ISSN 0027-1349, Moscow University Physics Bulletin, 2015, Vol. 70, No. 6, pp. 549–557. © Allerton Press, Inc., 2015. Original Russian Text © Yu.V. Barkin, 2015, published in Vestnik Moskovskogo Universiteta. Fizika, 2015, No. 6, pp. 120–126.

PHYSICS OF EARTH, ATMOSPHERE, AND HYDROSPHERE

On the Origin of a Zone of Lower Seismic Velocities of the Earth. Prediction of a Similar Zone on Mars at a Depth of Approximately 300 km Yu. V. Barkin Sternberg Astronomical Institute, Moscow State University, Universitetskii pr. 13, Moscow, 119991 Russia e-mail: [email protected] Received May 5, 2015; in final form, June 9, 2015

Abstract—In light of the planned space missions to the Moon and Mars to study the inner structures of these celestial bodies by seismic methods, theoretical studies of possible peculiarities of the inner structures of these celestial bodies are particularly relevant. Our previous investigations showed that the mechanism of forced oscillations of the core and mantle of a celestial body under the gravitational influence of other celestial bodies may play a key role. Moreover, it allows a number of planetary processes and phenomena on the Earth and the other planets to be explained. Specifically, this mechanism gives us an opportunity to reveal geodesic changes and to study the nature and origin of some of the inner formations of the Earth, the Moon, and Mars. In the present paper, we explain the presence of a zone of lower seismic velocities (LVZ) on the Earth at a mean depth of approximately 145 km and predict the analogous LVZ on Mars at a depth of approximately 300 km. Keywords: zones of lower seismic velocities of the Earth and Mars, core and mantle displacements, deformations of a viscoelastic mantle. DOI: 10.3103/S0027134915060065

INTRODUCTION In the present paper and some of our previous studies on geodynamics and geophysics, the geodynamic mechanism of forced relative oscillations, displacements, and rotations of the core relative to the mantle under the action of gravity of other celestial bodies found effective application [1, 2]. In the last decade, this mechanism has attracted the focused attention of specialists in different fields of Earth and planetary sciences. In the last 10–15 years, fundamental problems of geodynamics, celestial mechanics, geology, geodesy, and geophysics have been solved on the basis of this model. The secular polar drift of the rotation axis of the Earth, the nontidal acceleration of its axial rotation [3], and discontinuous changes in these phenomena [4] were explained and interpreted. A new interpretation of the solar–terrestrial and solar–planetary relationships based on the gravitational excitation of shells of celestial bodies was suggested [5, 6]. The unity of the mechanisms of cyclic, secular, and stepped changes in their activity was justified for the processes that occur on the planets and satellites of the Solar System [1, 4, 7]. The age-old problem of the secular buildup of the ocean level has been answered and the contrasting secular changes of the mean ocean level in the northern and southern hemispheres of the Earth have been predicted [8]. These results have been

already confirmed in recent studies by other authors [9, 10]. The inversion geodesic changes of the Earth’s shape in the present epoch [7, 11] and in the course of geo-evolution have been studied [12, 13] and the secular variations in the gravitational force that are observed at the leading gravimetric stations all over the world have been explained [9]. The contrasting secular variations in the lengths of latitude circles, viz., the parallels in the northern (shortening) and southern (lengthening) hemispheres, have been detected and explained based on the currently available data from space geodesy. All of the listed phenomena have been confirmed and explained in good agreement with the data of the high-accuracy modern observations. These studies formed the basis for the present paper, where we consider the nature of zones of lower seismic velocities (LVZs) on the Earth and predict the analogous zones on Mars. In the present paper, we report the results of an analysis of the probable role of forced relative oscillations of the core and mantle of the Earth, as well as Mars, in the formation of the shell structure of these celestial bodies. The first-priority issue is the existence and origin of LVZs, which is an important and unsolved challenge of geodynamics. The location of zones that correspond to extreme radial deformations of the mantle layers (or the olivine transition zones

549

550

BARKIN

Z

Fixed surface of the cavity of the core

Viscoelastic mantle

r0

Cc Cm

Core CmCc = ρ(t)

Intermediate layer

r1 Free surface of the mantle

Fig. 1. A model problem on the mantle deformation of the planet due to radial displacement of its core (the displacements of particles in the mantle base are zero, while the stress on the outer surface of the mantle is zero).

