On the Works of Prince B. B. Golitsyn in Seismology

Academician A. N. Krylov.

(Report at a meeting of the seismic commission dedicated to the memory of Prince B. B. Golitsyn.)

The works of Prince Boris Borisovich Golitsyn on seismology and, chiefly, on its measuring part—seismometry—constitute an entire literature, comprising more than 60 titles of his original articles and investigations.

It would be impossible to characterize them in a brief outline, but Boris Borisovich, with the hand of a master, assembled a considerable part of his investigations into a coherent whole—Lectures on Seismometry—to the review of which I shall confine myself.

Earthquakes are attributed either to underground explosions (volcanic), or to collapses in internal cavities of the earth, or to shifting of layers of rock. In all these cases there occurs a disturbance of the equilibrium of the internal parts of the earth in some region, called the focus of the earthquake. From this focus, through the thickness of the terrestrial sphere, elastic oscillations propagate; reaching the surface of the earth, they cause it to shake. These shakings may, in magnitude and velocity, be of the most varied sizes, beginning with those that destroy the sturdiest structures and ending with ones so slight that the most accurate and sensitive instruments are required for their perception.

The theory of elasticity shows that from the focus of an earthquake two systems of elastic oscillations may propagate:

1) longitudinal, or waves of expansions and compressions, and 2) transverse, i.e. shear waves.

The study of the laws of propagation of these waves constitutes the first of the tasks of theoretical seismology.

The simplest of the results obtained are the following:

1) The velocities of propagation of longitudinal and transverse waves are different, the ratio of the first to the second being close to $\sqrt{3}$, i.e. 1.73.

2) In addition to waves propagating through the thickness of the earth, along its surface there run so-called surface, or long, waves.

waves of long period. Their speed of propagation amounts to about 0.91 of the velocity of transverse waves; and since this latter, in the upper layers of the earth, is close to 4 km per second, the velocity of the surface waves is about 3.6 km, and that of the longitudinal waves about 7.5 km.

For each of the systems of waves passing through the thickness of the earth there will also be its own system of rays, i.e. of normals to the corresponding wave surfaces. These rays diverge from the focus of the earthquake like rays of light from such a source, and obey analogous laws of refraction and reflection; and if one assumes that the earth consists of concentric layers, each of which everywhere possesses the same plasticity and the same elastic properties, then the path of a ray through the thickness of the earth will present a complete analogy with the path of a light ray through the thickness of the atmosphere, and its principal property is expressed by the very same equation which is fundamental in the theory of astronomical refraction, i.e. that the product of the refractive index of a layer, the radius of this layer, and the sine of the zenith distance is a constant quantity.

For a seismic ray, the role of the refractive index is played by the ratio of the propagation velocities of seismic waves in the layers under consideration; instead of the zenith distance, its complement is considered—namely the so-called angle of emergence of the ray, reckoned from the horizon.

Just as, in the question of astronomical refraction, various hypotheses about the structure of the atmosphere lead to different expressions for refraction, so also in the question of the propagation of seismic rays the function expressing the dependence of the elastic properties and density of the layers on their distance from the center of the earth is of fundamental importance; but whereas in astronomy the agreement or disagreement between the observed refraction and the computed one serves merely to test one or another hypothesis about the structure of the atmosphere, here there is yet a second criterion—the velocity of propagation of the waves, which is likewise accessible to observations.

Consideration of the question “of seismic radiation,” referred to in the preceding words, convinced Boris Borisovich that, from the theoretical side, in the sense of studying the propagation of seismic rays, the precise measurement of the displacements of points of the earth’s surface and of the velocities of these displacements is of primary importance, and moreover for very small displacements, i.e. those produced by waves that have passed through a very considerable thickness of the terrestrial globe. The department of seismometry, “which studies the various properties of seismic rays,” he says in his lectures, “discovers, on the basis of observational material collected at various

seismic stations, a path toward the study of the physical properties of the deepest internal layers of the earth*.

“Seismic rays come to us from the very depths of the earth and bring with them tidings of its internal properties and peculiarities.”

