On Some Global Problems of Geophysical Fluid Dynamics (A Review)T (Gravitational Differentiation/Rotational Pole/Mantle Convection) A

Proc. Nati. Acad. Sci. USA Vol. 75, No. 1, pp. 34-39, January 1978 Geophysics

On some global problems of geophysical fluid dynamics (A Review)t (gravitational differentiation/rotational pole/mantle convection) A. S. MONIN P. P. Shirshov Institute of Oceanology, Academy of Sciences of the Union of Soviet Socialist Republics, Moscow, Union of Soviet Socialist Republics Contributed by A. S. Monin, September 28,1977 The development of the earth sciences during recent years has of the moon, the sun, and other planets are not taken into con- been associated with a wide use of geophysical fluid dynamics sideration. These simplifications do not distort too much the (i.e., the dynamics of natural flows of rotating baroclinic class of motions inside the earth that we are interested in; if stratified fluids), a discipline whose scope includes turbulence necessary, the simplifications can be removed by the intro- and vertical microstructure in stably stratified fluids, gravity duction of appropriate corrections. Equations of motion are waves at the interface, internal gravity waves and convection, written for each of the layers, with the right-hand parts con- tides and other long-period waves, gyroscopic waves, the hy- taining volume forces associated with the presence of the drodynamic theory of weather forecasting, circulations of the gravity and magnetic fields and stresses of the viscous and planetary atmospheres and oceans, the dynamo theory of the magnetic origin. A magnetohydrodynamic equation of the generation of planetary and stellar magnetic fields, etc. magnetic field evolution (induction equation) should be added to the equations of motion. The energetics of the processes in the layers under consideration can be represented by mutual POTENTIAL VORTICITY transformations of kinetic, magnetic, and internal energies. The One of the basic notions in geophysical fluid dynamics, com- equation for kinetic energy density of each of the layers contains bining fluid rotation and stratification nonlinearly, is the po- the terms describing mutual transformations of kinetic and tential vorticity potential energy in the gravity field and viscous dissipation of kinetic energy. The equation for energy density of the magnetic Q = p-1 rot u grad n, field contains in its right-hand side the terms describing ohmic in which u is the absolute velocity of fluid motion, p the density, dissipation of the magnetic field energy (i.e., joule heat gen- v the specific entropy; Q is the invariant of fluid particles in their eration) and mutual transformations of kinetic and magnetic adiabatic motions (see, for instance, ref. 1). The evolution of the energy owing to the action of Maxwell field stresses (pondero- Q and q fields is the main object of study in the hydrodynamic motive forces). The thermodynamic equation for the density theory of weather forecasting [2, 3]. of internal energy contains the terms describing the dissipation The similar object in magnetic field dynamics is the "mag- of viscous and magnetic stresses, heat flux generated by con- netic field charge" ductivity of the medium, external heat sources inside the earth (including radioactivity), and energy dissipation of the pre- X = p-1H grad I, cession and tidal motions. Integrating these equations over the in which H is the magnetic field intensity; the quantity X is also volumes of the mantle, the liquid layer, and the solid core (the the adiabatic invariant of moving particles. The evolution of indices introduced further correspond to this succession) results the If field should be the principal object in the dynamo theory in nine expressions for kinetic K, magnetic M, and internal E of the generation of magnetic fields of celestial bodies (1, energy of each of the three layers. A diagram of energy trans- 4-6). formations is shown in Fig. 1 (potential energy of the liquid More detailed equations of the hydrodynamic theory of the layer P2 and energy of the geomagnetic field outside the earth geomagnetic field generation are considered in refs. 7 and 8, MO are also introduced there). The diagram shows the estimates in which the motions inside the Earth are described as made of energy components (in joules/100 years) obtained in ref. 8. up of the mantle rotation (observed by the astronomical One of the most interesting elements of the diagram is the rate methods and usually