were fixed.

The (DC-biased) electrostatic force transmitter can also be

energized with a short burst, the carrier frequency of which is swept

at constant amplitude over the gamut of interest. The received

signal, gated to eliminate reflections, is displayed on a storage

oscilloscope, the sweep of which is synchronized with that of the

oscillator. The result is an amplitude spectrum which corresponds to

a 6-f unction Input on the transfer block. This system has the

advantage that it does not call for a spectrum analyzer. With it we

have calibrated a number of commercial wide-band transducers. Two

nominally identical 1-MHz units proved to be nearly matched in

11
sensitivity but not so well matched in frequency response. Of four

nominally identical 5-MHz transducers, the least sensitive had half

the sensitivity of the most sensitive. Similar results were obtained

for 10- and 15-MHz transducers.

In all of the above, we have calibrated transducers as

receivers. The same apparatus could be used to calibrate them as

transmitters

.

CONCLUSION

We have described some apparatus with which we hope to obtain

signatures of numerous acoustic-emission source events produced by

both plastic deformation and temperature-induced phase changes. For

very energetic source events, electrostatic receiving transducers

will be preferred because of their very large bandwidth. For lesser

events, it may be necessary to use wide-band piezoelectric

transducers, perhaps several covering different ranges of frequency

for each type of event. No doubt there are also source events so

feeble that they cannot be detected with wide-band transducers at

all; these will have to be ignored for the present. The apparatus

has proved to be useful for the "calibration" of transducers. In

particular, it becomes very easy to detect variations in sensitivity

and frequency response and to ascertain the effects of changes in

clamping force and couplant on response. Finally, we believe some of

our results will be of interest to seismologists and elasticians.

12
REFERENCES

'"R.W.B. Stephans and A. A. Pollock, "Waveforms and Frequency Spectra

of Acoustic Emissions," J. Acoust. Soc . Am. 50, 904-910 (1971).

2

L. J. Graham and G. A. Alers, "Frequency Spectra of Acoustic

Emissions Generated by Deforming Metals and Ceramics," Ultrasonics

Symposium Proc. IEEE, 18-21 (1972).

3

K. Ono, R. Stern, and M. Long, Jr., "Application of Correlation

Analysis to Acoustic Emission" in Acoustic Emission, ASTM STP 505

(American Society for Testing and Materials, Philadelphia, 1972)

pp. 152-163.

4

P. G. Bordoni and M. Nuovo, "A Tuned Capacitive Detector for High

Frequency Vibrations," Acustica ^, 351-362 (1958).

^D. Legros, J. Lewiner and P. Biquard, "Generation of Ultrasound by

a Dielectric Transducer," J. Acoust. Soc. Am. 52, 196-198 (1972).

J.W.C. Sherwood, "Elastic Wave Propagation in a Semi-Infinite Solid

Medium," Proc. Phys. Soc. 71, Pt. 2, 207-219 (1958).

^H. Lamb, "On the Propagation of Tremors over the Surface of an

Elastic Solid," Phil. Trans. Roy. Soc, Ser. A, 203, 1-42 (1904).

g C. L. Pekeris, "The Seismic Surface Pulse," Proc. Nat. Acad. Sci.

41, 469-480 (1955).

9Explicit expressions valid for any value of u have more recently

been given by H. M. Mooney, "Some Numerical Solutions for Lamb's

Problem," Bull. Seismol. Soc. Am. 64, 473-491 (1974).

13
'"^The effect of attenuation on the overall shape of the response can

be estimated from a treatment by L. Knopoff, "The Seismic Pulse in

Materials Possessing Solid Friction, II: Lamb's Problem," Bull.

Seismol. Soc. Am. 49, 403-413 (1959).

"^"'"C. L. Pekeris and H. Lifson, "Motion of the Surface of a Uniform

Elastic Half-Space Produced by a Buried Pulse," J. Acoust. Soc.

Am. 2_9, 1233-1238 (1957).

12

R. L. Bell, "Acoustic Emission Transducer Calibration - Transient

Pulse Method," Technical Report DE-73-3, Dunegan/Endevco

,

Liverm.ore, CA (Feb. 1973).

13

Now Hear This J^, No. 1, Dunegan/Endevco, Livermore, CA (1973).

14 it , Now Hear This 2, No. 1, Dunegan/Endevco, Livermore, CA (1974).

14
nuj-i (r-<t.V. 7-7J)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PURLICATION OR REPORT NO.

NBSIR 74-565

2. Gov't Accession

No.

3. Recipient's Acccs.sion No.

4. TITLE AND SUBTITLE

Acoustic Emission: Some Applications of Lamb's Problem

5. Publication Date September 1974

6. Performing Organization Code

7. AUTHOR(S)

F. R. Breckenridge, C. E. Tschiegg, and M. Greenspan

8. Hertorming Organ. Report No. NBSIR 74-565

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/W'ork Unit No. 2130111

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, Slate, ZIP)

in part by Office of Naval Research, Wash., D.C.

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less {actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A method for obtaining the signatures (waveforms) of certain acoustic emission events

has been developed. The waveform is that at the source, free of contamination by

ringing of the specimen, apparatus and transducer. The technique is based on the

comparison of two signals at the transducer, one from the event in question and one from an artificial event of known waveform. The apparatus is also adapted to the

calibration of transducers in a certain sense. The configurations of source (real or simulated acoustic-emission event) and receiving transducer correspond to those of some special cases of Lamb's problem. As a byproduct, the results may be of some

interest to seismologists.

17. KEY WORDS (six to twelve entries; alphabetical order, capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Acoustic emission; calibration of transducers; electrostatic transducers; Lamb's

problem; seismic pulses; ultrasonic transducers.

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