SEISMIC PHENOMENA DURING THE TESTING OF AN ATOMIC BOMB*)

L. Don Leet.

During the testing of the atomic bomb in the Jornada del Muerto valley (New Mexico) on July 16, 1945, records were obtained of ground vibrations that rank among the most important in the history of seismology.

Some data, for example on the distance and absolute displacement, have not yet been reported, but they are not significant for the principal results.

The seismograms presented in this article were obtained on Leet’s three-component seismograph¹, reconstructed somewhat for this purpose; this instrument makes it possible to obtain a photographic record of all three components of ground displacement.

Three lines on the seismograms denote: one—the longitudinal displacement, i.e., the horizontal motion in the direction of the seismic ray; another—the transverse displacement, representing a horizontal displacement perpendicular to the longitudinal one; the third—the vertical displacement.

The terminology adopted for designating displacements relative to these axes is indicated in Fig. 1. The seismogram recorded during the atomic-bomb test is shown in Fig. 2. The absolute amplitudes of displacement are not indicated in Fig. 2, but the magnitude of the relative displacements is reproduced accurately.

Fig. 1. Diagram illustrating the terminology for horizontal displacements.

Labels in the diagram: Seismograph; Transverse: left, right; Longitudinal: forward, backward; Explosion.

WAVES

Waves in the earth’s interior constitute the principal subject of seismology. They are to it what electromagnetic waves are to radio and sound waves to acoustics. Despite this, the literature on this question is strikingly poor in quantitative observations concerning the types of waves, propaga-

*) American Scientist, 34, April 1946. Translated by S. I. Kremer.

ing in the soil. This is due, on the one hand, to the youth of this science, and on the other—to the difficulties of controlling the conditions in the source of the waves created in the experiment.

Earthquakes, of course, belong to the category of uncontrolled sources. Artificial explosions are very convenient, although some of

Fig. 2. Record of ground displacements during the test of an atomic bomb, carried out at Jornada del Muerto (New Mexico) on July 16, 1945. For the scheme for distinguishing wave types, see Fig. 9.

the leading theoreticians have tried to discredit them, believing that they produce simple radially symmetric stresses emanating from a single point and are, therefore, too special a case to create all possible types of waves.

Such an assertion was justified theoretically, but it does not agree with observations.

Two of the basic types of waves are well known to science both theoretically and from observations: these are body waves, propagating in the elastic medium itself, in contrast to surface waves, propagating along the boundary of a free surface. One of them consists of alternating compressions and rarefactions; this is the longitudinal wave, or a wave of the same type as that which carries sound in air. In seismology this type of wave is denoted by the symbol “P,” since

...since these waves arrive first during earthquakes and were called Undae Primae.

If \(K\) is the bulk modulus of elasticity, \(M\) the shear modulus, and \(\rho\) the density, then the velocity of \(P\)-waves can be expressed as

\[ V_p=\frac{\sqrt{k+4\mu/3}}{\rho}. \]

The second type of seismic waves are shear waves; these are transverse waves. During earthquakes they arrive at the place of observation after the compressional waves and were called Undae Secundae, receiving among seismologists the symbol \(S\). The velocity of \(S\)-waves is expressed by the formula

\[ V_s=\sqrt{\frac{\mu}{\rho}}. \]

Theory shows that waves in the earth must be of the elastic type, that gravity does not affect shear waves \((S)\), while its influence on compressional waves \((P)\) appears in the second order \({}^{2,3}\).

A valuable contribution to the theory of elasticity and elastic waves was the work of Lord Rayleigh \({}^{4}\), who indicated that special waves must occur at the boundary of an elastic medium. These waves received the name Rayleigh waves.

Rayleigh’s work was published in 1885; however, complete experimental proof of the existence of these waves was published only in 1931 \({}^{5}\).

The agreement between observation and the classical theory proves to be, to a considerable extent, only qualitative even for compressional and shear waves \((P\) and \(S)\).

At the time of the arrival of compressional waves \((P)\) at a seismic station, displacement in the longitudinal and vertical directions predominates; while during the time corresponding to the arrival of transverse waves \((S)\), transverse oscillations usually, but not always, predominate. Exceptions are very frequent.

In 1904 Lamb \({}^{6}\) published solutions of the equations of the elastic wave, from which he obtained the form of the wave at a distant point caused by a unit impulse applied vertically to the earth’s surface. Figures 3 and 4 show the results of his calculations.