called the earth's rotation), magnetohy- of transformation K2 -* M2 describing the geomagnetic field drodynamic flows in the liquid layer ("liquid core"), and the generation by the dynamo mechanism in the liquid layer. displacement and rotation of the internal solid core. The motions of these three layers interact due to hydromagnetic stresses GRAVITATIONAL DIFFERENTIATION at the internal and the external boundaries of the liquid layer As the second example of the use of the geophysical fluid dy- and the deformations of the gravity field with the displacements namics let us consider, following refs. 9-13, the problem of of the internal core. The model suitable for the study of the gravitational differentiation of the interior of a spherically dynamics of these three layers was considered in refs. 7 and 8. symmetric and initially homogeneous planet consisting of two It contains three simplifications: (i) rheological-the mantle components: light "mantle" and heavy "core" ones. The and the internal core are assumed to be absolutely solid, which question in essence concerns the Earth's evolution-the for- excludes from consideration some types of internal motions in mation of its core and mantle, the process giving the basic them (elastic oscillations, tidal deformations, and convective to the balance of the The in- motions in the mantle and the continental drift they produce); contribution energy planet (14). (ii) geometric-the mantle and the internal core are assumed Abbreviation: TME, tectono-magmatic epoch. to be spherically symmetric bodies, so that, in particular, their t By invitation. From time to time, reviews on scientific and techno- flattening due to rotation (and hence the ability for precession) logical matters of broad interest are published in the PROCEED- is not taken into account; (iii) dynamic-gravitational effects INGS. 34 Downloaded by guest on September 27, 2021 Geophysics: Monin Proc. Natl. Acad. Sci. USA 75 (1978) 35

FIG. 1. Diagram of the Earth's energy transformation.

ternal structure of such a planet at different stages of its evo- with the parameters pi, al, and L chosen from the available lution can be estimated with the aid of the hydrostatic equation, information on the Earth's contemporary structure. The local which, with neglect of rotation, has the form equation of a planetary state is reduced to the form dp= Gm 2i7rGL m = 22Ck1= _p; g=2= 4 pr2dr. p = (p2 a F dr= Jo 272Ca a2ps2); k=ikark Here and further, p is the pressure, p the density, g the accel- The solutions of the hydrostatic equation in every chemically eration r con- of gravity, the radial coordinate, G the gravity homogeneous layer are given by the general integral stant. Under barotropic approximation (assumed for solid planets) the knowledge of the equation of state p = p(p) of 1 ar planetary material is sufficient for integrating the hydrostatic p=-(Asin.++Bcost); = L equation. Taking into account that the density variations in the planets of the solar system lie within a small interval of values The coefficients A and B can be found from the condition of 2 < p < 15 g/cm3, let us approximate the equation of state of continuity of pressure and the acceleration of gravity at the = each of the planetary composing materials by parabolas interfaces. Without loss of generality it can be put a2 1 and ail > 1. Let the planetary "core" material concentration be cl= c; then the "mantle" material concentration will be P = P1,2(P) = a,2Po(P); Po(P) = (P2 + 27rL2) C2= 1 - c. At some stage of the differentiation process char- Downloaded by guest on September 27, 2021 36 Geophysics: Monin Proc. Natl. Acad. Sci. USA 75 (1978)

Table 1. Calculated values for various parameters of Earth during its evolution

ri, r2, Pc, P+, P, Pc, P 1, II, x km km g/cm3 g/cm3 g/cm3 TPa TPa I/I. 1031 J 0 0 6393 11.34 0.230 - 1.12 0.89 0 0.2 2091 6386 12.38 10.86 7.43 0.289 0.204 1.09 0.92 0.32 0.4 2652 6381 12.93 10.45 6.96 0.323 0.183 1.06 0.94 0.73 0.6 3043 6376 13.38 10.05 6.48 0.351 0.163 1.03 0.97 1.11 0.8 3361 6372 13.75 9.65 6.00 0.375 0.144 1.01 0.99 1.49 0.863 3451 6371 13.86 9.52 5.84 0.382 0.138 1 1 1.61 1 3635 6368 14.08 9.25 5.50 -0.397 0.125 0.98 1.02 1.86 acterized by the fraction x of the already differentiated material proportional to the average concentration of core material in (the core mass is cxM) the average concentrations of the mantle the mantle: - and core material in the mantle are (1- c)/(1 - cx) and (c - cx)/(1 - cx), respectively, and the equation of state for