(OTZs)) is also studied. As has been shown, the LVZs correspond to spherical zones where the mantle deformations are absent and the directions of radial shifts are constant (tension zones). The present analysis is based on the solution of the elasticity problem for mantle deformations that are due to core displacements. This solution was obtained in our first studies of the above-mentioned two-shell geomodel [14, 15]. In the present paper, we will consider only the polar drift of the core with a constant velocity, ρ , relative to the surface of the planet. The scheme of the considered model is shown in Fig. 1. It is assumed that the core and the mantle are separated by a thin viscoelastic layer. In addition, the parameters of the core drift relative to the mantle are selected in accordance with the space-geodesy data on the northward displacements of the Earth’s center of mass with a constant velocity. In this particular case, the coordinate system C c xyz , which originates from the core’s center, C c , and with the axes that are parallel to the mantle coordinate system of the same name, C m xyz , will be also inertial. The radius vector of an arbitrary point of the mantle, M , in the considered coordinate system will be presented as

R(r, t ) = r + u(r, t ) − ρ(t ),

where r is the radius vector of an arbitrary point of the nondeformed mantle and u(r, t ) is the displacement vector. Here, ρ(t ) is the law for the polar motion of the Earth’s center of mass (in the present paper, this is a northward drift of the core’s center of mass with a constant velocity); ρ(t ) is a linear function of time. The noninertial effects that are caused by the mobility of the base coordinate system, C m xyz , were ignored here, as well as in [15]. The model problem on the mantle deformations induced by polar displacements of the core and its solution are considered in the “Radial deformations…” Section below. MODEL As in [15–17], we consider a two-shell planet that consists of a core and a mantle (Fig. 1). The mantle is regarded as a viscoelastic body with a free surface and a fixed spherical base. Moreover, the core is assumed to be an invariable body, whose center of mass moves weakly around the pole and nutates relative to the mantle. Such relative displacements can be produced due to a thin low-viscosity layer between the core and the mantle. These have been confirmed by high-accu-

MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

No. 6

2015

ON THE ORIGIN OF A ZONE

551

racy modern observations of the motions of the Earth’s geocenter [14, 18]. In the restricted formulation of the problem, it is assumed that the core is in prescribed motion along the polar axis (the secular drift and nutations of small amplitude). The displacements of the center of mass of the gravitating core, or, more specifically, its extra mass, that are caused by the difference between the densities of the core and the mantle, lead to the unidirectional displacements of the center of mass of the planet and induce deformations of all of the mantle layers (Fig. 1). These deformations were analytically described in [15]. In the present paper, we focus our attention on the analysis of the radial deformations of the mantle layers and on distinguishing peculiar zones of spherical layers that are subjected to the extreme gravity of the core or not subjected to such impacts. It is important to stress that the location of such zones is independent of the behavior of the motions of the core and their directions and determined by the elasticity parameters of the mantle and the sizes of the core and the mantle. This allowed preliminary studies of the location of special zones in the inner structure of the Moon and Mars, which were modeled as a core–mantle system, to be performed [16, 17]. The relative displacements of the core and mantle of these celestial bodies manifest themselves in cyclic changes and variations of their geophysical and geodynamic processes [18–20, 29].

ζ = 1 on the surface of the planet. The coefficients Bi and C i are known functions of the elasticity parameters of the mantle, λ and μ , and the geometric parameter, ζ 0 [15, 16]. For the considered models of the core and mantle of the Earth and Mars, ζ 0 = 0.5462 and ζ 0 = 0.4887 , respectively. Formula (1) was derived from a general one, Eq. (2), describing the deformations of the elastic mantle of the Earth under the gravitational influence of the northward-drifting core [15, 16]:

RADIAL DEFORMATIONS OF THE MANTLE OF A PLANET (THE EARTH, THE MOON, AND MARS)

3 2 2 B5 = − 1 λ rm ( 2λ + 3μ ) ⎡⎣( λ + 4μ ) rc − 2μ rm ⎤⎦ , 3Δ a

Radial displacements of particles in the mantle are determined by the formula that was given in [15–17]

ur = ρ K c ⎡⎣B0 + C 0 + ( B2 + C 2 ) ζ

u = K c ⎡⎣(B0 + B2ζ 2 + B3ζ 3 + B5ζ 5 ) ⋅ ζ −3ρ ( r ⋅ ρ) ⎤ + (C 0 + C 2ζ 2 + C 5ζ 5 ) ⋅ ζ −3 2 r ⎥ . r ⎦

