Planetary Sciences: American and Soviet Research/Proceedings from the U.S.-U.S.S.R. Workshop on Planetary Sciences (1991)

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The Thermal Conditions of Venus VLADIMIR N. ZHARKOV AND V.S. SOLOMATOV Schmidt Institute of the Physics of the Earth ABSTRACT This paper examines models of Venus' thermal evolution. The models include the core which is capable of solidifying when the core's temperature drops below the liquidus curve, the mantle which is proposed as divided into two, independent of the convecting layers (upper and lower mantle), and the cold crust which maintains a temperature on the surface of the convective mantle close to 1200°C. The models are based on the approximation of parametrized convection, modified here to account for new investigations of convection in a medium with complex rheology. Venus' thermal evolution, examined from the point when gravitational differentiation of the planet was completed (4.6 billion years ago), is divided into three periods: (1) adaptation of the upper mantle to the thermal regime of the lower mantle: approximately 0.5 billion years; (2) entry of the entire mantle into the asymptotic regime approximately three to four billion years; (3) asymptotic regime. The parameters of a convective planet in an asymptotic regime are not dependent on the initial conditions (the planet "forgets" its initial state) and are found analytically. The thermal flux in the current epoch is ~50 ergs cm2s-~. We consider the connection between the thermal regime of Venus' core and its lack of magnetic field. After comparing the current thermal state of thermal models of Venus and Earth, together with the latest research on melting of the Fe-FeS system and the phase diagram of iron, we propose that Venus' lack of its own magnetic field is related to the fact that Venus' core does not solidify in the contemporary epoch. The particular situation of the iron triple point (y - - melt) strengthens this conclusion. We discuss the thermal regime of the 174

AMERICAN AND SOVIET RESEARCH 175 Venusian crust. We demonstrate that convection in the lower portion of the crust plays a minor role in regions with a particular crust composition, but that effusive or intrusive heat transport by melt, formed from melting of the crust's lower horizons, is the dominant mechanism for heat transport to the surface. MODIFIED APPROXIMATION OF PARAMETRIZED CONVECTION Models of Venus' thermal evolution, calculated in approximation of parameterized convection (APC), were examined in the works of Schubert (l979~; lbrcotte et al. (~1~79~; Stevenson et al. (1983~; Solomatov et al. (1986~; and Solomatov et al. (1987~. In parameterizing, dependencies were used that were obtained from studying convection in a liquid with constant viscosity. They were inferred to be true in cases of more complex rheol- ogy. New numerical investigations of convection in media with rheology that is more appropriate for the mantle (Christensen 1984a, b, 1985a, by and theoretical research (Solomatov and Zharkov 1989) necessitated the construction of a modified APC (MAPC). Let the law of viscosity be expressed as (Zharkov 1983~: ~ = b/Tm-i exp [Ao/T (`p/po`) ] (1) where T denotes the second invariant of the tensor of tangential stresses, p is density; b and L are considered here to be the constants within the upper and lower mantles; m ~ 3; Ao denotes the enthalpy of activation for self diffusion (in K); and where p = pO is the reference value of density selected at the surface of each layer. 1b describe convection in such a medium, following Christensen (1985 a), we will use two Raleigh figures: R ttgp^Td3 (2) R c~gp/\Td3 `3' XrlT where ~ denotes the thermal expansion coefficient; g is the acceleration of gravity; AT is the mean superadiabatic temperature difference in the layer; d denotes layer thickness, X is the coefficient of thermal diflusivi~; and ale and AT are defined by the formulae: b Ao To = _~ exp T ; To = 0° d2 ~ Ao ~~ p )L x . (4) (5)