the cM-= 47rkr12 C - CX mantle material has the-parabolic form with-the parameter dt 1 -Cx' in which k ifthe coefficient of proportionality, assumed to be A p ~~1-Cx constant. Integrating this equation simultaneously with the a(3ai; ~=ai(1 - C) + c(1 - X remaining equations of the model gives x(t) for all the planets The radial distributions of density and pressure for an arbitrary of interest here, and the assumption-of their simultaneous for- planet of mass M at the stage x contain five unknown param- mation makes it possible to determine the coefficient k from eters aip,, L/a1, fi, and the radii of the core and the entire the earth's age (4.6 billion years at x = 04863), which turns out planet, ri and r2. The mass fixation of the core cxM and the to be equal to 3.34 g/cm2 year (10,11). mantle (1- cx)M, as well as the moment of inertia 5 yield three Table 2 contains tie results of thecomputations of the state equations, the simultaneous solution of which makes it possible and evolution parameters for the terrestrial planets, giving only to find the constants a,, ps, L (see ref. 9). For the contemporary the values corresponding to their present evolutional age. From state of Earth, M = 5.98 X 102 g, r2 = 6371 km; the dimen- Fig. 2, which shows the evolutional curves-x(t), it is easily seen sionless moment of inertia S1 = 0.3308; r, = 3451 km; the rel- that for Earth x* = 0.863, for Venus x* = 0.920, and for Mars, ative core mass cx = 0.3218. It has been assumed that the con- Mercury, and the Moon x* - 1. Table 2 also contains the times temporary earth's mantle consists of Ringwood pyrolite, and tm of the maximum value of dx/dt, which can apparently be that Fe2O, according to ref. 15, is the core material. In thisway identified, as a first approximation, with the time of the highest the values obtained were a, = 1.681; L= 4017 km; p, = 3.42 tectonic activity in the planetary interiors (for Earth t1-= 3.25 g/cm3; c = 0.373; and the Contemporary value of the evolu- billion years, which corresponds to the-Gothic tectono-mag- tional parameter x = 0.863. Knowing the parameters of tihe matic epoch); these times are marked with circles on the curves. model, one is able to calculate the structure of any planet of The values of t o in Table 2 correspond to x: t 1, i.e., to the time mass Mj with the "core" material concentration CG at any stage of decay of the gravitational differentiation process. Proceeding of the gravitational differentiation process 0 < x < 1. The from these data, it is believed that tectonic processes will con- above-mentioned algorithm was applied, apart from Earth, to tinue for some 1.9 billion years more on Earth and for some 1.3 the terrestrial planets: Mercury, Venus, Mars, and the Moon billion years more on Venus, whereas on Mars, Mercury, and (10-13); the parameters Cj were chosen so that the known the Moon these processes ceased 0.5, 4 and 2.5 years ago, re- planetary radii are obtained.t Besides, for all the planets the spectively. Note also a sharp decrease of the released gravita- moments of inertia 9 and released potential energy II were tional energy II as the planetary dimensions diminish (H - calculated at different values of the evolutional parameter x. M5/3). From this it follows that radiogenic heat sources (the total The calculation results for the Earth are presented in Table 1. power of which is -M) play an essential role in the heat balance It is seen from the table that as x grows the core radius r1 nat- of minor planets. urally grows, pressure Pi and densities p1+ and Pi- at the core boundary decrease, and pressure and density in the core center WANDERING ROTATIONAL POLE (pc and Pc) increase noticeably. The Earth's moment of inertia Our third example refers to the problem of the wandering of for the whole history decreases by 14%. Only an insignificant Earth's rotational pole, which has become classical. Let us contraction (the Earth's radius decrease) equal to 25 km for the consider this question following our recent work (17). The whole history of the Earth's evolution takes place. The potential present paleomagnetic and paleoclimatic data give an idea only energy released by the present time [4.6 billion (= 109) years] of relative displacements of the pole with respect to the Earth's II = 1.6 X 1031 J is 80% in excess of radiogenic heat estimated surface area from which samples serving as indicators have been in ref. 16, yet their sum is insufficient for a complete melting taken. The problem has become