“Just as light rays coming to us from cosmic space give us indications of the chemical composition and, in part, of the temperature and pressure prevailing in various heavenly bodies, and, in combination with the Doppler principle, make it possible to determine also the speed of their motion along the line of sight, so seismic rays give us the key to unraveling the hidden mysteries of the earth’s internal structure, precisely at depths which, by reason of their inaccessibility, are entirely removed from the field of investigation of modern geology.”

But Boris Borisovich saw the tasks of seismometry not at all in the purely scientific investigation of regions inside the earth that are wholly inaccessible.

“Of special attention, of course, is the careful study of the various phenomena preceding earthquakes, so that it might become possible to predict, with greater or lesser probability, the occurrence of earthquakes,” and he then outlines various paths toward “the solution of this problem, which has enormous practical significance in the sense of preserving human lives and various kinds of property.”

Perhaps confidence in these practical applications made it possible for Boris Borisovich to convince legislative institutions of them and to obtain the necessary funds for organizing a network of seismic stations.

The basic requirement that Boris Borisovich places upon seismometers is expressed in the following words: “for the rational study of various seismic phenomena, one must always pass from the readings of instruments to the true motions of the earth’s surface, since only on this foundation can the further successes of seismometry be based.”

A study of the existing types of seismographs showed Boris Borisovich that it was necessary to divide the problem and to measure the components or projections of displacement along three mutually perpendicular axes, one of which is vertical.

Boris Borisovich then began the study of horizontal pendulums, both from the theoretical and from the practical side.

In his investigations he confined himself to considering cases of “small oscillations,” the most important for the study of seismic rays.

Under such a restriction the problem is reduced to the study of “small oscillations” of a body with one degree of freedom about the position of its stable equilibrium; and the chief attention must be devoted to the “forced oscillations,” since they stand in a definite relation to the oscillations of the ground that produce them, and it is precisely these latter that must be found.

Free oscillations, being superposed upon the forced ones, only complicate the record furnished by the instruments; it is therefore very important to eliminate them. This elimination is most perfectly achieved by introducing a resistance “proportional to the first power of the velocity”; such a resistance is given with complete exactness by the magnetic method, i.e., by currents induced in a plate of red copper moving in a magnetic field perpendicular to its lines of force.

Thus, a detailed mathematical analysis, carefully carried out, first led Boris Borisovich to the construction of a horizontal pendulum with optical registration and magnetic damping carried to aperiodicity.

But Boris Borisovich did not stop there; he took a further step and, one may say, the final step in the matter of constructing seismometers.

Analyzing the usual methods of recording, i.e., the “mechanical” and the “optical,” he drew attention to a third method—the “galvanometric” one—in which what is recorded is not a quantity proportional to the relative displacement of the mass of the pendulum and its foundation, but a quantity proportional to the velocity of this displacement.

This achieves a whole series of very important practical advantages, such as: independence of the record from the equilibrium position of the instrument, the possibility of placing the recorder in a room separate from the pendulum, as far away from it as desired, the possibility of placing the pendulum in a vacuum, attainment of a higher degree of sensitivity, and so on. The development of the theory of the horizontal pendulum with magnetic damping and galvanometric recording was carried out by Boris Borisovich with exhaustive completeness, while the actual realization of the instrument was accomplished with astonishing constructive talent.

The study of the propagation of seismic rays leads to the establishment of a definite dependence between the angle of emergence of a ray and the total length of its path from the epicenter to the point of emergence. At the same time, the very shape of the ray, the depth of its lowest point, and the mean velocity of propagation of the oscillations are likewise in definite dependence on the density and elastic properties of the layers of the earth through which the ray passes. Hence the importance is clear of determining the angle of emergence, and therefore also the vertical component of the displacements of points of the earth’s surface. For this purpose the vertical seis-

seismometer, the theory of which Boris Borisovich developed with the same exhaustive completeness as that of the horizontal pendulum; and, on the basis of this work, to construct a vertical seismometer with magnetic damping and galvanometric recording, distinguished by the same merits as the horizontal pendulum of his design.

Thus, two mutually perpendicular horizontal pendulums, one installed in the plane of the meridian and the other in the plane of the prime vertical, and one vertical pendulum give all three mutually perpendicular components of the displacement of the place of their installation during seismic oscillations.