176 PLANETARY SCIENCES The dependence of the Nusselt number (determined in terms of the thickness of the thermal boundary layer b) on RaO and RaT, where m = 3, is parameterized by the formula Nu = 2f' = a]?~a§°Ra§T. In the case of free boundaries (lower mantle): a = 0.29 ,BO = 0.37, AT = 0.16. In the case of fixed boundaries (upper mantle): a = 0.13, ,l]O = 0.35, AT = 0.15. {~6) (7) (~8) The theoretical expression has the following appearance (Solomatov and Zharkov 1989~: 2`m+2'RaO RaT+2 =0.23Ra°4Ra02 (9) It is obtained from the balance of the capacities of viscous dissipation and buoyancy forces, and is in good agreement with (7) and (8~. The heat flow at the upper or lower boundary of the layer is equal to F. _ aeATi ~— ~ , (10) where ATi denotes the temperature difference across the thermal boundary layer. Velocities at the boundary (u), mean tangential stresses in the layer (~) and mean viscosity (~) are estimated by the formulae (mum: or ~d2 a= 4 6, T = (7'7lbe~ A ~ p ~ ) 71 =—r exp _° (I P ~ (11) (~12) t`13) The mean temperature of the layer, T. and the temperature of the top of the lower thermal boundary layer, To;, can be calculated from the adiabatic relationship through the temperature in the base of the upper thermal boundary layer, Tu: T = nTu; To = natty' where n and no are constants. (~14)

AMERICAN AND SOVIET RESEARCH 177 With large RaT/RaO, the very viscous upper thermal boundary layer becomes reduced in mobility, taking an increasingly less effective part in convection, and the previous formulae are not applicable. Solomatov and Zharkov (1989) estimated that the transition to a new convective regime occurs when RaT > RaT'r ~ 2Ra2; m = 3. DESCRIPTION OF THE MODEL (15) There is no unequivocal answer to the question of whether convec- tion in the Earth's mantle (or Venus') is single layered or double-layered. Previous works explored the single-layered models of convection. Possi- ble differences in the single- and double-layered model of Venus' thermal evolution were discussed by Solomatov et al. (19863 and Solomatov et al. (1987~. We propose here that convection is double-layered, and the bound- ary division coincides with the boundary of the second phase transition at a depth of approximately 756 kilometers (Zharkov 1983~. The thermal model of Venus (Figure la) contains a cold crust, whose role is to maintain the temperature in its base at approximately 1200°C (melting temperature of basalts), the convective upper mantle, the con- vective lower mantle, and the core. An averaged, spherically symmetric distribution, T (r,t) is completely determined by the temperatures indicated in Figure lb. The thermal balance equations for the upper mantle, the lower mantle, and the core are written as: 31r(Rr—R32)piCpi~i =4~Ri2Fi2 - 4~R~F~, (16) 3,r(R32—R3)p2Cp24~2 = 3~(Ri2 ~)P2Q2 - 4~R22F2l + 4~R2Fc' (17) —3,,R3CpCpc4tc + QC 1t = 4~R2Fc. (18) Indices "1," "2," and "C" relate, respectively, to the upper mantle, lower mantle and the core. T denotes the mean layer temperature, Fit is the heat flow from the mantle under the lithosphere. The heat flow at the surface of the planet is obtained by adding to Fit, thermal flow generated by the radiogenic production of heat in the crust (~11 erg cm~2s~~. The radius of the lithosphere boundary (R~) differs little from the radius of the planet (Ro) so that RL ~ Ro. It is supposed that almost all of the radioactive elements of the upper mantle migrated into the crust when the

178 dL ~cr RO ~~ ~ ;~ TB - 1200°C R,2 ~ \ convective lover mantle liquid outer core _ / solid Rj ~ ~ inner \ ~ core V (a) PLANETARY SCIENCES | T | Tm (r' '\\ 1 l\\ - 6CL \Tu2 1 1 (b) LT.2 W62P: 1I L' l\TR= 1~0°C ~11 Hits = 460°C ' I I I I ~ O Rj RC R12 RL RO R FIGURE 1 (a) Diagram of Venus's internal structure. Radii are indicated for: the planet Ro; the base of the lithosphere- RL; the boundary between the upper and lower mantles R12; the core Rc; and the solid internal core Ri. The dashed line illustrates the boundary of the lithosphere, which is an isothermic surface of TB = 1200°C = eonst; dCr and dL denote the thickness of the crust and the lithosphere. (b) Schematic, spherically symmetric temperature distribution in the cores of Venus. Reference temperatures are indicated for: the surface Ts; lithosphere base TB; base of the upper thermal boundary layer of the upper mantle Tut; peak of the lower boundary layer of the upper mantle TL1; boundary between the upper and lower mantles T12; base of the upper boundary layer of the lower mantle TU2; peak of the lower boundary layer of the lower mantle TL2; and the boundary between the core and the mantle Tom. Thicknesses of the thennal boundary layers are given: 51 for the boundaries of the upper mantle; 52 and [c for the boundaries of the lower mantle. The dashed line indicates the core melting curve, which intersects the adiabatic temperature curve at the boundary between the outer, liquid and inner, solid core. crust was melted. Fc denotes the heat how from the core. The heat flow at the boundary between the upper and lower mantles with a radius of R12 is continuous: F:2 = F21. Heat production in the lower mantle (Q2) is defined by the sum 4 Q2 = ~ QoiExp [Ai (to—t)] i=1 (19) where Qoi and Ai denote the current heat production of the radioactive

