Search for the local centres of the Tunguska explosions

Planet. Space Sci., Vol. 46, No. 213, pp. 1.5-154, 1998 0 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0032-0633/98 $19.00+0.00

Pergamon

PII: SOO32-0633(97)0013~0

Search for the local centres of the Tunguska explosions V. D. Goldine”

Tomsk State University, Lenin str., 36, NII PMM, Tomsk 634010, Russia Received 2 August 1996; revised 23 June 1997; accepted 30 June 1997

area of destruction. In this system of coordinates the mountain Farrington has the coordinates x = 42.8 km, y = 23.6 km, and Fast’s critical point is at x = 39.2 km, y = 20.7 km. Let us suppose that at point A, with coordinates (xA, yA), the falling tree has the azimuth CI.,+. (the angle between the Ox axis and the direction of this tree), and the tree at point B with coordinates (xB,yB) has the azimuth aB. On this data it is possible to construct straight half-lines in directions opposite to trees’ orientation, and to calculate the point M (x~,Y&, the intersection point of these half-lines (Fig. 1) : XM = In the search for the material of the Tunguska meteorite and also to construct a physical picture of its destruction at the final point of its trajectory, it is interesting to determine the region of energy liberation during the meteorite’s explosion. In particular, it is interesting to determine whether a single explosion or several explosions took place at Tunguska. A great body of information about the shock wave caused by the Tunguska explosion is contained in data of the forest destruction. As a result of numerous expeditions the directions about 75 000 fallen trees, located at about 1000 trial grounds, have been measured. These data have been gathered in catalogue by Fast et al. (1967, 1983). Fast et al. (1967), using methods of mathematical statistics, have determined the averaged picture of forest destruction, have studied the structure of the field of average directions of fallen trees, and have determined the critical point of this field-the projection of the explosion’s epicentre to the earth surface. In the present work an attempt is made to use another method to research the field of uprooting of trees. For further consideration the Cartesian system of coordinates Oxy, employed by Fast et al. (1967), is used : the Ox axis is directed to the north, and the Oy axis to the east; the origin of the coordinates is located outside of

RcosaA-Scosa, sin(a, - aA) Rsina,-Ssina,

YM

=

sin(a, --a*)

R = xgsina,-yBcosag S = x,sina,--yAcosaA. In this calculation satisfied :

following

conditions

(xA-xM)sina,+(yA--yM)cosaA

> 0

(Xg-XM)sina,+(yB-y~)CosCls

> 0.

The point

I

the

M can be considered

must

be

as “the source of the

X M f

A

’

/I /I

// ‘1\ \

\\

\

P Y

*E-mail : [email protected]

Fig. 1. Scheme for determining directions of two fallen trees

the point of intersection of the

1.52

Fig. 2. Scheme of constructing

V. D. Goldine:

a set of intersection

explosions

\\ \\

/I 1’

points

wave”, which has uprooted trees at points A and B. If this procedure is undertaken for many fallen trees, located at different points in the region, the appropriate points M will form a set (Fig. 2). This set may be characterized by a density of distribution P(x,JJ) : if one constructs a rectangular grid on a plane then P(x, v) can be defined as the number of points M in a cell, containing point (x, v). It is possible to assume that density P(x, y) is proportional to the density of probability distribution for location of the i.e. the points of a maximum of centres of “explosions”, of density P(x, y) correspond to their most probable locations. P(x, u) is an indicator of geometry of the shock wave’s propagation. This approach with the use of strings held tense in the directions of fallen trees was applied by Kulik to determine the epicentre of Tunguska explosion. In the present work such an approach is realized with a computer on the basis of all data gathered in the catalogue. It is necessary to note that this method is rather rough. For illustration of some its features two examples are considered. In the first example two points are considered. At each point 50 fallen trees are located ; the directions of these trees are random values, uniformly distributed within limits of t_ 10” about their means. In Fig. 3 these points are shown by small black squares. The izolines of the density function P(x, y) determined are also shown in Fig. 3 ; the intersection point of the mean directions is marked by x . In this case the point of a maximum of density is closer to initial points than to the point of intersection of mean directions. It is easy to prove mathematically that this displacement is in this case systematic. In the second example six points are given ; 50 trees with random directions, uniformly distributed within the limits of + 10” about their mean values, are located at each point; all six mean directions intersect at a single point. In Fig. 4 the points considered are also represented by black squares, the intersection point of mean directions is marked x ; on same drawing the izolines of the function P(x,v) are shown. In this case the results show that maximum of P(x, y) is close to the intersection point of mean directions. From examples considered it follows that the method

