Earthquake as kinetic process
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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут геофізики ім. С.I. Субботіна НАН України
2010
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| Назва видання: | Геофизический журнал |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/101314 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Earthquake as kinetic process / O. Groza, V. Groza // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 51-53. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1013142016-06-03T03:02:01Z Earthquake as kinetic process Groza, O. Groza, V. 2010 Article Earthquake as kinetic process / O. Groza, V. Groza // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 51-53. — Бібліогр.: 2 назв. — англ. 0203-3100 http://dspace.nbuv.gov.ua/handle/123456789/101314 en Геофизический журнал Інститут геофізики ім. С.I. Субботіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| format |
Article |
| author |
Groza, O. Groza, V. |
| spellingShingle |
Groza, O. Groza, V. Earthquake as kinetic process Геофизический журнал |
| author_facet |
Groza, O. Groza, V. |
| author_sort |
Groza, O. |
| title |
Earthquake as kinetic process |
| title_short |
Earthquake as kinetic process |
| title_full |
Earthquake as kinetic process |
| title_fullStr |
Earthquake as kinetic process |
| title_full_unstemmed |
Earthquake as kinetic process |
| title_sort |
earthquake as kinetic process |
| publisher |
Інститут геофізики ім. С.I. Субботіна НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/101314 |
| citation_txt |
Earthquake as kinetic process / O. Groza, V. Groza // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 51-53. — Бібліогр.: 2 назв. — англ. |
| series |
Геофизический журнал |
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AT grozao earthquakeaskineticprocess AT grozav earthquakeaskineticprocess |
| first_indexed |
2025-07-07T10:43:56Z |
| last_indexed |
2025-07-07T10:43:56Z |
| _version_ |
1836984605203234816 |
| fulltext |
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the earthquakes forecast is the prognosis of time of
strong earthquakes occurrence. There are three
models: dilatant-diffusion model, avalanche-unsta-
ble fracture model and stick-slip model. Unfortunate-
ly, while adequately describing the development of
earthquakes, these models cannot predict earth-
quake. Actually they are only scenarios of earth-
quakes. At the same time it is essentially impor-
tant that all these models consider earthquake as a
process. The models in question are based on solid
mechanics and the physics of rock fracture. We pro-
pose the other approach based on thermodynamics,
phase-transition theory and chemical kinetics. It al-
lows to enter explicitly time into description of the pro-
cess due to Arrhenius equation (as activation time).
For elementary dislocation it is 10 13 s.
2. The kinetic approach allows to explain why
aftershocks relaxation (Omori’s law) has hyperbo-
lic character and considerably differs from standard
exponential relaxation of mechanical systems. The
combination of the Boltzmann distribution law (statis-
tical thermodynamics) and the Arrhenius equation
(chemical physics) gives Omori's law (N t 1) directly.
From the same standpoint the role of fluctua-
tions in the relaxation processes has been also
analysed. Taking into account fluctuations it is neces-
sary to replace the standard relaxation equation by
Nt
N
N
dt
d
)(
relax
.
as critical event, and strength is accepted to a con-
stant of solid. Experience shows that it naturally
depends on time and temperature. At present it is
possible to state that such a limit of strength does
not exist. Tensile stress (load) p, fracture time and
temperature T are uniquely related to each other
[Zhurkov, 1968]:
The solution is “stretched exponent”, that is has
long (hyperbolic) tail.
The kinetics of relaxation to equilibrium is limi-
ted by the speed of establishing the concentration
fluctuations, which depends on the diffusion. In this
case relaxation has character N t 3/2 instead expo-
nential [Zel'dovich, Ovchinnikov, 1977]. Thus, in the
real process N t Cand C [1;1.5].
3. The kinetic approach allows to look at diffu-
sion in the crystals in the different way. The basic
idea is that the diffusion process is not continuous
— each act of displacement is accompanied by a
relaxation. If Fick's law is explicitly added by the
relaxation term, then instead of the diffusion equa-
tion the cable equation is obtained (it is similar for
generalization of Fourier law realized by Cattaneo).
Here it is essentially important that the problem of
infinite rate of diffusion in this case disappears.
4. The solid rupture is traditionally considered
Earthquake as kinetic process
O. Groza1, V. Groza2, 2010
1Institute of Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine
groza�igph�kiev�ua
2National Aviation University, Kiev, Ukraine
valentina.groza@gmail.com
1. At present time the forecast of earthquake is
one of the most actual problems of geophysics and
to a considerable degree one of the primary tasks
of Earth physics. The basic unresolved question of
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References
Zhurkov S. N. Kinetic concept of solids strength //
��
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— P. 46—52 (in Russian).
Zel'dovich Y. B., Ovchinnikov A. A. Asymptotic of
establishing equilibrium and concentration fluc-
tuations // J. Experiment. Theor. Phys. Lett. Theo-
retical Physics. — 1977. — 26!� 8. — P. 588—
591 (in Russian).
The Gibbs “free energy” G has the physical di-
mension of energy but it is not energy per se. The
Gibbs function is the pseudo-potential, which shows
the natural direction of the dynamics of a thermody-
namic system. The surface tension is defined is as
T , p,Ni
s
G
. Reducing the height of the barri-
er means that the slope of the tangent to the barrier
top decreases (in other words, the surface tension
decreases). It is possible state the reverse — de-
creasing of surface tension reduces the height of
the energy barrier. Since the surface tension is as-
sociated with the work expended to rupture of inter-
molecular bonds, then it is caused by these with
bonds and inversely. Actually, is represented as
work (per unit area) — cohesion work, i. e. it is a
measure of intensity of work necessary for rupture.
There are many reasons of decreasing the surface
tension and thus reducing the strength, that is why
it is difficult to define the strength limit uniquely.
const pkT ln
*
U .
According to Russian Academician S. N. Zhur-
kov, the mechanism of rupture is connected with
thermal fluctuation dissociation of bonds responsi-
ble for the strength. The sense of thermal fluctua-
tion mechanism is that the potential barrier interfer-
ing rupture of bond is overcame due to of energy
fluctuation. I. e. it is takes place over-barrier tran-
sition with characteristic exponential dependence
of expectation time on temperature.
Our approach consists in the fact that transition
occurs not due to the activation (energy excess),
but due to the decrease of barrier height. The back-
ground is that the Zhurkov formula is equivalent in
fact to ordinary thermodynamic relation
kT
G
t t* exp .
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