AMERICAN AND SOVIET RESEARCH 179 isotopes K' U. and Th for one kilogram of undifferentiated silicate reservoir of the mantle and their decay constants. The concentrations of K, U. and Th are selected in accordance with O'Nions et al. (1979~: U = 20 mg/t, K/[J = 104, Th/U = 4. The term, Qc dm/dt, in (18) describes heat release occurring when the core solidifies after the core adiabat drops below the core liquidus curve. It is supposed that the core consists of the mixture, Fe-FeS, and as solidification begins from the center of the planet, sulfur remains in the liquid layer, reducing the solidification temperature. The value Qc is composed of the heat of the phase transition and gravitational energy. According to the estimates of Loper (1978~; Stevenson et al. (1983), and Solomatov and Zharkov (1989), Qc = (1-2) 10~°erg go-. Mean temperature of the adiabatic core: TC ~ ncTcM (20) where nc ~ 1.2, the mean core density is p = 10.5 g cm~3, Cpc = 4.7106 erg g~ ~ K- ~ (Zharkov and ~ubitsyn 1980; Zharkov 1983~. The formulae for the melting Tamp) and adiabatic Tamp) curves are written as follows: 2.24 Tip) = To(1—OC x) (I Tacl(p)=Tcm~— P _ 1.224 - 0.009405R —0.1586 (R ) - 0.05672 (R ) (21) (22) (23) Here To denotes the temperature at which pure iron melts at the boundary core of the radius Rc, where p = PCM = 9.59 g cm~3; cat ~ 2; x is the mass portion of sulfur in the liquid core, depending upon the radius of the solid core Ri, and the overall amount of sulfur in the core, xO: x(Ri) = R3 - R3 (24) The intersection of (21) and (22) defines the radius of the solidified core Ri (Figure lb). Convection in the upper mantle is parameterized by the MAPC with the parameters (7) (for fixed boundaries) in the lower mantle; and by the same formulae with the parameters (8) (for free boundaries). However, the difference between (7) and (8) is not very substantial. The parameters for the upper mantle are: be = 4.3 · 10~5dyne3cm~6s, AL = 6.9 · 104 K,