more precise due to the suc- of the Earth. cesses of mobilism, which assumes the displacement of lithos- To obtain the dependence on time of all the calculated pa- pheric plates with respect to each other. Lack of coincidence rameters, it is necessary to know the law x(t). The law can be of the polar wandering trajectories constructed relative to dif- constructed, as a first approximation, if, following ref. 15, it is ferent plates gives forcible arguments in favor of mobilism, assumed that the reaction of a heavy component deposition at leaving open the question of the absolute displacement of the the core-mantle boundary is a surface one and that its rate is pole and hence the plates themselves. A possibility of consid- erable displacements of the Earth with respect to the axis fixed * The use of the two-component model does not allow an accurate in the stellar space is closely related to inelastic properties of the computation of the Moon's evolution; for this purpose the intro- the surface must be duction of a third, lighter, crustal material is required. Here the data mantle, because polar shifts over Earth's are presented on the evolution of the quasi-Moon, a planet with lunar accompanied by the corresponding displacements. of the mass and the lunar concentration of iron. equatorial bulge; the main reason for such movements is an Downloaded by guest on September 27, 2021 Geophysics: Monin Proc. Natl. Acad. Sci. USA 75 (1978) 37

Table 2. State and evolution parameters of the terrestrial planets XX tMI t.os r*, r2, ri, Pc, P1 +, P1-, Pc, P1, 1044 Y/M. H 109 109 No. Planet M/M1 km c % Fe km km g/cm3 g/cm3 g/cm3 TPa TPa g-cm2 r22 1031 J yr yr 1 Earth 1 6371 0.373 32.6 6371 3451 13.86 9.52 5.84 0.382 0.138 8.029 0.3308 1.610 3.25 6.46 2 Venus 0.815 6050 + 0.358 31.3 6051 3342 12.54 8.83 5.35 0.298 0.108 5.950 0.3337 1.154 2.94 5.93 5 3 Mars 0.10766 3394 i 0.183 16 3393.4 1615 6.99 6.47 3.85 0.0377 0.209 0.274 0.3712 0.0167 1.65 4.03 2 4 Mercury 0.0543 2439 i 0.792 69.3 2438.8 2144 6.76 5.89 3.50 0.0303 0.0038 0.0703 0.3639 0.00748 0.47 0.66 2 5 Quasi- 0.0123 1738 0.149 13 1680 759 6.02 5.91 3.52 0.0075 0.0046 0.0079 0.3778 0.000228 0.86 2.13 Moon irregular distribution of the Earth's masses with respect to the the continents and the oceans. Preserving in Liouville equation equatorial bulge (the existence of the continents and the oceans) only terms with the large factor Q and with the excitation (6, 18). function M', it can be reduced to the form dm/dt = M'/2QC, It is possible to calculate the proper motion of the poles with or, taking into account the expression for I'qj, to the form the aid of Liouville equation (dM/dt) + w X M = 0 expressing dmn the angular momentum M conservation law for the Earth ro- |s(k)n(k)(m * n (k)) C(m * n)ndS}, tating with an angular velocity c and written in the dynamic dt k S frame of reference rigidly associated with the Earth as a whole, in which k = wN/2QC, n(k) = m(t) + p(k(t), p(k)(t), the so that the function m(t) = wi describes polar wandering (the designated relative vectorial coordinates of the centers of rotation velocity w is assumed to be approximately constant gravity of the continental blocks counted from the paleopoles during the Phanerozoic period). Considering the Earth as a (according to Munk (ref. 18), N = 1.78-1039 cm g s; then K = viscoelastic Maxwell body with relaxation time T small com- 0.784.1023/n cm g s). If the continental block is only one we pared to the typical time of polar wandering, its approximate have T. Gold's problem on polar wandering under the action angular momentum can-(6, 18) be written in the form of a "beetle" crawling over the Earth's surface. If the continents dm 19 C-A do not move, so that all n(k) do not depend on time, we have the -M UC (m _2Q + Me, Q = (A7 problem of G. Darwin, M. Milankovitch, I. Burgers, and D. ()dt 4 pgR C Inglis on the wandering of poles towards their equilibrium Here C is the moment of inertia with respect to the rotation axis, position (for the contemporary distribution of the continents Q the dimensionless effective viscosity of the mantle [q is the it was determined by M. Milankovitch and W. Munk). Our dimensional viscosity, R the Earth's radius, (C - A)/C the equations give a problem on polar wandering under the action dynamic contraction; at v =o102 Pa-s (1 Pa-s = 10 poise) Q of several crawling "beetles" whose movement is predeter- 105], and M' the vector with the Cartesian components I'd wj. mined only with respect to the wandering