Coefficients Bi and C i are determined as functions of the elasticity parameters of the mantle, λ and μ , and the geometric parameter, ζ 0 [15]: 2 3 3 B0 = − 1 λ ( λ + 4μ ) rc ⎡⎣4μ rc + (3λ + 2μ ) rm ⎤⎦ , 18Δ a

B2 = −

rm λ (λ + μ) 9rc Δ a 5 3 2 5 × ⎡⎣9 ( λ + 4μ ) rc − 10μ rc rm + 2 (3λ + 2μ ) rm ⎤⎦ ,

2 3 3 C 0 = 1 λ ( λ + 4μ ) rc ⎡⎣4μ rc + (3λ + 2μ ) rm ⎤⎦ , 6Δ a

C2 = − (1)

where ϕ is the latitude, ρ = ρ(t ) is the specified timevariable distance between the centers of masses of the mantle and the core, K c = f Δ mc /(λ rm ) is a dimensionless coefficient, Δ mc is the extra mass of the core that determines the gravitational effect of the drifting core on the mantle deformation, and f is the gravitation constant; Δ mc = 4πrc3 ( δ c − δ m,l ) /3 , where δ c and δ m,l are the mean densities of the core and the mantle at its base, respectively. For the assumed two-shell models of the Earth, the Moon, and Mars, the following values were obtained: K с;Earth = 0.20883; K с;Mars = 0.003779 ; and K с;Moon = 0.0006520 . The dimensionless quantity ζ = r / rm , where r = r characterizes the position of an arbitrary point of the mantle with a radius vector r . For the points on the surface of a spherical core of the Earth, ζ = ζ 0 = rc / rm , while MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

λ2 , 6μ ( λ + 2μ )

B3 =

2

+ B3ζ 3 + ( B5 + C 5 ) ζ 5 ⎤⎦ ζ −3 sin ϕ,

(2)

λ ( λ + 4μ ) , 6μ ( λ + 2μ )

(3)

C 5 = 1 λ ( λ + 4μ ) rm3 ⎡⎣( λ + 4μ ) rc2 − 2μ rm2 ⎤⎦ , 3Δ a

Δ d = − ( λ + 2μ ) ⎡⎣4μ rc3 + (3λ + 2μ ) rm3 ⎤⎦ ,

Δ a = μ ( λ + 2μ ) ⎡⎣2 ( λ + 4μ ) rc5 + (3λ + 2μ ) rm5 ⎤⎦ . In the following, we will use the model values of the Earth’s parameters:

μ = 1.80 × 1011 N/m2,

λ = 2.57 × 1011 N/m2, (4)

δ m = 4.44 g/cm3, m⊕ / Δ mc = 5.1760 , K c = 0.20883, rc = 3480 km,

rm = 6371 km, ζ c = rc / rm = 0.5462 .

In Eq. (4), δ m is the mean value of the mantle density; rc and rm are the mean radii of the inner and outer surfaces of the Earth’s mantle, respectively. The elastic properties of the Earth’s mantle will be described by No. 6

2015

552

BARKIN

2.0 ur

Liquid core

0

−2.0

220 km

0.6

0.7

3630 km

0.9

0.8

80 km ζ 1.0

5600 km LVZ

−4.0

−6.0

−8.0

−10.0

−12.0

0.6920 3480 km

6151 6291 km km Fig. 2. Radial deformations of the Earth’s mantle.

the mean values of the Lamé coefficients μ and λ . Δmc is the extra mass of the moving core, m⊕ is the Earth’s f Δ mc mass, and K c = is the dimensionless fundaλ r1 mental parameter. The extra mass of the Earth’s core is Δ mc = 0.1932m⊕ . All of the listed values of the core and mantle parameters (4) were determined from the standards of the Preliminary Reference Earth Model (PREM) [21]. For the assumed values of the model parameters of the Earth (4), the following values of the coefficients Ai , Bi , and C i (i = 0,1,2,3) were derived from formulas (3)