Search for the local centres of the Tunguska

Ic

h

Fig. 3. First example : intersection points directions of trees, located at two points

are constructed

from

used in the case of a random distribution tree directions does not give an exact location of the source, although it permits an estimate to be made of its approximate disposition with respect to the initial trial grounds. Using the method described above for the data of forest destruction at Tunguska has yielded the following results. The first calculation was done using all the data from the catalogue (Fast et al., 1967,1983). In Fig. 5 the izolines of the density P(x, y) are shown ; numbers by continuous curves correspond to values of lg P(x, y). The location of the maximum density appears close to the point deter-

Ic I

I

I

I

I I

J

Fig. 4. Second example : intersection points are constructed directions of trees, located at six points

from

V. D. Goldine:

Search for the local centres of the Tunguska

153

explosions

42 I-

-2 z

40

38

i

I

12

I

14

I

16

I

18

I

20

1

22

24

42 -

E -Y

40-

z 38 0

10

20

30

40

50

Y (km)

Fig. 5. Izolines picture of intersection points density P(x,y), calculated using all the data from the catalogue of forest destruction : 0, epicentre, determined by Fast (1967)

by Fast as a projection of the explosion’s epicentre, this point is marked @ in drawing ; no other local maxima appear. In the vicinity of the maximum P(x, y) z lo7 points per km2. Some other features of the izolines shown on Fig. 5 have, in the author’s opinion, no physical sense and are due, on the one hand, to random deviations of the trees’ directions from their mean values, and, on the other hand, to the fact that directions in the catalogue are given as a discrete numbers with a step of 5”. For determination of a local critical point it is necessary to take into account only those trees that are located in small sections of the forest destruction region. For further calculations, rectangular sections were chosen. By changing the size of a rectangular and moving it to another region, one can obtain various pictures of the distribution density of calculated points. It rather hard work, and it has only in the initial stages. In many cases the maximum of the function P(.x, y) showed a tendency to be attracted to the main epicentre, even if the initial section did not contain this point. However, in some cases a peculiarity was found. Izolines of P(x, y) obtained for a section positioned to the west from the main epicentre are shown on Fig. 6(a) ; borders of the rectangular section are shown by dotted lines ; the location of Fast’s point is marked x . This section contain nine trial grounds with 897 fallen trees. In this case the density P(x, y) has two maxima : one is located inside the section, and other, less manifest, is about the main epicentre. The first maximum is located approximately 46 km to the west of Fast’s point. Results for a wider section are presented in Fig. 6(b). This section contains 42 points with 2476 trees ; thus the first maximum remains, but has become less sharp, and the region separated by two maxima has disappeared. Moving a section to the east results in a merging of the two maxima, and then to a disappearance of the first. Calculations for the sections close to that presented in Fig. 6(a) have shown that the location of the western maximum varies slightly,

I

12

,

14

I

I

I

I

I

16

18

20

22

24

16

18

20

22

24

mined

Y (km)

Fig. 6. Izolines pictures of the function P(x,y), constructed for trial grounds, located in some rectangular sections in the forest destruction region : x , position of main epicentre

although the form of the izolines changes significantly. Some distributions of the directions of fallen trees for several trial grounds near the western maximum are shown in Fig. 7. The external radii of the black sectors

Fig. 7. Distribution of directions of fallen trees for some trial grounds, located near the west critical point

154

V. D. Goldine: Search for the local centres of the Tunguska explosions

are proportional to the number of trees fallen in this direction ; the dotted lines show the directions from the main epicentre. Among the points considered are points with the trees’ orientation indicating Fast’s point (Fig. 7(a), (b)), points with a distribution of directions which has two peaks (Fig. 7(c)), and also points with trees’ directions significantly deflected from the main orientation (Fig. 7(d)-(f)). This feature cannot be explained by influence of the Earth’s surface relief, because its size is greater than the difference in heights in this region. Thus, the results obtained show that the forest destruction in a region about 3-6 km to the west of the main epicentre cannot be caused only by the central shock wave of the main explosion. This feature can be explained either by the destruction of a small piece of the main body, or by the flight of this piece on an ascending trajectory.

Acknowledgements.

The author expresses gratitude to I. A. Schepetkin for his help in data preparation for computer simulation. References Fast, V. G., Boyarkina, A. P. and Baklanov, M. V. (1967) The destructions, caused by shock waves of Tunguska meteorite. In Problem of the Tunguska Meteorite, Iss. 2, pp. 62-104. Tomsk University, Tomsk (in Russian). Fast, V. G., Fast, N. P. and Golenberg, N. A. (1983) Catalogue of fallen trees, caused by Tunguska meteorite. In Meteoritic and Meteoric Research, pp. 24-74. Nauka, Siberian Branch, Novosibirsk (in Russian). Fast, V. G. (1967) Statistical analysis of Tunguska meteorite parameters. In Problem of the Tunguska Meteorite, Iss. 2, pp.

40-61. Tomsk University, Tomsk (in Russian).