poles. It is the additional inertia tensor created by the distribution of As the initial information about the relative movement of the continents and the oceans, which is determined by the plates p(k)(6,X) = f8(k)(t),X(k)(t)l (X is the eastern longitude, 0 the equation colatitude in the paleopole system), Gorodnitsky and Zonen- shain's (19) paleogeographic reconstructions were used. Thus, Fj = -N {E Sk(k)nj(k)- SninjdS}; there were relative trajectories of 14 paleostable blocks for the - Phanerozoic period (570 billion years). Under the fixed present N = (pc - po)r4dr, position of the continents the equilibrium position of the in which n is the unit vector of arbitrary direction (from the northern pole was at a point with coordinates 0 = 62°, X = 1900, Earth's center), n(k) the direction to the center of gravity of the which is in quite good agreement with the results of the previous kth continental block, S(k) the area of this block (Sc the total area authors. Given the relative trajectories of the continental blocks, of all the the integration of our equations was performed at different blocks), S the Earth's surface area (dS its differential), values of the parameter K corresponding to the mantle's ef- and pc(r) and po(1) the typical vertical density profiles beneath fective viscosity from the interval of 1018 to 1024 Pass. For the optimum choice of k (and hence effective viscosity) a varia- tional principle related to the least-action principle was used: the value of K delivering the minimum total kinetic energy of the absolute displacements of continental blocks was sought. Such a value was found to be K =0.133, which corresponds to viscosity ii = 5.9-1022 Pass. North pole absolute trajectories in the contemporary geographic coordinate system are shown in Fig. 3. The minimum total energy trajectory (solid line) indicates that the pole shifted from a position close to the contemporary one approximately along the 180° meridian and returned back along a somewhat western trajectory slightly turning to the zero meridian side, 3 4 so that it looks as though a second loop started recently. The loop t, billion years is 860 long, and this result can be interpreted from the point of FIG. 2. Evolutional curves x(t) ofthe terrestrial planets. Numbers view of the large-scale cellular convection in the Earth's mantle for the planets are as in Table 2. The broken line indicates the (15, 17, 20). In fact, under axisymmetric convection in a uni- present. cellular regime the continents should crowd around the subsi- Downloaded by guest on September 27, 2021 38 Geophysics: Monin Proc. Natl. Acad. Sci. USA 75 (1978)

,|.:i I - i as 1 Al-;.

40c .150- / / f / i 50} / i

60C 140' / .' FIG. 3. Absolute displacements of the north pole (in the contemporary geographic system of coordinates) under three values for the Earth's effective viscosity. Values for k are on the right of the trajectories.

dence pole and the convection axis tends to become perpen- density convection penetrating the entire mantle and created dicular to the rotation axis; in a bicellular regime with closed by the gravitational differentiation of heavy (iron) and light cells the continents drift apart to the subsidence equator, and (silicates) materials at the lower boundary of the mantle, where the convection axis tends to coincide with the rotation axis. the mantle is in contact with the melted external layer of the Oscillations between these regimes with their axis of symmetry Earth's core. From fluid dynamics it is known that slow laminar preserved should result in periodic displacements by 900 of the convective motions are arranged horizontally into cells. It is rotation poles from the convection poles to its equator and back. natural to suppose that the alterations of the tectono-magmatic The loop in Fig. 3 shows a good fit to the oscillation pattern of epochs (TME) apparent at the Earth's surface can be created the convection regimes in the Earth's mantle (with the Phan- through the transformations of the forms of the convective cells erozoic sequence bicellular-unicellular-bicellular regime). in the Earth's mantle. Knowing the absolute polar trajectory, it is not difficult to The historic sequence of the forms of convection in the construct absolute trajectories of all the continental blocks under Earth's mantle could be the following. It reached intensity consideration. This procedure has shown that instead of the sufficient for breaking the protogenic lithosphere cooled by heat tendency