B0 = − 0.038154 , B3 = 0.402059 ,

B2 = − 0.099119 , B5 = 0.045443 ,

C 0 = 0.114462 , C 2 = − 0.376807 , C 3 = 0, C 5 = − 0.042124 . In Fig. 2, the relative radial distance, ζ , is plotted along the abscissa axis (the specified values correspond to the distances from the core surface to the current point of the mantle). In Fig. 2, the radial distances from the Earth’s center to the mantle base and the LVZ boundary (according to the PREM [21]) and the depths of the LVZ boundaries are also specified in

kilometers. The zone between 3630 and 5600 km, where the mantle deformations are strongest, is marked. The tomographic cross section of the upper mantle of the Earth is shown in the lower panel of Fig. 3 (by the red line in the upper panel). The position of the LVZs is shown in the lower panel of the plot (at a depth of approximately 145 km) [22]. It is based on the figure from [23] that illustrates the phenomenon of lenticular LVZ formations, the asymmetry in their positions relative to the opposite hemispheres of the Earth, and their level corresponding to the LVZ boundary (a lower panel of Fig. 3). The position of the Earth’s tomographic cross section is indicated by a red line in the map. The boundary at 145 km corresponds to the zone where the displacements of mantle particles change their directions (see Fig. 4). A NONPERTURBED STATE OF THE ASTHENOSPHERIC LAYER In the asthenospheric layer (at the depths from 80 to 220 km), the zones that are separated by a boundary at 145 km (Fig. 2) are subjected to extension of the opposite tendencies in their deformation states (Fig. 4). Particles of the outer asthenospheric layer move in the same direction as the core does, while

MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

No. 6

2015

ON THE ORIGIN OF A ZONE

−180

100 144

−120

−60

0

60

553

120

Lithosphere

180

100

LVZ

200

200 Asthenosphere

300

300

400

400

Fig. 3. Zones of lower seismic velocities (LVZ): how they are formed.

ur > 0

to the surface

ur = 0

LVZ 144.4 km

ur < 0

to the Earth's center

Fig. 4. On the nature of an asthenospheric layer: how zones of lower seismic velocities (decompaction zones) are formed. The zone where there are no deformations due to the moving core is a zone of lower velocities.

particles of the inner lithospheric layer move in the opposite direction (Fig. 4). The median line of the asthenosphere at a depth of 145 km is not perturbed in the radial direction regardless of the amplitudes and directions of the main displacements. This layer and its structure are clearly seen in the data on tomographic cross sections around the entire Earth (Fig. 3). Its lenticular shape is probably connected with the peculiarities of the dominating directions of the radial MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

displacements of the Earth’s core. Note that, in the earlier papers on tectonics [24–26], the model of lithospheric oceanic plates with a thickness d = 117 km was used. Thus, the LVZs can be confined to some planetary (spherical) zone of extension. Its origin is connected with the gravitational influence of the drifting core on the mantle layers. Oscillations and displacements of the core occur due to the gravitational influence of the No. 6

2015

554

BARKIN

ur(ζ) Base of the 0.1 mantle Radius 1680 km

3100 km 2149 km 0.915

0

−0.1

ζ = r/rm

0.634 0.6

0.7

0.8

1.0 3389.5 km

0.9

OTZ

LVZ

1240.5 km

289.5 km

−0.2 Depth 1710 km

Fig. 5. The radial displacements of the particles in the mantle of Mars at the polar axis.

external celestial bodies on the core–mantle system. The median LVZ line corresponds to the mantle sphere of a certain radius, where the radial deformation is zero. In other words, the radial displacements of mantle particles that are located on the geocentric sphere with a radius rLVZ = r1ζ LVZ are zero. For the assumed two-shell model of the Earth (Fig. 1), we determined the mean radius of this sphere of lower velocities rLVZ = r1ζ LVZ = 6226 km (located at a mean depth of 145 km) (Fig. 4).

a strip indicates the probable position of the LVZ of Mars, which corresponds to a mean location depth of approximately 300 km. The diagrams of the known model of the inner structure of Mars are also given in the plot [27, 28]. It is seen that the OTZ position corg, ρ 4 6

2149 km

RADIAL DEFORMATIONS OF THE MANTLE OF MARS. PREDICTION OF A ZONE OF LOWER SEISMIC VELOCITIES AT A DEPTH OF APPROXIMATELY 300 KM ON MARS In a number of earlier publications, we noted that the mechanism of forced relative oscillations of the core and mantle also effectively works on Mars. Thus, all of the phenomena that are induced by the secular drift of the center of mass of the planet also take place on Mars. We will not go into the details of different geodesic and geophysical phenomena on Mars [29]. However, we will note that Mars also very likely has an LVZ. In Fig. 5, the radial displacements of particles of the mantle expressed in the units of 10 −3 ρ are shown, where ρ is the relative displacement of the centers of masses of the core and mantle. In Fig. 6, on the right,

