The Kursk Magnetic Anomaly

On the Work of the Commission of the Academy of Sciences

(from July 1, 1919, to July 1, 1920)

P. Lazarev.

§ 1.

The question of the magnetic anomaly in Kursk Province began to interest researchers from the time of the first geomagnetic survey of Russia, undertaken in the period from 1872 to 1877 by I. N. Smirnov1, who discovered 2 points with anomalous magnetism in Kursk Province. N. D. Pilchikov, wishing to extend Smirnov’s observations, carried out 71 series of observations in the environs of Belgorod, several of which related to places with a sharply pronounced anomaly. The investigations of Pilchikov, begun at the suggestion of the Russian Geographical Society, were continued by the student Sergievsky, who made a magnetic survey at 155 points in the region of Belgorod and Nepkhaevo, where an anomaly was likewise established. In view of the great scientific interest of the Belgorod–Nepkhaevo anomaly, the Russian Geographical Society, on the proposal of E. E. Leist and M. M. Pomortsev, created a permanent Commission for the study of terrestrial magnetism, and in 1893 the student Rodde was entrusted with carrying out further study of the anomaly in the region of Kursk Province, and Rodde succeeded in making a survey at 133 localities. However, this investigation did not appear in print.

At the same time, among the members of the magnetic commission the idea arose of inviting, for work in Kursk Province, the Director of the Paris Magnetic Observatory, Moureaux, who agreed to take part in the investigations of the Russian scientists on condition that a permanent magnetic station be established in Kursk for observing variations of terrestrial magnetism. In 1896, with the assistance of the Kursk Provincial Zemstvo Board

a magnetic pavilion was set up for variational instruments, and P. G. Popov took charge of the pavilion. During the short time of Moureaux’s stay in Kursk Province, he made 149 series of observations at 102 stations; however, his work was not conducted systematically, so that it did not prove possible to compile maps from his observations. Moureaux’s investigations revealed that in the village of Kochetovka the anomaly was even more significant than at Nepkhaevo and Belgorod, so that the question naturally arose of the need to study the whole of Kursk Province from the magnetic point of view.

This task was undertaken by E. E. Leist, who, using the classical methods of investigation (inclinator, magnetic theodolite), investigated Kursk Province over the course of 22 years, determining at 4500 points the declination \(D\), inclination \(I\), and horizontal component \(H\). The extensive numerical material, comprising the values \(D, I, H\), as well as maps, made it possible to characterize fully the magnetic anomaly in Kursk Province, both from the scientific and the scientific-practical sides. In a very interesting report, read in the spring of 1918 at the Physical Colloquium of the Scientific Institute, Leist gave a general characterization of the anomaly, without providing tables or coordinates of the places where the anomaly was observed. It followed from the report that the Kursk magnetic anomaly divides quite clearly into two regions: the northern one, passing through Dmitrovsky Uyezd of Oryol Province and further through Fatezhsky, Kursky, Shchigrovsky, and Timsky Uyezds of Kursk Province, and extending into the region of Voronezh Province. According to Leist’s work, the direction of the anomaly is from northwest to southeast, and the width of the anomalous belt with maximum deviations of the elements from the norm should be about 2–3 versts.

To the south of the first belt, a second belt extends through Oboyansky, Belgorodsky, Korochansky, and Novooskolsky Uyezds, including Nepkhaevo, Belgorod, and Kochetovka. The general direction and width of the southern belt of anomalies are the same as those of the northern one. The space between the belts is also anomalous, but the anomaly here is weaker.

The places with the greatest anomaly were noted by Leist in the northern belt of the anomaly. In the conclusion to his report, Leist offered some considerations on the possible causes of the anomaly and on the depth of occurrence of the magnetiferous layer. With respect to the cause of the anomaly, Leist expressed himself quite definitely in favor of the presence of iron, considering other causes too inconstant and too small to produce an anomaly like the one observed. In the manuscript reproducing the report and transmitted for publication in the proceedings of the Physical Institute to P. P. Lazarev, Leist writes directly: “Taking into account that

deposits in Kiruna¹) are no more than 10 kilometers in length, while in the Kursk gubernia both ridges are 500 kilometers long and the maximum is \(Z = 14{,}782\) gauss; i.e., greater than in Kiruna. It must be assumed that the Kursk deposits are incomparably richer in iron ores with a high percentage of iron than the Lapland ones.”

Leist determined the depth of the magnetic rocks according to rules established chiefly by Swedish mining engineers, on the assumption that the magnetic anomaly is caused only by a point pole containing all the magnetism of a given sign. Using this rough representation, Leist finds the depth of occurrence to be about 300 meters.

The printing of Leist’s report, submitted to the editorial office of the Archive of the Physical Sciences in the summer of 1918, was delayed; Leist went to Germany and died there in mid-summer. In the autumn it turned out that it was impossible to obtain the map and numerical material with the coordinates of the points needed for printing, since, according to rumors, he had supposedly remained in Germany, and therefore printing had to be postponed. At the same time it became known that Leist and Stein had published in Germany, in German, a brochure intended to acquaint the general public with the practical significance of the Kursk anomaly, the brochure directly pointing to iron as the cause of the anomaly.

In view of the importance of the question and the impossibility of obtaining Leist’s authentic documents determining the position of the points at which the anomaly had been observed, in the autumn of 1918 People’s Commissar L. B. Krasin approached P. P. Lazarev with a proposal to create a commission to work out this question. At the suggestion of L. B. Krasin, Lazarev convened a meeting composed of Lazarev, Arkhangelsky, Prilezhaev, and Bastamov, which noted first of all the enormous importance of studying the anomaly and the desirability of carrying out work that would restore Leist’s data, and indicated that it was possible that the investigations would not lead to practical results, since the cause of the anomaly might not be iron. After P. P. Lazarev’s report to the Academy of Sciences on the state of the work on studying the anomaly in Kursk gubernia, the Academy attached the Commission to the Moscow Branch of the Permanent Commission for the Study of the Natural Productive Forces of Russia under the Academy of Sciences; after funds had been allocated by the Extraordinary Commission for Supplying the Army, organizational work was begun under Lazarev’s direction.