towards the northern components of relative dis- emission to the outside to form the first rifts and plate subduc- placements, there appears another regularity on the absolute tion zones and make a start for magmatic outflows, mantle trajectories-rapid displacements along very smooth trajectories during the Lower Paleozoic and looplike "marking time" during the Meso-Cenozoic that might be completed by now; this pattern corresponds quite well to the oscillations between 150 the unicellular and the bicellular convection regimes. TECTONO-MAGMATIC PROCESSES The oscillations between the unicellular and the bicellular convection during the Phanerozoic period make possible an *'W100 assumption that such oscillations occurred during the Pre- EM. cambrian time too. An attempt was made in ref. 20 to use such oscillations for establishing tectonic periods in the Earth's his- 0 tory, which naturally divides itself into epochs of high and low 50 intensities of tectono-magmatic processes measured by the quantity of volcanic and metamorphic rocks of the corresponding age in the Earth's continental crust. The histogram constructed by Dearnley (21) to show the ages of such rocks (Fig. 4) reveals four maxima with the ages of 2.6, 1.9, 1.0, and 0.4-0.25 billion years. -4 -3 -2 -1 0 The tectono-magmatic processes observed at the Earth's Billion years surface are, undoubtedly, a reflection of the deep processes. FIG. 4. Histogram of the ages ofvolcanic and metamorphic rocks According.to the modem plate tectonics theory, the basis of the [after Dearnley (21)]. Tectono-magmatic activity is given in terms of deep processes is convection in the Earth's mantle; as assumed relative amounts of volcanic and metamorphic rocks in the Earth's by 0. G. Sorokhtin, V. P. Keondjian, and A. S. Monin, this is continental crust. Downloaded by guest on September 27, 2021 Geophysics: Monin Proc. Natl. Acad. Sci. USA 75 (1978) 39 degassing, and hydrospheric condensation, probably Asey:- Pernmian; see the seeond peak of the fourth maximum in Fig. as the Catarchean time during the second half-billion years of 4) they united with Gondwanaland to form the fourth super- the Earth's existence. Evidence in favor of this was found in continent in the Earth's history-Pangea of A. Wegener. After southwest Greenland in the form of the most ancient volcanic that a bicellular convection developed again, which broke (granitoid gneiss) and sedimentary (limonite) rocks, with ages Pangea during the Kimmeriyskaya TME and is continuing now of about 3.8 billion years (this may be their metamorphization to move Pangea's fragments apart. age, and their formation may be still older). During the Belo- The assumed scheme outlined above includes 9 convective zerskaya TME in the Early Archean (3.5 billion years) and the form successions in the Earth's mantle, dividing its tectonic Kolskaya TME in the Middle Archean (3 billion years) the first history into 10 epochs (a bicellular Lower Archean epoch might islets of the continental crust with plagiogranites and granite be identified additionally). An extra support for the Phanerozoic migmatites were formed (during the 3.5- to 3-billion-year pe- part of this scheme can be given by the bicellular form of the riod convection might be bicellular). The maximum intensity contemporary geoid with two poles of negative anomalies (near in the unicellular convection was reached, probably, during the New Guinea and in the North Atlantic) and a wide zone of Kenoranskaya TME in the Late Archean (2.6 billion years). This positive anomalies along the equator, corresponding to these is the first maximum on Dearnley's histogram (Fig. 4); at that poles. time within the framework of the primary supercontinent the cores of all future continental platforms were formed. 1. Monin, A. S. (1974) "On the equations of geophysical fluid dy- After that, there might appear a form with two closed cells namics," Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 10, that broke the 119-126. primary supercontinent and existed during the 2. Monin, A. S. (1972) Weather Forecasting as a Problem in Physics whole Lower Proterozoic until the Baltic TME (1.9 billion years, (Nauka, Moscow). the second maximum on Dearnley's histogram). Then again a 3. Monin, A. S. & Gavrilin, B. L. (1976) "Hydrodynamic weather unicellular convection developed that combined all the ancient prediction," in Theoretical Applied Mechanics, ed. Koiter, W. continents into the secondary supercontinent, the Megagea of T. (North Holland, Amsterdam). H. Stille, and reached the greatest intensity during the Karel- 4. Monin, A. S. (1971) "On the description of slow magnetohydro- skaya TME (1.7 billion years), which marked the completion dynamic processes," Dokl. Akad. Nauk SSSR 200,21-93. of the formation of the ancient continental platforms. 