6

g

T 3

3100 km

OTZ

LVZ

K, μ 4

2

4

ρ

Radius 1680 km

0

2

μ

2

0

2000 1600 1200

K

1

T 2400

800 400

290 km

500 1000 1500 2000 2500 3000

0

0

Fig. 6. The inner structure model and the predicted LVZ location for Mars. The main parameters of the model are: the acceleration of gravity, g (m/s2), the density, ρ × 103 (kg/m3), the Lamé parameters, K and μ × 102 (GPa), and the temperature, T (K). The hypothetical LVZ and OTZ are marked.

MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

No. 6

2015

ON THE ORIGIN OF A ZONE

responds to the location of extreme radial deformations of the mantle of Mars due to displacements and oscillations of the planetary core. There is no doubt that this association requires a more thorough analysis. In the present section, we consider the two-shell model of Mars that is analogous to the above-discussed model of the Earth (Fig. 1). The model parameters are taken from modern studies of the inner structure of Mars [16, 17]: λ = 1.03 × 1012 Pa and μ = 0.78 × 1012 Pa are the Lamé parameters of elasticity of Mars; δ m = 3.70 g/cm–3 and δ с = 6.7 g/cm–3 are the mean densities of the mantle and core of Mars, respectively; Δ mc / mM = 0.00894479 ; and the fundamental parameters are K с = 0.0037787 and ζ 0 = rc / rm = 0.4957 . The mean radii of the mantle and the core of Mars are rm = 3389.5 km and rc = 1680 km, respectively; the mass of Mars is mM = 0.64185 × 1024 kg. In the considered modeling task, the radial component of the displacement vector of the mantle of Mars is expressed by formula (2), although the values of the parameters are different. For the assumed values of the model parameters of Mars, formulas (3) yield the following values of the coefficients Bi and C i (i = 0, 2, 3, 5):

B0 = − 0.029654 , B2 = − 0.087524 , B3 = 0.399851, B5 = 0.082512 ,

(6)

C 0 = 0.08896121, C 2 = − 0.352647 , C 3 = 0, C 5 = − 0.077824 . For these assumed parameters of the two-shell model of Mars, the radial displacements of the mantle particles versus the relative depth can be easily plotted (Fig. 3). The displacements of particles are indicated in conventional units along the ordinate axis. For Mars, the radial displacements are largest at a depth of 1240.5 km (ζ = 0.6920 ); in the northern hemisphere are largest to the depths of 300 km and they are directed to the center of the planet. We especially note that at some depth in the mantle, roughly at 300 km, the radial displacements of the particles are zero. According to the considered geomodel and the mechanism of forced displacements and oscillations of the core and mantle of Mars, the red line corresponds to the median line of the LVZ (Fig. 4). Our studies of the dynamics of Mars as a system of gravitating and mobile shells confirm that the mechanism of forced oscillations of the core and mantle works effectively on Mars, as well as on the Earth [29]. Thus, all of the phenomena that are caused by the secular drift and oscillations of the center of mass of a planet (or, simply stated, by displacements of the core) that are known for the Earth should also exist on Mars. We will not treat these phenomena at length. However, we will note that Mars very likely also has an LVZ that occurs, MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