In view of the impossibility, within a short time, of obtaining the necessary number of observations by classical point methods, and in view of the impossibility of obtaining a large number of instruments of this kind, the commission

¹ In Lapland.

of specialists—magnetologists, physicists, and hydrographers—which met in Petrograd on March 6, 1919, decided, at the suggestion of Academician A. N. Krylov, to use for the investigation of the anomaly the de Colong deflector method, employed in our fleet in the study of a ship’s magnetic anomaly. The Commission unanimously agreed with Krylov’s opinion, entrusting the head of the magnetic section of the fleet, V. Ya. Pavlinov, with adapting the instrument for work in Kursk Province. Thanks to the kindness of the Head of the Chief Hydrographic Administration, E. L. Byalokoz, the Commission succeeded in obtaining 10 de Colong instruments; moreover, experienced hydrographer-magnetologists attached to the Chief Hydrographic Administration were assigned to work with them, and these formed the detachment for the investigation of the Kursk Magnetic Anomaly, under the command of K. S. Yurzhevich, with A. D. Zaborovsky in charge of the magnetic section.

After the report by P. P. Lazarev, the Moscow Commission of specialist magnetologists joined in the opinion of the Petrograd meeting and resolved to adopt the de Colong instrument and method, bearing in mind that, given the great depth of occurrence of the magnet-bearing layers, the greatest possible accuracy is necessary in the magnetic data that determine the coordinates of the magnet-bearing layer. The de Colong instrument gives an accuracy of about one quarter of a percent and, although this accuracy is less than that of the methods of classical magnetometry used by Leyst, it is nevertheless sufficient for obtaining the data needed for practical and scientific purposes. In addition, it had already been decided in advance that in places with the greatest anomaly a survey should be carried out by the classical method, using a Lamont magnetometer and an inclinometer. The methods of Thalen and Tiberg and their modifications, ordinarily used in searches for iron, were rejected from the very beginning, since with these methods an error in determining the force is possible reaching 10% and even more; this accuracy is sufficient in determining shallow deposits (about 10–25 sazhen) and is entirely unsuitable for determining a magnet-bearing layer lying at a depth of 100–200 sazhen, as may be the case in the Kursk anomaly. With such an opinion agree the statements of so authoritative a scholar as E. Naumann, who was director of the topographic-geological survey of Japan and studied the famous Japanese anomaly in the Fossa magna region. Here is what Naumann writes on this matter1: “the method proposed by Thalen for the search for iron ores seems to me too theoretical and based on insignificant factual data; moreover, his methods of measur—

visions are not sufficiently accurate. In any case, the manifestation of the magnetic forces of ore deposits cannot be interpreted without precise knowledge of the distribution of magnetism in the given locality. The magnetic investigation of a deposit must go hand in hand with a detailed magnetic survey, or even follow such a survey. Smock1 reports in detail on the use of instruments which for more than a hundred years have been employed to search for deposits of magnetic iron ore in New Jersey. Of particular interest to us is Smock’s assertion that large and well-known iron mines often show little magnetic attraction, and that from the magnitude of the deflection of the magnetic needle, or from the magnitude of the force, no definite conclusion can be drawn as to the existence of deposits or their size. Thus the question remains open whether it is possible to go so far as to determine precisely the location and magnitude of deposits from exact measurements and calculations.

The doubts expressed by Naumann are especially applicable to deep-lying deposits of magnetic minerals; and in this respect the Kursk magnetic anomaly, as caused by centers of magnetism that may lie deep, must require precise methods of investigation, and among them, after the classical method, which requires an enormous amount of time, first place is occupied by the method of de Colong.

The methods of the usual rough determination of deposits, employed by geologists for iron deposits, prove inconvenient for Kursk Province in yet another respect. In the combined Tiberg–Thalen instrument, or in Tiberg’s inclinometer, the normal magnetism is compensated by the action of a weight, the magnitude of which is selected, in a neighboring place to the anomaly, in a normal region of the earth’s magnetism, so that under the action of the normal field the instrument’s needle is horizontal. In this case, when a local anomaly exists, an inclination of the needle is obtained, and from its magnitude one can easily judge the field of the anomaly. In any case, when using the Tiberg–Thalen instrument it is necessary to know the magnitude of the normal field at the point of observation from observations in the neighborhood. In view of the fact that the region of the Kursk anomaly is very extensive, and that it is impossible to find normal places adjacent to anomalous places, compensation of the magnetic force by a weight, or determination of the normal field by experiment, may produce enormous errors, and the separation of the anomaly field can be carried out only by an accurate determination of the magnitude of the resultant field and by extracting from it, by computation, the field of the anomaly.

In his report “On the Kursk Magnetic Anomaly” (1918), Leist writes: “In the region of the greatest geomagnetic anomaly in the world, it is hardly possible to find a place with normal magnetic elements,

to compare with them other places where the normal quantities are explicitly expressed. Although between the two magnetic ridges there is a broad strip, in places up to 60 kilometers wide, it lies within the field of strong and extensive magnetic masses acting from both sides. Maps of isogons, isoclines, and isodynams show that even in this comparatively calm belt of normal equilibrium of magnetic forces there is nowhere—at least not to the degree required for establishing normal magnetic conditions in order to base upon them the degree of abnormality. Likewise, observations made at some distance from the anomalous region cannot serve this purpose, since it is not known how far the anomaly itself and its influence extend.”

Finally, the last reason for choosing the de Kolong deflector method was the circumstance that the methods of Tieberg and Thalen could not provide, as is easy to show by calculation, details of isolines at small distances from the vertical lying over the cause of the anomaly, owing to the low accuracy of the methods and the great depth of the magnet-bearing strata occurring in Kursk Province.