180 PLANETARY SCIENCES on = 3 · 10-5K-i, pi = 3.7 g cm-3, X~ = 10-2cm~2s~i, ~~ = 4.5 · 105erg cm~is. 107erg g and for the lower mantle: b2 = 1.1 10~7dyne3cm-6s, Ao2 = 1.3 105K, cx2 = 1.5 10-5K-i, P2 = 4.9 g cm~3, X2 = 3 · 10~2cm~2s~i, ae2 = 1.8 · 106erg cm~is~iK~i, g = 900cm s-2, Cp2 = 1.2 107erg g~i, n2 = 1.13, nr2 = 1.26. NUMERICAL RESULTS AND ASYMPOTOTIC SOLUTION OF THE MAPC EQUATIONS The evolution of the planet began approximately 4.6 billion years ago. The initial state of the planet was a variable parameter. The initial value of TU2 is the most significant, since Tut, due to the low thermal inertia of the upper mantle, rapidly adapts to the thermal regime of the lower mantle (t < 0.5 billion years). The core has little effect on the evolution of the planet in general and the majority of models do not take into account its influence. TU2 was selected as equal to 2500, 3000, 3500 K The upper value is limited by the melting temperature of the mantle, since a melted mantle is rapidly freed from excess heat. The upper mantle adapts to the thermal regime of the lower mantle for the first approximately 0.5 billion years (Figure 2a, b). Then, after approx- imately three to four billion years the entire mantle enters an asymptotic regime which is not dependent upon the initial conditions. The evolution picture in general is similar to the one described by Solomatov et al. (~1986~; and Solomatov et al. (1987~. The planet is close to an asymptotic state in the present epoch. Contemporary parameters of the models are: Tu, = (1700-1720) K, TO = (2500-25303 K, TU2 = (2840-2870) K, FL. = (35-40)erg cm-2 Al = (28-30)km a2 = (13~140)km, s, u1 = (2.1-2.4)cm yr~ u2 = (0.~1.0)cm yr~ At = (5-6) bars, r2 = (110-120) bars, hi = (1-2~102i poise, 02 = (3-10~1~2 poise. According to the criterion (15) MAP C are applicable throughout the entire evolution, just as with the quasistationary criterion (Solomatov et al. 1987~. The asymptotic expression for F~ in the first approximation is formu- lated as (Solomatov et al. 1987~: FL, = FQ (~1 + ~ ), (25) where FQ denotes the thermal flow created by the radioactivity of the lower mantle, and tr is the characteristic time of decay:

AMERICAN AND SOVIET RESEARCH 3500 'at 2500 Lo Q LO 2000 1 500 ~ 100 CD G ace 0~ 11 50 I I - TU2(0) = 2500K 2 - TU2(0) = 30OOK 3 - TU2(0) = 3500K ~ L 1 , 0 1 2 3 4 4.6 AGE t, BILLION YEARS \ 0~ ~ I - TU2(0) = 2500K \ \ 2 - TU2(0) = 30OOK \ \ 3 - TU2(0) = 3500K 0 1 2 3 FIGURE 2 (a) Evolution of the base temperatures, TUT, T12 and Tu2, with differing initial conditions. The core is not taken into account and is considered to be Tom = TL2 (Figure 1~. (b) Evolution of the thermal flow under the lithosphere, FL, with differing initial conditions. The thermal flow to the surface is obtained lair adding ~ 11 erg cm~ls~1 to FL, generated by the radioactive elements of the crust. The dashed line indicates the thermal flow generated bar radioactive elements of the lower mantle. 181

182 dlnQ2 ~ ~ dt ) equal ~5.67 · 109 years at the current time. The time scale of thermal inertia of the mantle is equal to tin = tint + tin2( 1 + t) ~ PLANETARY SCIENCES (26) (27) where toll and 4n2 are the time scales for the inertia of each of the layers individually: s _ MlnlCpl~Tl (1 + At + ~lAl(TUi—TB)) d2A2(Tu2Ui Tl2)~- tint M2Q2 tins = 2 Q2 2 (~1~2 + - - T2 ~~ ) (28) (29) 1 + nLls 1 + in + p2 - 1/3(~So—2~B2)Ao2(Tu2—Tl2)Tu22 an 1 + Al + >1A1(Tul—TB)TUI2 ' ~~ M1 and M2 denote the layer masses, s = R122 / Rr2. The values of (27) through (30) are calculated in a zero approximation: Fl = FQ, and A = Awn (p/pO)~. The time scale for thermal inertia, as compared with models based on the conventional APC (Solomatov et al. 1986, 1987), has increased from ~ 2.5 · 109 years to ~3.5 · 109 years. The mantle and core temperatures obtained are somewhat lower (by 300 K near the core). In the models with the core, Tom ~ 3720K and Fc ~ 15 erg cm-2s-t in the contemporary epoch. Since the adiabatic value is FC ~ 30 erg cm-2s-i, there is no con- vection if solidification is absent, and a magnetic field cannot be generated (Stevenson e! al. 1983~. MAGNETISM AND THE THERMAL REGIME OF THE CORES OF EARTH AND VENUS We will estimate the temperatures in the Earth using the MAP C. MAPC is not applicable to the Earth's upper mantle, since convection in the Earth involves the surface layer, and rheology is, in general, more complex. However, MAPC is applicable to the Earth's lower mantle. Let us assume a value for the temperature at the boundary between Earth's upper and lower mantles of T12 = (2300 - 2500)I(, (Zharkov 1983), and the thermal flow at this boundary is (31)