555

according to our calculations, at a depth of approximately 300 km [16, 17]. In Fig. 5, the radial displacements of the particles of the mantle of Mars along the polar axis of the planet are plotted in units of 10 −3 ρ . The main graph is shown against the background of the known model diagrams of the inner structure of Mars [27, 28]. Here the OTZ is also shown, while the hypothetical LVZ is marked by a strip. The median line of the LVZ is shown in red. For the Earth, this line approximately corresponds to a depth of 145 km. For Mars, the position of this line, as well as the LVZ itself, is unknown. It corresponds to the location where the displacements of the mantle particles change their direction from the center to the surface of the planet and vice versa (see Fig. 3). The graph of the radial displacements of particles of the mantle of Mars along the ordinate axis at ϕ = π/2 is shown in units of 10 −3 ρ . The relative radial distance, ζ (the specified values correspond to the distances from the core surface to the current point of the mantle), is shown along the abscissa axis. In Fig. 2, the radial distances from the center of Mars to the mantle base and the LVZ boundary and the depths of the LVZ boundary are also shown in kilometers. Because of this, all of the phenomena that are caused by a secular drift of the center of mass of a planet (more exactly, its core) that were considered above for the Earth should also exist on Mars. We will not treat all of these phenomena at length. However, we will note that Mars also has an LVZ that is located, in accordance with our calculations, at a depth of approximately 300 km; this layer may be detected in the proposed space missions to Mars. CONCLUSIONS We have found important signs that the origin of the LVZ of the Earth and its location are determined by the action of forced displacements and oscillations of the Earth’s core relative to the mantle due to the influence of the gravity of the Sun and planets (in the course of the geological history of the Earth). In the present paper, an analogous LVZ is predicted for Mars; its median line is at a depth of approximately 300 km. For Mars and the Earth, the behaviors of the deformations of the mantle layers that are induced by the displacements and oscillations of the core and the mantle have much in common. Due to this, a zone of small radial velocities at a depth of 300 km on Mars may actually exist. This confirms our previous hypothesis that the mechanism of forced relative oscillations of the core and mantle of Mars is vigorous and that it controls the activities and intensities of the natural processes of the planet [29]. These data and preliminary results are of high importance for preparing and carrying out seismic experiments on the surface of Mars and other No. 6

2015

556

BARKIN

celestial bodies in planned space missions in order to find the LVZs of planets and satellites. Such LVZs are formed due to the gravitational influence of the drifting core. These results are critical for preparing and performing seismic experiments that are aimed at the detection and examination of the mentioned zones in the scheduled space missions on the surface of Mars.

ACKNOWLEDGMENTS This study was supported by the Russian Foundation for Basic Research, project no. 15-05-07590. REFERENCES 1. Yu. V. Barkin, Izv. Sekts. Nauk Zemle Ross. Akad. Estestv. Nauk, No. 9, 45 (2002).

CONCLUSIONS A special technique has been developed and effectively applied to the analysis of the depth of the LVZ zone for the Earth (with the median line at a depth of 145 km) in order to study seismic zones of lower velocities and their locations in planets and satellites. It was theoretically predicted that an analogous zone exists on Mars and that the mean depth of its location is approximately 299 km. For the moment, the inner structure of Mars is poorly known, as compared to the structure of the Earth and, to a lesser degree, the Moon, which have been studied with the use of the seismic data. Seismographs were mounted on the Viking 1 and 2 landers as early as during the expeditions in 1976. One of the instruments did not operate properly, while the seismometer of the Viking 2 lander, which was a three-component short-period instrument, failed to detect any noticeable seismic event (Mars tremor), although it was almost continuously in operation for 19 months. In the last 25 years, different seismic experiments have been developed for several space stations on the surface of Mars (the Mars-96, Marsnet (ESA), InterMarsnet (ESA/NASA), and ExoMars missions (ESA and NASA stand for the European Space Agency and the National Aeronautics and Space Administration, respectively)). For a number of reasons, none of these seismic experiments has been carried out. In the Solar System, the Moon is the only celestial body, except the Earth, that can be described with actual seismic data. We are currently in the lead-up to important seismic experiments on Mars: the InSight mission that is planned by NASA and the mission that has been developed by the Russian Federal Space Agency (Roscosmos) and the ESA. One of the main objectives of the seismic experiment on Mars is to develop a more accurate model of the inner structure of this planet. Thus, there are grounds to believe that the LVZ of Mars can be detected with seismic methods in the earliest space missions to this planet. This would be an important confirmation that the mechanism of the forced onset of oscillations of the core and mantle of Mars under the gravitational influence of the Sun and planets is actively occurring. The author’s papers that are contained in the reference list and the other papers on the considered subject are available on the Internet websites http://istina.msu.ru/ and http://istina.msu.ru/profile/BarkinYV/.