Among Lamb’s conclusions was the following: “It must be admitted that our theoretical curves differ greatly, in two respects, from seismograph records. First of all, they give nothing resembling the successive series of longitudinal oscillations that is characteristic of seismograms. Apparently such data, since they are sufficiently reliable and not caused by distortions of the instrument, must be ascribed to a series of successive impulses, which in itself is quite plausible. This difficulty, encountered by almost every theoretical explanation, is clearly recognized by seismologists, who are therefore inclined to doubt the reliability, in this respect, of the records of their instruments.”

Considering Fig. 4, it should be noted that the solution of the equations of elasticity found by Lamb predicted that from a vertical impact at a remote point there should pass to the observation point first a compressional wave ($P$), followed by an interval of rest, then a shear wave ($S$), and, finally, a Rayleigh wave. Each of them should have appeared as a single pulse. The long-lasting oscillations observed on the seismograms Lamb explained either as a series of successive pulses, or as imperfections of the instruments, inclining toward the latter assumption.

Fig. 3. Rayleigh waves computed by Lamb; longitudinal and transverse records and the orbit of a particle of the earth.

On July 16, 1945, the conditions from which Lamb proceeded in his theory were for the first time realized experimentally. The oriented three-component seismograph had a magnetic damping of about 0.7 of critical, so that there could be no question of distortions caused by the natural oscillations of the instrument.

The source was a single simple instantaneous vertical impact on the ground, produced by the explosion of an atomic bomb at a height of 100 feet; thus there was no series of pulses that could explain the oscillations not provided for by the theory. Comparing Fig. 2 with Fig. 4, one can see the discrepancy between theory and observations.

Fig. 4. Displacement of the ground computed by Lamb; longitudinal and vertical records at a certain distance from a vertical source of shaking.

ANALYSIS OF TYPES OF WAVES

The deciphering of seismograms is based on analysis of the motion of a particle of the ground during the passage of waves. For some of the waves the displacement of the particle occurs only in a vertical plane, and the results can be easily represented. If this is not the case, then one-

one of the fundamental problems is to determine, from the record, which particular components are involved in the motion of one and the same wave. This determination is based on the assumption that the components involved in the motion of a wave of a definite type must have the same period and usually also similar amplitude variations. But there are undoubted cases in which the amplitude and period of the transverse component differ from those of the other two components. In such cases the most probable cause of the transverse motion is an independent transverse wave.

PRELIMINARY RESULTS

In studying records from seismic stations it is necessary to use earthquakes that happened to occur in one of the directions of orientation of the horizontal seismographs, i.e., usually in the meridional or latitudinal direction from the station. This was also done in determining the properties of the Rayleigh wave noted above.^5 Two years later Macelwane pointed out:^7 “Evidently, it is beyond doubt that the complex surface waves which we observe do not even approximately correspond to Rayleigh’s theory, and that the term ‘Rayleigh wave’ as applied to them is a misunderstanding.”

In developing this idea, he writes: “One must regard as settled in advance, and in the affirmative, the question of the existence of true Rayleigh waves in order to have the right to assert, as Gutenberg did, that a seismograph recording the vertical and longitudinal components records only Rayleigh waves, while oscillations simultaneously recorded by a transverse seismograph will be Love surface waves. Apparently the same assumption was made by Leet, who expresses confidence in the accuracy of plotting the vector in the plane of propagation of the wave and at the same time casts doubt on the result of plotting in the horizontal plane, since in this case, for practically the entire time, there is a ‘transverse component of unknown magnitude.’” The quotation from Leet given at the end of this excerpt explains that, in order to separate the longitudinal and transverse components, the horizontal seismographs must be accurately oriented with respect to the direction of arrival of the wave.

In full, this excerpt reads: “It is clear that not a single component of the horizontal record of a wave whose azimuth of arrival does not coincide with the azimuth of orientation of the instrument can with certainty be ascribed to \(R\)-waves; there is always present a transverse component of independent magnitude.”

What has been said has no bearing on the question of the existence or nonexistence of Rayleigh waves in earthquakes. The question of whether the result of observations in earthquakes is described by Rayleigh waves exactly or with sufficient approximation was answered in the affirmative, although, evidently, the author’s exposition was not clear.

Thus we have reached 1933 with Gutenberg’s assertion of the existence of Rayleigh waves in earthquakes, with Leet’s observations requiring verification, and with Macelwane’s confidence in a positive resolution of this question. The acquisition of further data was the order of the day.