AMERICAN AND SOVIET RESEARCH F2l=R2° (F—Fcr+CpM1 dtl)~80erycm~2s~l, 183 where F—FCr ~ 70 erg cm~2s~1 is the medium thermal flow from the Earth, after deducting heat release in the crust (according to the estimates of Sclater et al. 1980), dT~/dt ~ -100KJbillion years. (Basaltic Volcanism Study Project 1981~. We will assume the following values for the rheologic parameters: b = 6.6 · 10~6dyne3cm~6s, A = 1.5 · 1051(, andAO = 1.3 · 105K. The remaining parameters are listed in Zharkov (1983~. As a result, we have: TU2 = (2800-2900) K, T';2 = (3600-3800) K, TCm = (3800-40()()) K' [2 = 1~. The value of TCm - TL 2 depends upon Fc, which we will assume to be equal to the adiabatic value of Fall ~ 30 erg cm~2s~~. Therefore, the temperature at the boundary of the Earth's core, TCME is greater than for Venus (TCMV) by a value of TCME—TOM v = ( 100—300) If. (33) In order for Venus' core not to solidify, it is necessary that the adiabat of the Venusian core not drop below the solidification curve during cooling. Otherwise, solidification of the core will cause the core to mix by chemical or thermal convection, and it will trigger the generation of a magnetic field (Stevenson et al. 1983~. We will estimate the difference between TCME and the temperature, TCrv (which is critical for the beginning of solidification), at the boundary of Venus' core, with a single pure iron melting curve, Tm (P) and a single equation of the state for iron p(P). TCME is found from the intersection of the adiabat of the Earth's core (22) and the liquidus curve (23), with a sulfur content in the core of XE at the boundary of the Earth's inner core. Tcrv is obtained from the intersection of the adiabat of Venus' core (22) and the liquidus curve (23) with a sulfur content of xv. We then obtain (Solomatov and Zharkov 1989~: TCME—Tcrv = (+300) . ( - 300),K, (34)

184 PLANETARY SCIENCES where XE—XV = 0 . o.m. Therefore, if xv ~ XE—(0 . 0.02) = 0.07 . 0.12; (with XE = 0.09 . 0.12; Aherns 1979), the core of Venus is not solidifying at the present time, and a magnetic field is not being generated. Complete solidification of the core would have led to the absence of a liquid layer in the core and would have made it impossible for the magnetic field to be generated. However, for this, the temperature near the boundary of Venus' core should have dropped below the eutectic value, which, according to the estimates of Anderson et al. (1987) is ~ 3000 K and according to Usselman's estimate (1975) is ~ 2000 K Such low temperatures of the core seem to be of little probability. Pressure in the iron triple point, ~ - ~—1, (liquid) approaches the pressure in the center of Venus. This is significant for interpretation the absence of the planet's own magnetic field. According to the estimates of Anderson (1986), Pip ~ 2.8 Mbar (Figure 3), but is also impossible to rule out the larger values of Pip. In the center of Venus, PA ~ 2.9 Mbar; at the boundary of the solid inner Earth's core, PIE = 3.3.Mbar; and in the Earth's center, POE = 3.6 Mbar (Zharkov 1983). If Pcv < Pip, the conclusion that there is no solidification of Venus' core is further supported, since, in this case, the core's adiabat (critical for the beginning of solidification) drops several hundred degrees lower. This stems from the fact that reduction in the temperature of solidification of the mixture, ~— Fe—FeS is greater than for the mixture ~—Fe—FeS by AS~/AS~ times, where AS`/AS, denotes the ratio of enthropy jumps (during melting) equal to ~ 2, according to Anderson's estimates (1986). The latest experimental data on the melting of iron allow us to estimate the melting temperature in the cores of Earth and Venus. Figure 3 shows melting curves obtained by various researchers, and the ~—~ boundary, computed by Anderson (1986~. With x = 0.09-0.12 and c' = 1 - 2 (formula 21), the full spread of temperatures at the boundary of the Earth's core, leading to the intersection of the liquidus and adiabat curves, is equal to TCME = 3500 . 47001(, - with data from Brown and McQueen (1986) and TCME = 4300 . 5400K, (35) (36) - with data from Williams et al. (1987~. The effect of pressure on viscosity of the lower mantle reduces the effective Nusselt number and increases the temperature Of TCME and TCMV by ~ 300 K (Solomatov and Zharkov 1989~. We obtain the estimate TCME = 3800 . 4300If, which is the best fit with (35). (37)