It is quite clear from similarity that if, at a depth of occurrence of 10 sazhens, we can make observations with Tieberg’s and Thalen’s instrument every 10 sazhens, then at a depth of 300 sazhens, if the magnet-bearing layer remains similar to the former one, the same observations must be made every 300 sazhens.

The Commission attached to the Mining Council agreed with the choice of the method of work of the Academic Commission; at its meeting of June 15, 1920, it adopted the following resolutions.

“At the meeting it was established that the instruments used by the Academic Commission give more accurate results than the commonly applied methods for investigating iron-ore deposits and are not inferior in speed of determination. The difference between the results of the investigation by the Commission attached to the Academy of Sciences and ordinary magnetic-geological measurements consists only in the greater accuracy of the results of the Commission attached to the Academy.” (Resolution of P. P. Lazarev.) “Continuing the work on the investigation of the Kursk magnetic anomaly now being conducted by the Academy of Sciences, investigations of the points with the greatest magnetic anomalies should be carried out with more accurate instruments.” (Resolution of A. D. Arkhangelsky.) Against these resolutions, especially in favor of the methods of Tieberg and Thalen, engineer Kiselnikov, Professor Klyuchansky, and docent Ortenberg spoke; they proposed resolutions that were rejected by the meeting.

An analogous resolution was also adopted at a meeting of the N. T. O. V. S. Kh. N. after Ortenberg’s report.

Finally, after Ortenberg’s report at the 1st Congress of the Russian Association of Physicists, the section of cosmic physics unanimously opposed

Ortenberg adopted the following resolution: “Considering the method described by Ortenberg for determining the depth of magnetic layers to be based on a number of misunderstandings, and the Swedish-type instruments to be insufficiently accurate, the cosmic-physics section of the 1st congress of the Russian Association of Physicists considers its application in the region of the Kursk magnetic anomalies impossible, and considers it necessary to continue the investigation of the Kursk Magnetic Anomalies by the deflector method, with subsequent study of the places of anomaly maxima by the classical methods of the Lamont instrument and the inclinometer, and with study of the variations of the geomagnetic elements with height.”

§ 2.

Since the application of de-Colong’s deflector to geomagnetic measurements was made for the first time, we consider it useful to give a general characterization of this method, which is important for magnetic surveying.

The de-Colong method makes it possible to determine the horizontal and vertical components \(H\) and \(Z\) with an accuracy of up to a quarter of a percent. From this it is easy to find the total magnitude of the force \(F\) \((F=\sqrt{H^{2}+Z^{2}})\) and the inclination \(I\), i.e., the angle between the plane of the horizon and the axis of a magnetic needle suspended at its center of gravity, \(\operatorname{tg} I=\frac{Z}{H}\). In addition, the method makes it easy to find, from the simplest astronomical observations (from the sun, using tables), the position of the local meridian and consequently to determine the angle between the axis of the magnetic needle and the plane of the meridian \(D\), called the declination.

The method of determining \(H\) and \(Z\) is clear from the following schematic description.

Let us have a magnet \(M\) rotating about the vertical axis \(S\) (Fig. 1), connected with a light movable circular disk (card), having divisions around its circumference and marks for north, south, east, and west \((N, S, O\ \text{and}\ W)\).

Fig. 1.

The bobbin also bears degree divisions.

Let the disk connected with the magnet $NS$ be set in the plane of the magnetic force; opposite the mark $S$ of the disk an index $P$ is brought up, connected with a divided circle fixed on the glass cover of the vessel (boiler) containing the column $K$ and the rotating disk with the needle $NS$. The index $P$ is so arranged that it permits an accurate optical reading of the position of the disk. With the divided rotating circle located on the cover of the instrument there is rigidly connected a support, allowing a copper column with the magnet $N_1S_1$ to be placed on the continuation of the axis of rotation $MR$, always arranged so that the plane of the axis of the magnet passes through the axis of rotation $MR$ and $P$, and the south pole $S_1$ of the magnet is always turned toward $P$; perpendicular to this first magnet, which can be moved up and down, there is placed a second and weak magnet $N_2S_2$. Under these conditions the magnet $N_1S_1$ gives an additional field, shown in Fig. 1 by a dotted line and directed horizontally, opposite to the terrestrial field being investigated.

By moving the magnet $N_1S_1$ downward, without changing its direction, we increase the magnitude of the additional field; by moving it upward, we decrease it. In this way it is possible to achieve that the horizontal component $H$ of the field under investigation is compensated by the field of the magnet $N_1S_1$. In this case, if the movable magnet $NS$ is sufficiently small in its dimensions and the magnet $N_2S_2$ is remote, then no forces will act on $NS$ in the horizontal plane, and it can be set in any position with respect to the plane of the force under investigation.

In order to know whether this moment has been reached, in the plane perpendicular to the axis of the magnet $N_1S_1$ and passing through the axis of rotation $MR$, a second weak magnet $N_2S_2$ is installed, the so-called perpendicular magnet. After compensation of the investigated field by the field of the magnet $N_1S_1$, the only acting field will be the field of the magnet $N_2S_2$, as a result of which the bobbin with the magnet $NS$ will turn with its point $S$ toward the pole $N_2$ of the magnet $N_2S_2$, and the point $O$, 90° distant from $S$, will come up to the index $P$. It is clear that, if the magnet $N_2S_2$ is turned and the pole $S_2$ of the magnet is directed to the west, then the pole $N$ of the movable magnet will approach it, and opposite the index $P$ will stand the mark $W$.

Knowing to what horizontal fields a given position of the magnet $N_1S_1$ corresponds—which is achieved by a preliminary, accurately performed calibration—one can determine, in relative or absolute units, the magnitude of the component of the field $H$.

If we call the magnitude of the horizontal component of the terrestrial field $H$, the magnitude of the field of the magnet $N_1S_1$ at the point $M$—$H_1$, and the field of the magnet $N_2S_2$—$H_2$, then, denoting the angle between the magnetic meridian and the axis of the needle $NS$ by $a$, we have

$$ \operatorname{tg} a = \frac{H_2}{H - H_1}. $$

If $H - H_1 = 0$, that is

the terrestrial field is compensated by the field \(N_1S_1\), then \(tgd=\infty\) and \(\alpha=90^\circ\), i.e., the magnet \(NS\) becomes perpendicular to the meridian.