The next investigation was carried out with the aid of controlled dynamite explosions. The waves were recorded in three directions, and the horizontal components were oriented in the longitudinal and transverse directions.

The results were published in 1939.^8 The most important of them, in brief, was the proof that the following surface waves arise in a dynamite explosion:

1. The Rayleigh wave “\(R\).”
2. The surface shear wave “\(Q\),” or Love wave (Love).
3. The coupled wave, or “\(C\)-wave.”

Of these, the first two are known in theory. The coupled wave, or “\(C\)-wave,” had neither been observed nor predicted earlier.

1. The Rayleigh wave \(R\). A particle under the action of this wave moves along an elliptical orbit in accordance with the theory; the minor axis is longitudinal, and the major axis is vertical. In the upper part of its elliptical orbit the particle moves in the direction toward the source, so that its motion was called retrograde.

Thus, during the passage of the wave the particle moves in the following sequence: forward, upward, backward, downward.

Fig. 5. Record of a Rayleigh wave.

The ratios of the magnitudes and velocities of displacement (Fig. 5) made it possible to establish that this is indeed a Rayleigh wave. In the present case the transverse motion is absent, or so irregular that it is evidently not connected with the longitudinal and transverse waves. On the basis of this and many other observations, it must be considered that the Rayleigh wave really exists.

1. The surface shear wave \(Q\), or Love wave. The theory of a surface shear wave without a vertical component was developed by the British mathematician A. E. Love.^9 Some seismologists call this wave the Love wave, while others prefer to denote it the \(Q\)-wave (from Querwellen — transverse waves), without connecting it with the repeated internal reflection required by Love’s theory. The seven records in Fig. 6 show the development of the wave form at a dis—

at distances from −550 to 1000 feet from the site of the dynamite explosion. This distance is sufficient to detect \(Q\) as a special independent wave having only a transverse component. At a distance of 900 feet it is expressed better, and the independence of its motion from the oscillations in the two other components is more clearly visible; it is also less

Fig. 6. Experimental curves illustrating types of waves.

In all records:

upper line — longitudinal oscillations
middle line — vertical oscillations
lower line — transverse oscillations

\(\leftarrow\) backward
\(\rightarrow\) forward
\(\leftarrow\) to the left
\(\rightarrow\) to the right

ft/sec

complicated by partial overlapping with the volumetric shear waves. Tracing in both directions from 900 feet requires a little imagination, since the conditions are somewhat more complicated. Here, as in other places, \(Q\) is characteristically distinguished by the fact that the group begins with a maximum amplitude, passing at the end to smaller amplitudes and shorter periods. The Rayleigh wave in Fig. 6 is distinguished by the fact that, with increasing distance, the maximum amplitude lags behind the motion of the front of the wave group.

3. Coupled wave. This wave, not predicted by the usual theory of elasticity, was first discovered in 1939.[^8] Since then it has received no attention. In Fig. 6 it is denoted by \(C\). Its distinctive feature is that the particle moves along the diagonal of a rectangular parallelepiped oriented in the longitudinal direction. The result—

component of this motion is the simultaneity of maxima and minima for all three components. In Fig. 6 its motion can be seen (to the right, upward, forward, to the left, downward, backward).

TYPES OF WAVES AT A DISTANCE OF 200 FEET

A preliminary experiment with a charge of 200 feet of ordinary high explosive, carried out before the atomic-bomb test for the purpose of checking the control circuits at a distance, gives an interesting picture of the wave form at a distance of 200 feet from the explosion. The record is shown in Fig. 7. The orbits of the particle during the initial compression wave and during the passage of the \(R\)-wave are shown in Fig. 8. The \(Q\)-wave is well expressed. Its arrival after \(R\) at this short distance could have been foreseen from Fig. 6.

Fig. 7. Record of ground oscillations at a distance of 200 feet from the site of the explosion of 200 feet of high explosive. Jornada del Muerto Valley.

Fig. 8. Particle orbit during ground oscillations at a distance of 200 feet from the site of the explosion of 200 feet of explosive. Reproduced from the record in Fig. 7.