2. Yu. V. Barkin, in Proc. 36th ESLAB Symp., Noordwijk, Netherlands, 2002, p. 201. http://adsabs.harvard.edu/ full/2002ESASP.514.201B 3. Yu. V. Barkin, Rotational Motion and Inner Dynamics of Solar System Bodies (Moscow, 2015) [in Russian]. 4. Yu. V. Barkin, in Proc. XX Int. Sci. Conf. (School) on Marine Geology, Moscow, Russia, 2013, p. 21. 5. G. Ya. Smolkov and Yu. V. Barkin, Astron. Tsirk., No. 1619 (2014). 6. I. P. Shestopalov, Yu. V. Barkin, and S. V. Belov, in Smirnov Anthology 2014 (Scientific–Literary Miscellany) (Moscow, 2014), p. 134 [in Russian]. 7. S. V. Belov, I. P. Shestopalov, E. P. Kharin, et al., Atlas of Temporal Variations of Natural, Anthropogenic, and Social Processes, Vol. 5: Man and Three Ambient Environments (Moscow, 2013), p. 172 [in Russian]. 8. Yu.V. Barkin, Moscow Univ. Phys. Bull. 66, 398 (2011). 9. S. Jevrejeva, A. Grinsted, J. C. Moore, and S. Holgate, J. Geophys. Res. 111, C09012 (2006). doi 10.1029/2005JC003229 10. G. Woppelmann, M. Marcos, A. Santamaria-Gomez, et al., Geophys. Res. Lett. 41, 1639 (2014). doi 10.1002/2013GL059039 11. W.-B. Shen, R. Sun, Yu. V. Barkin, and Zi-Yu Shen, Geodyn. Tectonophys. 6, 45 (2015). doi 10.5800/GT2015-6-1-0171 12. M. A. Goncharov, Yu. N. Raznitsin, and Yu. V. Barkin, Geodyn. Tectonophys. 3, 27 (2012). doi 10.5800/GT2012-3-1-0060 13. M. A. Goncharov, Yu. N. Raznitsin, and Yu. V. Barkin, Dokl. Earth Sci. 455, 383 (2014). 14. Yu. V. Barkin and V. G. Vilke, Astron. Astrophys. Trans. 23, 533 (2004). doi 10.1080/ 10556790412331319668 15. Yu. V. Barkin and A. V. Shatina, Astron. Astrophys. Trans. 24, 195 (2005). doi 10.1080/10556790500496339 16. Yu. Barkin, H. Hanada, S. Sasaki, and M. Barkin, in The Third Moscow Solar System Symposium, Moscow, Russia, 2012. Book of Abstracts, p. 244. 17. Yu. Barkin, H. Hanada, S. Sasaki, and M. Barkin, in The 118th Meeting of the Geodetic Society of Japan, Sendai, Japan, 2012. Book of Abstracts, p. 147. 18. Yu. V. Barkin, Geofiz. Issled. 11, 18 (2010). 19. Yu. V. Barkin, in Scientific Aspects of Ecological Problems of Russia, Ed. by Yu. A. Izrael’ and N. G. Rybal’skii (Moscow, 2012), p. 46 [in Russian].

MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

No. 6

2015

ON THE ORIGIN OF A ZONE 20. Yu. V. Barkin, in Physical Problems of Ecology (Ecological Physics), Ed. by V. I. Trukhin, Yu. A. Pirogov, and K. V. Pokazeev (MAKS Press, Moscow, 2013), Vol. 19, p. 54. http://ocean.phys.msu.ru/ecophys/ecophys19_pp3-180.pdf 21. A. M. Dziewonski and D. L. Anderson, Phys. Earth Planet. Inter. 25, 297 (1981). 22. H. Thybo, Tectonophysics 416, 53 (2006). 23. F. Riguzzi et al., Tectonophysics 484, 60 (2010). doi 10.1016/j.tecto.2009.06.012 24. Yu. V. Barkin, Astron. Astrophys. Trans. 18, 751 (2000). http://images.astronet.ru/pubd/2008/09/28/ 0001230490/751-762.pdf 25. Yu. V. Barkin, Astron. Astrophys. Trans. 18, 763 (2000). http://images.astronet.ru/pubd/2008/09/28/ 0001230496/763-778.pdf

MOSCOW UNIVERSITY PHYSICS BULLETIN

Vol. 70

557

26. Yu. V. Barkin, Astron. Astrophys. Trans. 19, 1 (2000). http://images.astronet.ru/pubd/2008/09/28/0001230498/ 1-11.pdf 27. V. N. Zharkov, Internal Structure of the Earth and Planets (Moscow, 1978) [in Russian]. 28. T. V. Gudkova, P. Lognonne, V. N. Zharkov, and S. N. Raevsky, Sol. Syst. Res. 48, 11 (2014). 29. Yu. V. Barkin, presented at The European Planetary Science Congress (Potsdam, Germany, 2009). http://meetingorganizer.copernicus.org/EPSC2009/EPSC2009118-1.pdf

Translated by E. Petrova

No. 6

2015