To obtain the vertical component of the field under study, \(Z\), a magnetic needle \(NS\) is used, rotating about a vertical axis (Fig. 2) together with a graduated circle and at the same time rotating about a horizontal axis \(AB\). A thin and small magnet \(NS\) is fastened on a horizontal axis so that, in the demagnetized state, its axis would lie horizontally. In a field in which there is a vertical component \(Z\), directed downward, the northern end of the magnet \(NS\), rotating about the axis \(AB\), will sink downward so that the resultant of all the forces coincides with the axis of the magnet \(N_1S_1\). To compensate the vertical field, an additional magnet \(N_1S_1\) is placed vertically so that its axis coincides with the intersection of the axis of rotation \(MK\), vertical, and \(AB\), horizontal, and so that the same pole is turned downward as the pole of the needle \(NS\) that has risen upward. Then, if the magnet \(NS\) is sufficiently small, the field around the magnet \(NS\) from the additional magnet \(N_1S_1\) is uniform and, by moving it downward or upward, one can diminish the upward force \(Z\) acting on \(N\), and bring it to the point where it cancels the force \(Z\). Then the needle \(NS\) will take a horizontal position, which is extremely easily determined with great accuracy by eye. In addition to determining \(I\) from the ratio \(\dfrac{Z}{H}\), in some cases this quantity was found directly with an inclinometer.

Fig. 2.

The magnets of the instrument of de-Colong, bearing the name of the de-Colong deflector, were checked from time to time at a special station located in Ovsyannikov’s estate. Recently, a member of the Magnetic Commission, V. Ya. Pavlinov, made important improvements to the de-Colong deflector, allowing it to be used for very large values of \(H\) and \(Z\) in the region of an anomaly.

The entire apparatus is enclosed in a copper vessel (boiler) secured in a copper Cardan suspension on a tripod. The apparatus, as is understandable, contains no iron parts. The size and weight of the apparatus are such that it can conveniently be moved and carried by one person, and in this respect it is an indispensable instrument for field geomagnetic work in anomalous regions.

§ 3.

The work in 1919 began, owing to delays in assigning the hydrographers, only in June; on June 17 the detachment arrived in the village of Belyi Kolodez, whence, on the instructions of the Chairman of the Commission, P. P. Lazarev, the work was to begin. Initially a general orientation survey was carried out, an astronomical point was determined, and systematic observations were begun in the region of the discovered anomaly, in rows at definite intervals. It must be noted here that the working conditions were (during the summer) extremely unfavorable: in July there were only 11 working days in all; the rest of the time, because of rain and bad roads, it was impossible to work. The general situation also did not favor the work. At the very beginning, rumors spread in the nearest village that a detachment had arrived in Ovsyannikovo to restore the power of the landlords, and only by the skillful and energetic measures of the head of the detachment, K. S. Yurzhevich, was it possible to secure a conscious and reasonable attitude toward the expedition on the part of the citizens. In addition to all that has been listed, the proximity of the front greatly interfered with calm work. At the very beginning of the expedition the detachment was delayed at Orel station, since even military trains were not being admitted to Kursk. Later, during the work, it was repeatedly necessary to think about evacuation, until finally on August 16 the head of the detachment had to issue an order for evacuation. In Yurzhevich’s journal it is noted: “On August 16 the whole locality was without authority; all institutions of Tim were evacuated to Karandakovo, Beloe, and Marmyzhi.”

Further, during July, one of the responsible workers of the expedition fell ill with typhus, and this disrupted the proper regular work. Despite the exceedingly unfavorable circumstances that had arisen, the expedition succeeded not only in carrying out a general qualitative survey, but also in surveying an area of 260 square versts, making quantitative observations over this space at 443 points. In this process, in the vicinity of the village of Lozovka, it was possible to observe a point with the maximum value \(Z=15.77\) gauss (for Leist the maximum \(Z\), according to some data, was 14.78, and according to others 18.36).

The summer field work of 1920 began in April and already by

by June 1 gave almost twice as much material as compared with the summer campaign of 1919. In all, by August 1 more than 1600 points had been measured.

§ 4.

The general regularities in the region of the anomaly may be characterized as follows. Lines with equal inclination \(D\), the isogons, in the region of Kursk guberniya, in the absence of an anomaly, should be lines running from south to north and spaced at approximately equal distances. The anomaly, first, brings the isogons closer together and, second, causes them to bend so that in the region of the anomaly the isogons extend from northwest to southeast. The anomalous belt passes west of Tim, taking in the region of Lozovka (southwest of Shchigry). In a number of places the isogons form closed lines, enclosing regions with maximum eastern or western inclination. Lines of equal inclination \(I\) (isoclines) are on the earth lines extending from east to west and, if the magnetism of the earth were produced by an infinitely small magnet placed at the center of the earth, then the isoclines, being magnetic parallels, would also have to be lines of equal potential. In the studied region of the Kursk anomaly the isoclines are curved relative to their normal course, in places strongly brought together; in general they take a course from northwest to southeast and in places form closed lines, enclosing points with maximum (or minimum) inclination. The lines of equal vertical \(Z\) and horizontal \(H\) field intensity have the same anomalous character. These lines, in the case of an infinitely small magnet, coinciding with equipotential lines on the earth’s surface, are sharply curved and brought together in the region of the anomaly, in places enclosing areas with closed isodynams of the horizontal and vertical components. We give in Figs. 3, 4, 5, and 6 maps of isoanomals (lines with equal values of the elements of the anomalous field), calculated from the survey data of 1919, as well as maps of the 1920 survey (up to June 1) (Figs. 7, 8, 9) and the anomalous field computed from them (Figs. 10, 11, 12).