TYPES OF WAVES IN THE RECORD OF THE ATOMIC-BOMB EXPLOSION

The main conclusions concerning the types of waves recorded during the atomic-bomb explosion and presented in Fig. 2 are given in the diagram of Fig. 9. In Figs. 10–13 all of them (with the exception of pure transverse waves) are shown in the order of arrival time by smoothed diagrams of particle orbits.

\(P_2\) is the ordinary body compression wave. From the apparent angle of incidence of the wave front, and also from velocity data obtained from other sources, it can be established that this first wave was refracted in a medium in which the propagation velocity is greater than in the surface layer. The symbol \(P\) is accordingly given the subscript 2, indicating passage through the second layer. There are no data proving that this is the second and not the third, fourth, or fifth layer, but this is unimportant for our present purpose.

It is assumed that \(P_1\) is a compressional body wave that propagated in layer 1, i.e., at the ground surface. Its apparent angle of incidence is noticeably gentler than that of \(P_2\). \(S_2\) is an independent transverse wave, which should be regarded as a refracted body wave, judging by its velocity and period.

Fig. 9. Diagram for Fig. 2 for identifying wave types.

It should be noted that transverse motion existed from the very beginning of the record. This has been observed repeatedly in other experiments as well, but often could be attributed to not entirely accurate placement of the seismographs.

In the present case the transverse oscillation arriving simultaneously with \(P_2\) is so significant that explaining it by inaccurate orientation is highly doubtful. It is quite possible that in the near future observations will be accumulated concerning a transverse wave with a velocity corresponding to the longitudinal wave; they will require detailed analysis.

\(C\)—the coupled wave—was briefly described above, and the motion of a particle during its passage is shown in Fig. 11. This is a new wave, first discovered in 1939. In the atomic-bomb explosion this wave proved to be double. There is a wave \(C\) with a period of about 0.4 sec., arriving at exactly the same time and coexisting with a wave having a period of 1.0 sec. The motion was to the left, upward, forward—to the right, downward, backward.

$Q$—a surface shear wave—appears precisely when the longitudinal and vertical components of wave $C$ die out. Other similar groups $Q$ begin at approximately 10.5 and 16.5 sec.

Fig. 10. Particle orbits during the passage of waves $P_2$ and $P_1$.

Fig. 11. Particle orbits during the passage of connected waves $C$. The upper one is the longitudinal, vertical plane; the lower one is the horizontal plane. The numbers at the break points indicate the time in seconds elapsed after the appearance of $P_2$.

Wave $H$ appears at about the 8th second (Fig. 2). This is a new wave in seismology. It forces the particle to move in a longitudinal-

vertical plane is completely independent of transverse displacements. An exceptional and important circumstance in this motion is that it is opposite in comparison with the motion of a particle during the passage of a Rayleigh wave, and in the upper part of the inclined elliptical orbit there is a displacement forward, as for a particle when a wave propagates on the surface of water. For this reason it was called a hydrodynamic wave and is here denoted by \(H\). The orbit of the particle is shown schematically in Fig. 12. There is reason to believe that the occurrence of such a wave as \(H\) is explained by the special properties of the soil in the Muerto Hills, Colorado (alluvial sands and gravel). Unfortunately, at present exact data on the thickness of this layer are unknown. Presumably it is rather several hundreds than tens of feet.

Fig. 12. Orbit of a particle during the passage of the hydrodynamic wave \(H\).

Another example of a successfully recorded \(H\)-wave is given in Fig. 14. This record was made on the same test site on which the data shown in Fig. 6 were obtained. From refraction seismic prospecting and drilling it is known that the upper part of the soil section consists of a surface layer of 55 feet of sand, lying on a layer of 165 feet of clay.

In Figs. 12 and 14 it may be noted that, for \(H\), the horizontal component predominates over the vertical one and that the major axis of the elliptical orbit is inclined to the horizontal plane at an acute angle.

Fig. 13. Orbit of a particle during the passage of the Rayleigh wave \(R\).

\(R\)—the Rayleigh wave—causes the motion of particles along the orbit shown in Fig. 13, during the time indicated in Fig. 9.

The ratio of the vertical component to the horizontal for \(R\) is greater than for \(H\), but nevertheless does not reach the classical ratio

\[ \frac{\text{vertical}}{\text{horizontal}}=\frac{1.5}{1}. \]

\(R\) is shown together with \(H\) on the record presented in Fig. 14.