AMERICAN AND SOVIET RESEARCH 8000 7000 6000 By 5000 LLJ ~ 4000 i: LL LL 3000 2000 1 000 : ~ 1 1 ~ me/ ~ / of/ , ,11 , 1 1 I- ~ LL LL 1o ~1 1 1 1 1 l / 1 l 1 1 1 1 1 1 - 1 1 1 1 1, 1 1 1 185 2 Pressure, Mbar 3 FIGURE 3 Pure iron melting curves according to venous data and the boundary of the phase transition fly Fe ~ Fe. The figures indicate melting euchres: 1 is from the study by Williams et al. (1987~; 2 is from the study by Anderson (1986) and experimental data from Brown and MeQueen (1986~; and 3 is based on the Lindeman formula with the Grunehaisen parameter of G = 1.45 = eonst, using experimental data from Brown and MeQueen (1986~. The transition boundary, ~—c, was constructed in the study by Anderson (1986) and together with the melting eume gives us the location of the triple point. The vertical segments illustrate errors in determining temperature for curves 1 and 2. The boundary labels are as follows: CM is the boundary between the core and the mantle; C denotes the center of the planet; I is the boundary of the solid inner core; and the final letter indicates Earth (E) or Venus (V). fly - ~ -1 denotes the location of the triple point. THE THERMAL REGIME OF THE VENUSL\N CRUST What are the mechanisms by which heat is removed from Venus's interior to the surface? Global plate tectonics, like Earth's, are absent on the planet (Zharkov 1983; Solomon and Head 1982), although in individual, smaller regions, it is possible that there are features of plate tectonics (Head and Crumpler 1987~. A certain portion of heat may be removed by the mechanism of hot spots (Solomon and Head 1982; Morgan and Phillips

186 PLANETARY SCIENCES 1983~. Conductive transport of heat through the crust clearly plays a large role. However, with a large crust thickness ~ > 40 km), as indicated by data from a number of works (Zharkov 1983; Anderson 1980; Solomatov et al. 1987), the heat flow of F ~ (40-50) erg cm-2s~i triggers the melting of the lower crust layers and removal of approximately one half of heat flow by the melted matter. The latter flows to the surface as lava or congeals in the crust as intrusions. We shall discuss the possibility of solid-state convection in the crust as an alternative mechanism of heat removal through the Venusian crust. The crust is constituted of an upper, resilient layer with a thickness of de and a viscous one with a thickness of do = dCr—de. The crust thickness of dCr is constrained in our model by the phase transition of gabbro-eclogite, since eclogite, with a density higher than that of the underlying mantle, will sink into the mantle (Anderson 1980; Sobolev and Babeiko 1988~. The depth of this boundary is dependent upon the composition of basalts of Venus' crust. We assume that dCr = 70 km (Yoder 1976; Zharkov 1983; Sobolev and Babeiko 1988~. It is considered that radioactive elements are concentrated in the upper portion of the crust, and the primary heating occurs via the heat flow from the mantle of For; ~ 40 erg cm-2s~~. The boundary (de) of the resilient crust is defined as the surface of the division between the region effectively participating in convection and the nonmobile upper layer. Crust rheology is described by law (1) with the parameters from Kirby and Kronenberg (1987~. Four modeled rocks are considered: quartz diorite, anorthosite, diabase and albite. Parameter m in (1) is close to 3 for them, so that the formulae MAP C with parameters (8) for fixed boundaries is fully suitable for estimating. In addition, criterion (15) is used to define the boundary, de. At this boundary, which is regarded as the upper boundary of the convective portion of the crust, the temperature is equal to To = 733 + 20de (km), K. The following physical parameters are assumed (Zharkov et al. 19693: p = 2.89 cm~3,or = 2 · 10-5I(-i, Be = 2 . 105erg cm~is~iI(~i (38) . Computations have demonstrated that the thickness of the resilient crust is 20-30 kilometers. The mean temperature of the convective layer of the crust has been calculated at ~ 1600K, 1700K, l900K and 2000K, respectively, for quartz diorite, anorthosite, diabase, and albite, and exceeds the melting temperature for basalts by hundreds of degrees. This means that convection does not protect the crust from melting, and heat is removed by the melted matter.