For the computations of the anomalous field, let us imagine that we have resolved the full magnitude of the magnetic force \(F\), including the normal and anomalous components, along three coordinate axes. One of the axes \(Z\) goes vertically downward, another \(X\) in the horizontal plane toward the north, and the third \(Y\) in the horizontal plane toward the east. Then the components of the force \(X, Y, Z\) are obtained by projecting the force onto the coordinate axes.

The forces \(X, Y, Z\) are obtained from the components along the same axes of the normal field \(X_n, Y_n, Z_n\) and from the components of the anomalous field \(X_a, Y_a, Z_a\).

Thus:

Fig. 3.

\[ X = X_h + X_a \]

\[ Y = Y_h + Y_a \]

\[ Z = Z_h + Z_a \]

Fig. 4.

Since \(X_n, Y_n, Z_n\) can be determined by the Petersen–Neumayer formulas for every point of the terrestrial globe, while \(X, Y, Z\) are found from

Fig. 5.

of direct determinations, then from this \(X_a, Y_a, Z_a\) are easily obtained, which fully characterize the anomalous field and make it possible to determine, in addition to the magnitude of the vertical anomalous component \(Z_a\),

Fig. 6.

also the horizontal anomalous component \(H_a\), the anomalous inclination \(I_a\)

Fig. 7.

D (1920)
1 km

\[ H_a=\sqrt{X_a^2+Y_a^2} \]

\[ \operatorname{tg} I_a=\frac{Z_a}{\sqrt{X_a^2+Y_a^2}}. \]

finally, the anomalous declination \(D\) is determined as follows:

\[ \operatorname{tg} D_a=\frac{Y_a}{X_a}. \]

By this method, for all points of the survey of 1919 and 1920, A. I. Zaborovsky

Fig. 8.

calculations of the anomalous field were carried out, and the corresponding anomalous isolines are shown on the maps given below. In doing so, no correction was made for the diurnal variations of the normal field, since the diurnal variations amount to approximately 0.15% of the normal magnitude of the field, while the accuracy of the method is 0.25%.

In the precise determination of the constants of geomagnetism in places with

Fig. 9.

the maximum anomaly, in making an accurate survey, one should introduce a correction for the diurnal variation of the earth’s field by setting up a magnetic station in Kursk province. It should be noted here that in anomalous places, as is easy to prove, the variations of the elements may increase or decrease as compared with normal places.

Indeed, let us have a force \(H\), composed of the force of the earth’s field and the field of the anomaly; let a horizontal

Fig. 10.

the horizontal component of the variation \(H_v\), and let the variation make an angle \(D\) with the direction \(\Pi\); then, if the \(X\)-axis is directed in the plane of the magnetic meridian toward the north and the \(Y\)-axis toward the east, then

Fig. 11.

\[ X = H_i + H_v \cos D_1 \]

\[ Y = H_v \sin D_1 . \]

Hence we have that the tangent of the angle of deflection of the magnetic needle from its position in the meridian is

Fig. 12.

\[ \operatorname{tg} D=\frac{Y}{X}=\frac{H_i \operatorname{Sin} D_1}{H+H_i \operatorname{Cos} D_1} \]

\(D\) is the change in declination; all other conditions being equal, \(D\) will increase as \(H\) decreases, if \(H\) has the appropriate sign; the same, of course, also applies to the other elements of magnetism.

All these data can conveniently be verified experimentally, and this

the verification was made by V. I. Prishletsov1, who created an anomalous field in a certain region with the aid of artificial magnets and showed the corresponding change in the variation of the elements. For corrections in exact investigations it has been proposed to study the variations at the maximum and minimum of the anomaly in the region of the Kursk anomaly.

As is easy to see from the isolines of anomalous force, we are dealing with a definite direction of the anomaly, from southwest to northeast, and there are extensive regions with closed isoanomalies.

In conclusion it is interesting to note that the lines of maximum values of \(I_a\), \(Z_a\), and \(F_a\), and of the minimum value of \(H_a\), in the Kursk anomaly almost coincide. (See Fig. 21).

Through this same region also passes the line \(PP\), toward which all the vectors \(H_a\) are directed. These data are taken from the processing of the results of the 1919 expedition.

In the maps presented, the anomaly-field map of 1919 and the anomaly maps of 1920, the determination of the geographical coordinates (latitudes of localities), which in the 1919 report contained errors owing to an erroneous division of the planchettes, has been corrected. This applies especially to the western part, where the error proved to be greatest.

§ 5.

As regards the cause of the anomaly, Leist, rejecting earth currents and magnetized meteors, as well as displacements of rock strata, as the cause of the anomaly, dwells in detail upon iron, which in other places on the earth causes anomalies. Leist especially emphasizes the analogy between the distribution of magnetism in the Swedish iron deposits at Kiruna and in Kursk Province. However, in view of geological considerations (the opinion of A. D. Arkhangelsky, Ya. V. Samoilov, and A. E. Fersman), it scarcely seems possible to transfer the conclusions drawn for the Swedish deposits to Kursk Province, all the more so since one and the same pattern of the distribution of magnetism on the earth may be produced by the most diverse causes. The famous Japanese anomaly, studied by Naumann, shows a very interesting connection with the geological structure of the anomaly region. Here is what Naumann writes on this subject2: “The isogone corresponding to \(5^\circ W\) coincides in general with the tectonic line3. This is a very important result. We may say that the entire mountain chain in the region of the Fossa magna has a bend. The isogones give a similar bend in this region. Up to now, of such a

one could not have thought of so close a coincidence of magnetic and tectonic phenomena, and it is difficult to imagine a better example of this than what occurs in Japan. Many mountain ranges, intersected by magnetic lines, cause a deflection of these lines, and in reality the influence of mountains on magnetic lines is, as a rule, considerable; but where the lines intersect, the influence is not so clearly manifested, and in such cases it appears difficult to establish a connection with geological processes. Japan has the great advantage that the isogons show a fairly close parallelism with the general direction of the mountain chain.”