CONCLUSIONS

The test of an atomic bomb in New Mexico on July 16, 1945, for the first time reproduced experimentally with precision, at large amplitudes, the conditions required by Lamb’s theory (1904). Lamb obtained a solution of the equation of elasticity describing the displacement of the soil at a point distant from the place where a vertical impulse is applied to the earth’s surface. The displacement of the soil was recorded by a damped three-component seismograph with oriented horizontal components.

Fig. 14. H-waves and R-waves arising in the explosion of a small dynamite charge.

The results of the observation differ substantially and significantly from the predictions of the theory. One previously described type of waves (double waves), not provided for by the theory, carries a noticeable fraction of the energy of all the waves. Another (hydrodynamic waves) had not been found or predicted earlier. These waves produced the largest displacements in amplitude on the record.

Longitudinal and transverse body Rayleigh waves and surface shear waves were also identified. This record represents a most important achievement in solving the seismic problem—the establishment by observation of the types of waves propagating in the earth—one of the fundamental problems of this science.

REFERENCES CITED

1. Leet L. D., Trans. Amer. Geophys. Union 26, part I, pp. 33–36.
2. Macelwane James B. L., Theoretical Seismology, John Wiley & Sons, New York (1936).
3. Love A. E. H., Treatise on the Theory of Elasticity, Cambridge University Press (1892).
4. Rayleigh Lord, On Waves Propagated along the Plane Surface of an Elastic Solid, Proc. of the London Math. Soc. 17, pp. 4–11 (1885).

1. Leet L. D., Publications of the Dominion Observatory Ottawa 7, No. 6, pp. 263—322 (1931).
2. Lamb Horace, Phil. Trans. Roy. Soc. London, A, 203, 1 (1904).
3. Macelwane James B. L. J., Earthquake Surface Waves, Bulletin No. 90 of the National Research Council (1933).
4. Leet L. D., Bulletin of the Seismological Soc. of America 29, pp. 487—496 (1939).
5. Love A. E. H., Some Problems of Geodynamick, Cambridge University Press (1911).

On Don Leet’s article “Seismic Phenomena during the Testing of an Atomic Bomb”

The propagation of seismic waves in the earth is a very complex phenomenon. As is known from the classical theory of elasticity, on which theoretical seismology is based, in an unbounded elastic homogeneous medium the simultaneous occurrence of two types of elastic waves (longitudinal and transverse) is possible; these propagate with different velocities characteristic of them, depending on the physical properties of the medium. Any boundary along which media with different physical properties are in contact greatly complicates the phenomenon, since when an elastic wave is incident upon it, along with the appearance of new waves (two refracted and two reflected) and of so-called “indirect disturbances” of longitudinal and transverse type, surface waves of a special type are also formed. The presence of several boundaries is accompanied by phenomena of interference and diffraction of elastic waves. Finally, the dispersion of seismic waves, discovered in the analysis of seismograms and also theoretically, in many cases owes its origin to the deviation of the real rocks composing the earth’s crust from ideal elasticity.

Even in studying the oscillations of an elastic layer lying on an elastic half-space, theoretical seismology has encountered difficulties almost insurmountable in the present state of the mathematical apparatus, caused by the boundary phenomena indicated above. Therefore, at present it is difficult to count on an effective theoretical analysis of seismic phenomena occurring in the earth’s crust. In this connection, attempts to approach the investigation of seismic waves by a purely experimental route are met with interest by seismologists. It is precisely from this point of view that one should approach the translation, published in the journal, of the article by the American scientist Don Leet.

The article may be divided into several parts of differing significance.

Don Leet constructed reliable apparatus for the investigation of seismic phenomena during explosions—although it has low sensitivity, nevertheless, owing to the direct optical recording employed by him, it is free in the range of peri-

[[unclear: beginning of word]] from distortions. Synchronous recording on a single tape of the three displacement components enables the author, more fully and accurately than previous investigators, to follow the motion of a particle of the Earth’s surface during the passage of various waves; moreover, observations of the angle at which the wave front emerges help him to identify refracted waves of the Mintrop type.

Of particular interest is the record—published for the first time, unfortunately only in schematic form—of oscillations from the explosion of an atomic bomb.

The author’s conclusions concerning his discovery of new types of seismic waves appear somewhat bold and debatable. Finally, the author’s comparison of the seismogram he obtained during the explosion of an atomic bomb with Lamb’s displacement graph, calculated by the latter in analyzing the propagation of an impact at the boundary of an elastic half-space, is naive and incorrect.

D. Khariya