AMERICAN AND SOVIET RESEARCH 187 We can estimate that portion of the heat which is removed by con- vection. For this, let us assume the temperature in the base of the crust to be TB = 1500K (approximately the melting temperature). We obtain the Nusselt number from the formulae of MAPC, and find that it is ~1.7; 1; 0.6; and 0.5, respectively, for quartz diorite, anorthosite, diabase, and albite. For ~ = const, and for complex rheology, as in (1), (Christensen 1984a and 1985a), convection begins at Nu ~ 1.5-2, as calculated according to the formulae of APC (MAPC). Thus, where dCr ~ 70km, perhaps only quartz diorite is convective, removing 25-30 erg cm-2s-i, while 10-20 erg cm-2s-i is removed by the melt. The rate of convective currents is three to five millimeters per year. It can be demonstrated that Nu ~(dCr—de)°9 (39) With dCr ~ 120 fun, convection also begins in anorthosite, while in quartz diorite it occurs virtually without melting. These estimates show that convection in the crust may play some role in individual regions, depending on the thickness and composition of the crust. It is not excluded that in individual regions, convection in the crust makes its way to the surface. The bulk of the heat is, apparently, removed by melted matter. The rate of circulation of material from the crust is, with this kind of volcanism, 50-100 km3yr~~. This is three to five times greater than crust generation in the terrestrial spreading zones. Another process by which basalt material circulates is where new portions of melted basalt reach the crust from the upper mantle, and basalt returns back to the mantle in the eclogite phase. This process may trigger the accumulation of eclogite in the gravitationally stable region between the upper and lower mantles. It may lead to the chemical differentiation of the mantle. This process has been noted for the Earth by Ringwood and Irifune (1988~. Figure 4 illustrates various processes involved in heat and mass trans- port. The geological structures observed on Venus may be related to these processes. Flat regions may be tied to effusive, basalt volcanism. Linear structures in the mountainous regions may be related to horizontal defor- mations which are an appearance of convections in the crust or mantle. Ring structures may stem from melted intrusion or hot plume lifted towards the surface from the bottom of the upper mantle. Convection both in the mantle and in the crust is, apparently, nonsta- tionary (as on Earth). This nonstationary nature stems from instabilities occurring in the convective system. The characteristic time scale for such fluctuations is t ~ d/u, where d ~ 1()~-109 cm is the characteristic dimension, and u ~ 1 cm per year is the characteristic velocity. Therefore, character- istic "lifespans" for various occurrences of instability are t ~ 108-109 years.

188 PLANETARY SCIENCES (a) Conductive heat (b) Heat removal by melted matter (c) Convection in the crust ~ ~ ~ (d) Lift of the mantle plume (e) Mande convection reaches (f) Basalt exchange between the _~ it, ~ ,,~4 ~ ' ~ -, 9-i-?- FIGURE 4 Process of heat transport through the Venusian crust: (a) transfer of heat camed from the mantle by the mechanism of conductive thermal oonducti~t~r, (b) heat removal by the melted matter which is formed as the basalt crest melts. The melted matter may flow to the surface or form intrusions; (c3 convection in the crust which does not reach the surface or reaching the surface; (d) lifting of hot plume from the bottom of the upper mantle to the crust of Venus, taggenng enhanced heat flow, a flow of crust matenal, and the sinking of the crust; (e) involvement of the crust in mantle convection with the formation of spreading zones; (f) basalt exchange between the crust and the mantle. Basalt is formed when the upper mantle partially melts and is returned back as eclogite. Regional features of tectonic structures, thermal flows, volcanic activity and so on, can exist for this length of time. CONCLUSION 1. Modification of the approximation of parameterized convection for the case of nonNewtonian mantle rheology led to no marked increase in the time scale of thermal inertia of the mantle from two to three or three to four billion years in comparison with the usual parameterization. The thermal flow at the surface of Venus of ~ 50 erg cm~2s~i, is the product of radiogenic heat release from the mantle (50%), heat release in the crust (20%), and cooling of the planet (30%~. These figures for Earth are approximately 40, 20, and 40% for the double-layered convection models. Temperatures in the upper portion of the mantle are approximately 1700 K, which is 50-100 K greater than on Earth. Given the existing uncertainties in the concerning parameters, Tom ~ 3700-4000 K at the core bc>;undary and may, possibly, be greater. This temperature is 100 300 K less than for the Earth. 2. The magnetic field on Venus is absent. This is most likely due to the lack of core solidification and, respectively, the lack of energy needed