Here it is curious to note that earthquakes can produce, far beyond the limits of the center of shock, magnetic phenomena whose causes apparently must be sought in displacements of magnetized rocks. At the moment when magnetized masses are displaced, we have a disturbance which propagates in the form of a wave and makes itself felt at a considerable distance. That the movements of magnetographs in this case do not depend on the shock produced by the earthquake is proved by the experiments of Moureaux¹), who showed that while during earthquakes an ordinary bifilar magnetometer shows oscillations, a copper rod suspended bifilarly, in exactly the same way as the magnet, shows no motion whatever.

As Arrhenius points out, the bifilar magnetometer at Parc St. Maur recorded the earthquake in Calcutta on June 12, 1897; the magnetometer in Potsdam recorded the great Japanese earthquake of March 22, 1894. After displacement, evidently the magnetism of rocks partly disappears²). The anomaly in Japan is small, but it is possible to imagine large magnetic phenomena as well; moreover, it should not be overlooked that the iron-ore deposits known up to now also do not show the enormous anomalies that exist in Kursk province, and this circumstance may also speak against iron as the cause of the anomaly.

Thus the question of the cause of the Kursk anomaly cannot be resolved by analogy, and geological investigations are necessary, which will make it possible to resolve this important question.

The question of the depth at which the magnetic layers lie is also uncertain. Leyst, in his article and in his report at the Scientific Institute, gives practical rules for determining the depth of occurrence, and these rules are as follows (see Fig. 13):

1) The depth of occurrence of the magnetic masses is equal to the distance on the earth’s surface between the points $H = O$ and $H = Z$.

2) The depth of occurrence of the magnetic masses is equal to the distance on the earth’s surface between the points where $I = 45^\circ$ and $I = 90$.

¹) Cf. S. Arrhenius. Lehrbuch der Kosmischen Physik, p. 990. Leipzig, 1903.

²) Arrhenius, loc. cit., p. 990.

3) The depth of occurrence of the magnetic masses is equal to the distance of the points on the earth’s surface where \(H=Z\) and \(Z\) is equal to its maximum.

4) The depth of occurrence is equal to one half the distance of the pair of points for which \(H=Z\) (or for which \(I=45^\circ\)).

Fig. 13.

As is easy to understand, these rules, as Leyst also notes, apply to a unit pole.

The same rules also apply to an entire series of poles of equal strength, arranged on one straight line parallel to the surface of the earth. However, such arrangements are hardly realized in nature. It is possible to analyze theoretically certain cases that may be of significance for those arrangements which produce a magnetic anomaly.

The cases of two poles were examined by magnetologist geologists for the purposes of ore prospecting for iron, but these cases cannot apply to the Kursk anomaly, where we are dealing with an entire magnetized ridge, which at times should give the picture of the arrangement of a continuous series of magnets with the north pole below and the south pole above. If one imagines magnetized plates in the earth—magnetic sheets—magnetized in a plane, then with respect to magnetic sheets with uniform magnetization one can derive rules for determining the depth of occurrence\(^1\) from the following considerations:

Let us have a magnetic sheet in the form of a half-plane, whose rectilinear edge lies parallel to the plane of the earth’s horizon. In such a sheet one surface is covered uniformly with northern magnetism, the other with southern. Let the section of this half-plane by a plane perpendicular to the plane of the drawing (Fig. 14) be \(MN\), and in the direction of \(N\) the half-plane extends to an infinite distance. Let \(SS\) be the surface of the earth, and let \(MN\) intersect the surface of the earth at the point \(K\) at an angle \(\theta\). Through the point \(M\) draw a plane passing through the bounding straight line. This plane gives the trace \(MT\). Let in this plane there be a point \(A\), about which we describe a sphere of unit radius. Then the potential given by the magnetized half-plane at the point \(A\) is equal to the magnetic strength of the sheet \(\Phi\) multiplied by the solid angle \(\omega\) under which the positive side of the sheet \(MN\) is visible from the point \(A\). It is easy to understand that this angle is obtained as a part of the surface of a sphere of unit radius, bounded by two planes passing perpendicular to the po-

\(^1\) P. Lazarev, Izv. Phys. Inst. M. N. I., vol. I, issue 4, p. 147, 1920.

surface of the drawing through \(A\), with one plane giving the trace \(MT\), and the other, parallel to the magnetized half-plane, giving the trace \(UW\). For all points of the plane perpendicular to the plane of the drawing and passing through \(MT\), the angle \(\omega\) is the same, and consequently the plane whose trace is \(MT\) is an equipotential surface. Calling the angle \(MAW\) between \(MT\) and \(UW\) \(\alpha\), we find \(\omega = 2\alpha\). Thus the potential \(V\) of the sheet at the point \(A\) is

\[ V=\Phi\omega=2\Phi\alpha. \]

Hence the force normal to \(MT\) is

\[ F=\frac{dV}{d\alpha}\,\frac{1}{r}=\frac{2\Phi}{r}, \]

where \(r\) is the distance \(MA\).

Fig. 14.

The lines of force in the drawing form circles whose centers lie at \(M\), and the systems of isodynams lie on circular cylinders with center at \(M\). The force at the point \(C\), lying on the perpendicular to \(SS\), is

\[ H=F=\frac{2\Phi}{R} \]

\((1)(R=MC)\); the vertical component \(Z=0\); on both sides of this point the total force decreases, since the distance \(R_1\) increases according to the law

\[ R_1=\frac{R}{\operatorname{Cos}\varphi}, \]

where \(\varphi\) is the angle between the line \(MD\), going from \(M\) to the point of observation \(D\), and the vertical \(MC\), and consequently

\[ F=\frac{2\Phi\cdot \operatorname{Cos}\varphi}{R}; \]

the horizontal component at this point is found by multiplying \(F\) by \(\operatorname{Cos}\varphi\), so that

\[ H=\frac{2\Phi\operatorname{Cos}^2\varphi}{R}, \]

and this quantity is the same on both sides of \(MC\) at an equal distance from \(C\).