The merits of Boris Borisovich’s instruments, constructed, as is evident, on theoretical foundations elaborated in detail and with precision, proved so superior that they were adopted not only for our seismic stations, but many foreign stations as well, having convinced themselves of the accuracy of the Pulkovo seismic observations, introduced Boris Borisovich’s instruments, with which the instruments of foreign systems could not compare, despite their far more complicated construction and bulkiness.

As has already been said, the velocity of propagation of longitudinal and transverse waves is different. Longitudinal waves arrive first, and on the seismogram the moment of the arrival of the waves, or the beginning of the oscillations, is clearly visible; it is conventionally denoted by the letter \(P\) (undae primae). The arrival of the transverse waves, denoted by the letter \(S\), is reflected in a more or less sharp change in the character of the instruments’ record.

The difference between the moments \(S-P\) makes it possible at once to determine the distance to the epicenter, which, as a first approximation, in view of the comparatively small depth of the earthquake focus, may be taken as the source of the oscillations. For this determination of distances special tables or curves have been compiled.

It is clear that from the known distances to two stations two points on the earth’s surface are determined which could serve as the epicenter. The distance to a third station decides the question.

But Boris Borisovich was not satisfied with such a solution, although he had done much for its detailed development; he went considerably further.

The accuracy of the indications of the instruments of his system made it possible, from the two horizontal components of the displacement, to determine its azimuth, and consequently also the direction along which the seismic ray reaches the point under consideration; thus, in addition to the distance, the azimuth of the epicenter is also obtained, and hence from observations at a single station the position of the epicenter is found as well.

These determinations by Boris Borisovich’s instruments and by the method,

...the method indicated by him, developed by him in all its details, using, for example, the data of the Pulkovo seismic station, prove to be just as precise as those obtained from the readings of several stations; and the region in which the epicenter is located is obtained within several tens of versts, while the distance to it is several thousand versts, sometimes more than 10,000.

This alone can already give some idea of the merits of Boris Borisovich’s instruments, if one recalls that the displacements of the ground observed in earthquakes so remote from Pulkovo are expressed in tenths of a millimeter, and therefore the hypotenuse of a triangle extended over a distance of thousands of versts, whose legs have a length measured in tenths of a millimeter, indicates the sought location of the epicenter.

But Boris Borisovich did not stop even at this: he penetrated with his mind’s eye into the very thickness of the earth’s crust and indicated a method by which, from an analysis of the records of his instruments, one may judge the depth at which the very focus of an earthquake lies. He was working on this question in the very last period, and two of his communications to the Paris Academy were printed in the Comptes Rendus only after his so untimely death.

All the instruments mentioned above, of extraordinary sensitivity and precision, are intended for recording exceedingly small oscillations far from the focus.

But earthquakes near the focus sometimes manifest themselves in those catastrophes whose memory is preserved for ages.

As to the destructive force of earthquakes, the consequences of their action do not make it possible to have an exact numerical judgment, and the force of an earthquake was evaluated in degrees, scarcely comparable with one another in view of the complete subjectivity of such an evaluation.

Boris Borisovich proposed and developed a dynamic scale, in which it was possible to judge, from the overturning of parallelepipeds of various sizes placed upright, the magnitude of the accelerations to which they were subjected, so as in this way to make the evaluation objective instead of subjective.

And here, once he had set himself a task, Boris Borisovich pursued it and sought out its solution to the end.

To judge the force by the acceleration imparted by it to a given mass, Boris Borisovich also constructed an instrument for the direct measurement of accelerations, making use of the property of quartz to become electrified when the pressure to which it is subjected changes.

This instrument could have found broad application in other fields as well, besides seismometry—namely, in naval and artillery work—and the Naval Department turned to Boris Bori-

sovich with a request to construct an instrument of his system satisfying certain specified requirements, placing at his disposal the appropriate means as well; but this work was interrupted at its very beginning.

I do not know whether I have succeeded in showing that the name of Boris Borisovich is indelibly inscribed in the annals of world science as that of an independent creator within it of an entirely new field.