PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
anomalies reflect sections of shift, compression or tension of rocks, as well as of jointing and higher
permeability zones, which are developed along depth faults. Our heat model of subvertical inter block zone
for analysis of seismogene dynamics [1] corresponds Foothills (in other words, Pshekish-Tirnaus) fracture,
which controls zones of high seismicity. This fracture is traced for 300 km from the south to the North and
presents itself a zone of narrow plates, falling under the monocline construction. Fissures along the plates in
the depth come close into one vertical fracture. This fracture splits the frontal part of the Daghestan wedge
and forms an almond–shaped structure. The focal point of the Daghestan earthquake 1970 is connected with
it (M=6,6; H=13 km; Jo=96).
Geological characteristics of this fault correspond in details to a well-known seismodynamic model
I.A.Volodin [2]. Model is built in 2 variants of passive and active fractures as eradiating sources. This model
is elaborated by means of using mechanism of Fraunhofer non-linear diffraction. The united vertical fracture
in the depth forms an intensive eradiating resonator – the source of non-linear diffraction of the wave seismic
field [2, p.149-157].
The I.A.Volodin model as well as the Foothills fracture, contains a zone of narrow plates, alternating with
the fissures. The differences are mainly in the fall of the Foothills fracture, between the two tectonic blocks
of the crystal base but not under “the monocline construction” as in the model [2, p.155]. “The faults limiting
these plates, are coming close at the depth into united vertical fracture, in the I.A.Volodin model are the
similar. Together they form an intensive, eradiating resonator, “which selects from the common disturbance
field longitude along orthogonal direction according boundaries of fracture harmonics with integer numerical
relations between the fracture width and wave length” [2, p.150]. The resonator is the source of non-linear
diffraction of Fraunhofer regarding the waveguide seismic field which is described by the asymptotic
formula. The indicated intensity of resonator is manifested “in the dynamic of landscape… in the erosion
activity of the soils, caused by the background high frequency vibration, which in the first approximation can
be regarded proportional to it. This makes it possible to regard, that the diffraction pattern, described by the
formula…, will be really presented in the aero-space photographs (Our Italics – А.B.) as an assemblage,
packet of lineaments, parallel to the direction of the fracture in the crystal foundation. The analysis of
distances between them by means of using this formula allows defining the radiation intensity and the depth
of the source. This, as a result, can be interpreted as the location of the fracture and some it’s qualitative
characteristics” [2, p.154].
Derivation of the design formulae for such model [2, p.151-155] was made by I.A.Volodin on the basis of
introducing coordinate system, orthogonal to the direction of the fracture.
The wave field of disturbance weakly changes in the direction of the fracture that is independence
condition from the third coordinate is introduced. This formulation of problem is a consequence of the
transverse wave model [2, p.107-108], where the equation with coordinates: X2 – along the foundation
orthogonal to the fracture, Y1 – in the vertical direction along the earth’s radius is examined. The equation is
reduced to the following form [2, p.152]:
i2k∂A/∂X2 + ∂ 2 A/∂Y1 2 + k 2 b|A| 2 A = 0, (1)
where the amplitude of the transverse waves A2 = A {See[2], p.107, formula (2.38) – A.B.}, k – the wave
number of asymptotical number field (of the plane seismic wave), b – arbitrary constant, determined as
velocity of solution of the seismic field in reference to the non-linear equation of Shredinger describing
solution effects. From the formula (1) is determined the space configuration of intensity I wave field,
proportional to the square of its amplitude, for this purpose is used asymptotical formula which describes
non-linear diffraction of Fraunhofer of the wave field on the slots with parameters A0 and S, having the view
[2, p.152]:
dI/dφ = (k/πb)ln{(k 2 φ 2 /4 + a 2 )/(k 2 φ 2 /4 + a 2 cos 2 [s(k 2 φ 2 /4 + a 2 ) 1/2 ]}, (2)
where parameter a 2 = k 2 b/|A0| 2 /2 is determined by initial conditions, and φ – is an angle between the
directions of propagation of radiation from the source and earth’s radius. It must be noted, that the diffraction
formula (2) is true only when the source intensity is weak, specifically under the condition I = s|A0| 2 < IКР,
where critical meaning of intensity IКР = π 2 /(2sbk 2 ).
The lines of field intensity antinodes on the diurnal surface are determined from the formula of diffraction
as lines, which derivative of intensity of waveguide seismic field is equal to zero. When X – a distance along
the earth’s surface in the direction orthogonal to the fracture, and H – is the depth of the radiation source
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