The vertical component \(Z\) is in this case equal to the full magnitude of the force

\[ \frac{2\Phi}{R}\operatorname{Cos}\varphi, \]

multiplied by \(\operatorname{Sin}\varphi\), so that

\[ Z=\frac{2\Phi\operatorname{Cos}\varphi\cdot \operatorname{Sin}\varphi}{R} =\frac{\Phi}{R}\operatorname{Sin}2\varphi \]

The inclination \(I\) is determined from the relation

\[ \operatorname{tg} I=\frac{Z}{H}=\operatorname{tg}\varphi \]

and consequently at the point where \(\varphi = 45^\circ\), and where consequently \(I = 45^\circ\), \(H = Z\); since, moreover, above the point \(M\) (at \(C\)) \(H\) has its maximum value and \(Z = O\), we thus obtain, for this second case, data determining the depth of the layer that are entirely different from the data of Leyst’s determination.

The crest of the ridge lies at the point whose depth beneath the earth is equal to the distance between the points at which \(I = 0^\circ\) and \(I = 45^\circ\). It is very important here to note that the infinite ridge \(MN\) may extend at any angle \(\theta\) to the surface of the earth \(SS\); the distribution of the forces remains the same, although in one part (to the right of \(C\)) enormous magnetic masses will lie beneath the earth, while in the other (to the left of \(C\)) there will be none. Boreholes made from \(C\) in the direction toward \(K\) will give no results, and therefore one borehole in this case should certainly not lead to any definite conclusions.

Finally, it is possible to solve the question concerning a sheet of finite width. The field of such a sheet can be obtained if one considers the field of an infinite sheet representing the half-plane \(A\), and at a distance \(d\) from the boundary line places closely against it an infinitely thin sheet \(B\), likewise representing a half-plane, with equal magnetic intensity \(\Phi\), the direction of which is opposite to the direction of the intensity of sheet \(A\).

If the section of such a sheet by a plane perpendicular to it and to its parallel edges is \(MN\) (Fig. 16), then at the point \(A\) the potential will be equal, as is clear from the preceding, to \(V_1 = 2\Phi\alpha\), and the equipotential surface will be represented in section by a circle subtending the angle \(\alpha\).

Fig. 15.        Fig. 16.

For the point \(B\), lying outside the circle \(MAN\), there is another circle with its center lying on the line passing through \(O\) perpendicular to \(MN\), which represents the section of the equipotential surface by the plane of the drawing.

Thus, in the present case the equipotential surfaces are parts of the surfaces of circular cylinders.

For practice, the case may be of interest when an infinite sheet of limited width lies parallel to the horizontal surface of the earth. In this case one of the equipotential lines will intersect the surface of the earth in such a way that the total force perpendicular to the equipotential line will make an angle \(B = 45^\circ\) with the surface of the earth (Fig. 15). If in this case the last procedure of Leist is applied, then it is clear that we shall find the center of the equipotential surface \(O\), which may lie at any distance from the ridge \(MN\), and since, moreover, the forces issuing from \(MN\), on the line \(DK\), perpendicular to \(MK\) and passing through \(O\), are perpendicular to the surface of the earth at the point \(D\) and have no horizontal component at this point, it is clear that Leist’s rules lead to erroneous conclusions.

A judgment about the depth of occurrence of magnetic masses from two observations may give results absolutely inconsistent with reality and lead to completely false and diminished conclusions about the depth of the magnetic layer.

Correct conclusions in this latter case can be obtained by constructing two equipotential surfaces from the observations of a pair of points where \(I = A\) and of another pair where \(I = B\); for one pair, (\(A\), for example), \(I\) may be equal to \(45^\circ\).

From Fig. 15 it is easy to see the mutual arrangement of the equipotential surfaces. Knowing the distances \(DB = e\) and \(DA = f\), one can compute the depths of occurrence of the centers of the equipotential surfaces, equal to \(DO = e \tg B\) and \(DO_1 = f \tg A\). The radii \(OB\) and \(O_1A\) of the two circles are respectively equal to \(R_1 = \dfrac{e}{\Cos B}\) and \(R_2 = \dfrac{f}{\Cos A}\); consequently, knowing \(DO\) and \(DO_1\) on the one hand, and \(R_1\) and \(R_2\) on the other, one can graphically find the points of intersection \(M\) and \(N\) of the two equipotential surfaces, and likewise graphically find the depth \(DK\).

It is very interesting to note that the sheet \(MN\) may also be non-flat; it is only necessary that the two straight lines bounding it, perpendicular at \(M\) and \(N\) to the plane of the drawing, be parallel to the surface of the earth. The sheet itself in section may represent any form, and \(K\) may descend by any amount below the line passing through \(M\) and \(N\).

If in this case drilling is carried out vertically at \(D\), and reaches the plane \(MN\), we shall not find any magnetic layer, since the magnetized layer lies deeper.

The relations may be still more complicated if the plane of the lines bounding the sheet lies obliquely to the surface of the earth and if,

the surface of the earth is tangent to the circle \(MDN\) at one of the points \(D\); then \(DO\) represents the vertical, and, determining the depth according to Leyst’s rules, we may drill to any desired distance from the surface and not find the stratum, as is readily seen from Fig. 17.

Fig. 17.

Thus, in the general case, although, as Mascart1 believes, “the residual anomalous field makes it possible to find the position and nature of the causes that produce this field,” this problem presents enormous difficulties.

If, for example, it is observed that the curves of equal value for the vertical component and for the inclination are symmetric with respect to a common straight line, one may conclude that the disturbing causes themselves are symmetric with respect to a vertical plane passing through this straight line. If the magnetic causes producing the effect are concentrated in a space considerably smaller than their distance from the points of observation, they may be likened to a small magnet. However, Mascart further remarks on p. 339 that “anomalies are rarely represented in such a simple form, and it would be erroneous (illusoire) to attempt to derive from them the distribution of the acting masses.” Finally, it must be remembered that to a given field there may correspond infinitely many different distributions of masses producing the same field. This, of course, also applies to the Kursk anomaly.