AMERICAN AND SOVIET RESEARCH 189 to maintain convection in the liquid core. For this, it is enough for the sulfur content in Venus' core to be even a little bit less than on the Earth (but not more than 2~30% less). This conclusion is stronger if the triple point in the phase diagram for iron, ~—~—1, lies at pressures that are greater than in Venus' center, but approximately less than in Earth's center. 3. At the values obtained for heat flows from Venus' mantle, the crust melts, and the melted matter ~ < 100 km3 per year) removes about one half of the entire heat. The remainder is removed conductively. In individual regions, depending on the crust thickness and composition, a portion of the heat may be removed by convection, reducing crust temperature and the portion of heat removed by the melted matter. Flow velocities comprise several millimeters per year. Due to the insufficiently high temperature of the surface, convection in the crust separates from the surface as a highly viscous, nonmobile layer with a thickness of 2~30 kilometers. In individual regions, crust convection may emerge to the surface. Basalt circulation also occurs by another way: the basalt is melted out of the upper mantle and returned back in the form of eclogite masses, which sink into the lighter mantle rock. It Is possible that this process triggers the accumulation of eclogite at the boundary between the upper and lower mantles, resulting in the chemical separation of the mantle. These processes may explain the formation of various geological structures on Venus. 4. The nonstationary nature of convection In Venus' mantle and crust determine regional features of tectonic, thermal and volcanic appearances on the surface of the planet which have a characteristic duration of ~ 108-109 years. REFERENCES Ahrens, TO. 1979. J. Geophys. Res. 846:985-990. Anderson, D.L. 1980. J. Geophys. Res. Lett. 7:101-102. Anderson, O.L. 1986. Geophys. J. R. Astron. Soc. 84:561-579. Basaltic Volcanism Study Project. 1981. Basaltic volcanism on the Terrestrial Planets. Pergamon, New York. Brown, J.M., and R.G. McQueen. 1986. J. Geophys. Res. 91:7485-7494. Chnstensen, U. R. 1984a. Geophys. J. R. Astron. Soc. 77:343-384. Chnstensen, U. R. 1984b. Phys. Earth Planet. Inter. 35:264282. Chnstensen, U.R. 1985a. Phys. Earth Planet. Inter. 37:183-205. Christensen, U.R. 1985b. J. Geophys. Res. 90:2995-3007. Head, J.W., and L S. C~umpler. 1987. Science 238:1380-1385. Kirby, S.H., and A K Kronenberg. 1987. Rev. Geophys. 25:1219-1244, 16~1681. Loper, D.L~ 1978. Geophys. J. R. Astron. Soc. 54:389~W. Morgan, P., and R.J. Phillips. 1983. J. Geophys. Res. 88: 8305-8317. O'Nions, R.K, N.M. Evensen, and PA. Hamilton. 1979. J. Geophys. Res. 24:6091-6101 Parmentier, E.M., D.L. Il~rcotte, and K.E. Torrance. 1976. J. Geophys. Res. 81:1839- 1846. Richter, F.M., H.C. Nataf, and S.F. Daly. 1983. Fluid Mech. 129.173-192. Ringwood, A.E., and T. Irifune. 1988. Nature 331:131-136. Schubert, G. 1979. Ann. Rev. Earth Planet. Sci. 7:289-342. Sclater, J.C., C. Jaupart, and D. Galson. 1980. Rev. Geophys. Space Phys. 18:269-311.

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