5. Gavrilin, B. L. & Monin, A. S. (1972) "On possibilities of the After the Karelskaya TME the character of the Earth's crustal calculation of the geomagnetic field evolution," Dokl. Akad. development changed: bicellular convection might be formed, Nauk SSSR 205, 1349-1351. 6. Monin, A. S. (1974) Earth's Rotation and Climate (Radok- in the Lower Riphean with closed cells and in the Middle Ri- Radhakrishnan, Delhi). phean, after the Gothian TME that created in the Earth's crust 7. Monin, A. S. (1973) "On the Earth's internal rotation," Dokl. a new system of mobile belts (the "great renovation" of the Akad. Nauk SSSR 211, 1037-1100. Earth's crust structural plan, the beginning of the Neogean), 8. Gavrilin, B. L. & Monin, A. S. (1974) "On the rotation of the with open cells (and a tendency towards the formation of two Earth's internal layers," Izv. Acad. Sci. USSR, Phys. Solid Earth, supercontinents near the subsidence poles on the rotation Eng]. Ed., No. 5,293-296. equator). It is believed that such a bicellular convection did not 9. Keondjian, V. P. & Monin, A. S. (1975) "Model of gravitational exist very long relatively and by the Middle Riphean it had been differentiation of the planetary interiors," Dokl. Akad. Nauk replaced by the unicellular one that reached the maximum SSSR 220,825-829. intensity during the 10. Keondjian, V. P. & Monin, A. S. (1975) "Model of the evolution Grenville TME (1 billion years, the third of the terrestrial planets," Dokl. Akad. Nauk SSSR 223, 599- maximum on Dearnley's histogram). The possible formation 602. at that time of the Tertiary supercontinent is attested by the 11. Keondjian, V. P. & Monin, A. S. (1977) "Calculations of the ev- consolidation and adjoining to the Epikarelian platforms of olution of the planetary interiors," Tectonophysics 41, 227- geosyncline belts initiated during the Early Neogean. 242. The Middle Riphean unicellular convection existed, proba- 12. Keondjian, V. P. & Monin, A. S. (1976) "Calculation of the evo- bly, until the Delhi TME (850 million years) and was replaced lution of the planetary interiors," Izv. Akad. Nauk SSSR, Physics by the bicellular convection with closed cells before the Ka- of the Earth 4,3-13. tanginskaya (Early Baikal) TME (650 million years) and then, 13. Keondjian, V. P. & Monin, A. S. (1976) "On the evolution of the possibly, the one with open cells before the Salairskaya (Late terrestrial planets," Gerlands Beitr. Geophysik, Leipzig 85, 169-174. Baikal) TME (520 million years), as a result of which the 14. Monin, A. S. (1977) History of the Earth (Nauka, Leningrad). Gondwana supercontinent was formed near one of the subsi- 15. Sorokhtin, 0. G. (1974) The Global Evolution of the Earth dence poles (whereas the continental platforms of the northern (Nauka, Moscow). hemisphere probably did not manage to gather around the 16. Lubimova, E. A. (1974) Thermics of the Earth and the Moon second subsidence pole). (Nauka, Moscow). Subsequently, the bicellular form seems to have been re- 17. Keondjian, V. P. & Monin, A. S. (1977) "On polar wandering due placed by the unicellular one, so that one of the old subsidence to continental drift," Dokl. Akad. Nauk SSSR 233, 316-319. poles in Gondwanaland was preserved, while the other, in the 18. Munk, W. H. & MacDonald, G. I. (1960) The Rotation of the northern hemisphere, was replaced by the uplift pole that set Earth (Cambridge Univ. Press, London). the northern continental platforms in motion towards Gond- 19. Gorodnitsky, A. M. & Zonenshain, L. P. (1977) "The Paleozoic and Mesozoic reconstructions of the continents and the oceans," wanaland. During the Caledonian TME (with the maximum Geotectonics 11,83-94. at about 400 million years; see the first peak of the double fourth 20. Monin, A. S. & Sorokhtin, 0. G. (1977) "On tectonic periods in maximum on Dearnley's histogram) they came into collision the Earth's history," Dokl. Akad. Nauk SSR 234, 413-416. and formed Laurasia and then, during the Gertsinskaya TME 21. Deamley, R. (1966) "Orogenic fold-belts and hypothesis of Earth (with the maximum at about 260 million years during the Early evolution," Phys. Chem. Earth 7, 1-114. Downloaded by guest on September 27, 2021