Under the direction of P. P. Lazarev, calculations are being carried out of the depths at which the magnetic stratum lies, under the assumption that the magnetized stratum is a magnetized elliptic cylinder, a parabolic cylinder, or else is magnetized along one of the axes of an ellipsoid. Cases of magnetization of cylinders and of an ellipsoid have been studied by investigators previously, and at present the results obtained have to be applied directly to particular concrete cases of the distribution of lines of force in the Kursk anomaly. Usually these results, too, can give only an order of magnitude; therefore it seems desirable to obtain at least an approximate idea of the character of the distribu-

division of the potential of the anomalous field. For this purpose it is proposed to study the variation of the field from airplanes, which will give the distribution of the force at different heights. Finally, an experimental study is needed of the model of the magnetized ridge, undertaken by the Academic Commission for the Study of the Kursk Anomaly at the Physical Institute of the Scientific Institute and at the Institute of Biological Physics of the N. K. Z.

Below we shall give, for the center of the circle outlined by the dotted line (Fig. 4), calculations of the depth of the layer made under the assumptions that there are two rows of poles, lying one above the other in the form of a ridge extending over a great distance (theoretically infinitely great).

From this assumption are derived the equations of the lines of force, which are represented graphically on paper (see Fig. 18). From a comparison of the distribution of the inclination on the earth’s surface at different points, with the data obtained graphically from the theoretical scheme, the depth of the summit of the ridge, its inclination to the horizon, and its thickness are found. In applying this method, A. I. Zaborovskii and V. V. Kollodakin obtained the following data for the occurrence of the magnetic layer for the point encircled by the dotted line.

Fig. 18.

Depth below the surface: 490 meters.
Width (distance between the northern and southern poles): about 600 meters.
Inclination of the bed to the horizon: 67°.

If the depth of the acting masses is determined from simpler assumptions—namely, by admitting that the dimensions of the magnet are large in comparison with its distance from the earth’s surface, and we may consider that the lines of force near the upper pole are straight—then, if \(x\) is the distance of the upper pole from the earth’s surface, \(d\) the distance between the points, \(I = 90^\circ\), and \(I = i\), we find:

\[ x = d \cdot \operatorname{tg} i = \frac{Z}{H} \]

In this way A. I. Zaborovskii obtained the following data for the depths of occurrence along the line \(\alpha\beta\), etc. (see Fig. 4).

The order of magnitude obtained is the same as with the first method of calculation, but the depths often turn out to be two or three times greater than by the first method. We shall, of course, not attach decisive importance to these calculations and present them in order to give an idea of the order of magnitude of the distances that may be expected to be found.

With regard to the possible arrangements of magnetic masses, the following rules have been established. Let a magnetic bed be formed underground by a continuous row of poles arranged along a straight line. Let the line of poles be projected onto the horizontal

Fig. 19.              Fig. 20.

surface of the earth in the form of the line \(AA\) (Fig. 19). Above this line the horizontal component of the anomaly is equal to zero; as for the vertical component, it is equal to a maximum. At two points lying symmetrically with respect to the ridge, the resultant of the anomaly is equal to \(R\) and is directed in exactly opposite directions; therefore, if the declination in the region of the anomaly is equal to zero and consequently \(H\), depending on the earth’s field, is directed along the geographic meridian, then to the north of the ridge at the point \(B_n\) we shall observe a western declination, and to the south an eastern one, as is clear from the figure, the isogons being parallel to the line \(AA\). The Kursk anomaly in a certain part po-

shows these relations approximately; in fact, in Figure 20 the bends lying close to one another are visible; the difference from the theoretical case consists in the fact that, with respect to the line with declination \(0^\circ\), the northern and southern bends are situated asymmetrically and, in the north, their density is greater than in the south. This circumstance may be explained by the fact that the ridge, representing the shape of a sheet of limited dimensions (or a system of two poles), is situated not parallel to the surface of the earth, but in such a way that its edge directed northward is closer to the surface of the earth than the one directed southward; and the surface covered by southern magnetism is turned toward the earth, being exposed to the lines of terrestrial force, which can approach the ridge approximately normally. At the same time, as is clear from Figs. 19 and 20, to the north and to the south of the ridge equal forces must lie at different distances. Finally, from the appended anomaly maps obtained in 1919 (Figs. 4, 5, 6), and also from the determination of the total magnitude of the anomalous field \(F_a\), it is evident (Fig. 21) that the maximum \(I_a, Z_a\) and \(F_a\), the minimum \(H_a\), and, finally, the line toward which the forces converge—the line \(PP\)—coincide with one another over a considerable part of their extent. If we had a sheet bounded by two straight lines, then the isodynamic lines of the horizontal component would have to be straight lines parallel to the ridge. This, however, is not observed, and it depends on the fact that the ridge now descends, now rises; and the only means of obtaining an idea of the disposition of the magnetized masses is experimental laboratory reproduction of the anomaly with all its peculiarities. In doing so, as is clear, one must assume either that the magnetization is produced by the earth’s field by induction, or that magnetic layers magnetized in deep strata of the earth’s crust, possessing the same degree of magnetization, have been pushed into more superficial layers, thereby giving rise to the phenomena of a local magnetic anomaly.

Fig. 21.

At the present time, a special Commission for deep drilling has been established under the Supreme Council of the National Economy. The task of the Commission consists in carrying out deep drilling in places selected for this purpose by the Commission. Whatever the results of the drilling may be, in any case this work should solve one of the most interesting problems of geomagnetism, providing certain important indications also for the theory of the phenomenon of an anomaly that represents the largest anomaly on the globe.

Moscow. Physical Institute
of the Moscow Scientific Institute and the Institute of Biologi-
cal Physics under the People’s Commissariat of Health.
September 1920.

1. E. Mascart. Traité de magnétisme terrestre, p. 337. Paris. 1901. ↩↩↩↩↩

2. E. Naumann, loc. cit., p. 19. ↩

3. Italics are Naumann’s. ↩