流变边界层及其对华北克拉通热/地震岩石圈底界差异的意义

二维热传导/对流数值模型显示,纯传导的固体岩石圈与纯对流的流体软流圈之间存在一过渡层,即流变边界层,其间传导与对流共同作用来传递热量.流变边界层厚度主要由软流圈黏性系数（η）控制,而受固体岩石圈厚度及热状态影响很小.随着η从1×10²¹Pa·s降低至1×10¹⁹ Pa·s,流变边界层也随之减薄,流变边界层的厚度与lg（η）成正比. 流变边界层的存在是造成热岩石圈与地震岩石圈厚度差异的重要因素. 全球典型克拉通岩石圈的对比结果表明,地震岩石圈厚度普遍大于热岩石圈厚度,二者的差异多数在70~90 km,很好地验证了流变边界层的存在. 研究发现二者的差异在华北克拉通自西向东逐渐减小：由西部鄂尔多斯的约80 km减少至渤海湾盆地的约20 km. 反映出华北克拉通岩石圈下部流变边界层厚度自西向东减薄,意味着软流圈黏性系数自西向东逐渐降低.这可能与中生代太平洋俯冲脱水形成的低黏大地幔楔有关,从一侧面印证了太平洋俯冲对华北克拉通破坏的影响.     

The influence of thermochemical convection on the fixity of mantle plumes

A general feature of both isochemical and thermochemical studies of mantle convection is that horizontal plume velocities tend to be smaller than typical convective velocities, however, it is not clear which system leads to a greater fixity of mantle plumes. We perform two- and three-dimensional numerical calculations and compare both thermochemical and isochemical cases with similar convective vigor to determine whether presence of a dense component in the mantle can lead to smaller ratios of horizontal plume velocity to surface velocity. We investigate different viscosity and density contrasts between chemical components in the thermochemical calculations, and we perform isochemical calculations with both free-slip and no-slip bottom boundary conditions. We then compare both visually and quantitatively the results of the thermochemical and isochemical calculations to determine which leads to greater plume fixity. We find that horizontal plume velocities for thermochemical calculations are similar to those from isochemical calculations with no-slip bottom boundary conditions. In addition, we find that plumes tend to be more fixed for isochemical cases with free-slip bottom boundary conditions for two-dimensional calculations, however, in three dimensions, we find that plume fixity is similar to that observed in thermochemical calculations.     

The mantle convection model with non-Newtonian rheology and phase transitions: The flow structure and stress fields

The mantle convection model with phase transitions, non-Newtonian viscosity, and internal heat sources is calculated for two-dimensional (2D) Cartesian geometry. The temperature dependence of viscosity is described by the Arrhenius law with a viscosity step of 50 at the boundary between the upper and lower mantle. The viscosity in the model ranges within 4.5 orders of magnitude. The use of the non-Newtonian rheology enabled us to model the processes of softening in the zone of bending and subduction of the oceanic plates. The yield stress in the model is assumed to be 50 MPa. Based on the obtained model, the structure of the mantle flows and the spatial fields of the stresses σ_xz and σ_xx in the Earth’s mantle are studied. The model demonstrates a stepwise migration of the subduction zones and reveals the sharp changes in the stress fields depending on the stage of the slab detachment. In contrast to the previous model (Bobrov and Baranov, 2014), the self-consistent appearance of the rigid moving lithospheric plates on the surface is observed. Here, the intense flows in the upper mantle cause the drift and bending of the top segments of the slabs and the displacement of the plumes. It is established that when the upwelling plume intersects the boundary between the lower and upper mantle, it assumes a characteristic two-level structure: in the upper mantle, the ascending jet of the mantle material gets thinner, whereas its velocity increases. This effect is caused by the jump in the viscosity at the boundary and is enhanced by the effect of the endothermic phase boundary which impedes the penetration of the plume material from the lower mantle to the upper mantle. The values and distribution of the shear stresses σ_xz and superlithostatic horizontal stresses σ_xx are calculated. In the model area of the subducting slabs the stresses are 60–80 MPa, which is by about an order of magnitude higher than in the other mantle regions. The character of the stress fields in the transition region of the phase boundaries and viscosity step by the plumes and slabs is analyzed. It is established that the viscosity step and endothermic phase boundary at a depth of 660 km induce heterogeneities in the stress fields at the upper/lower mantle boundary. With the assumed model parameters, the exothermic phase transition at 410 km barely affects the stress fields. The slab regions manifest themselves in the stress fields much stronger than the plume regions. This numerically demonstrates that it is the slabs, not the plumes that are the main drivers of the convection. The plumes partly drive the convection and are partly passively involved into the convection stirred by the sinking slabs.     

Numerical model for the generation of the ensemble of lithospheric plates and their penetration through the 660-km boundary

In the kinematic theory of lithospheric plate tectonics, the position and parameters of the plates are predetermined in the initial and boundary conditions. However, in the self-consistent dynamical theory, the properties of the oceanic plates (just as the structure of the mantle convection) should automatically result from the solution of differential equations for energy, mass, and momentum transfer in viscous fluid. Here, the viscosity of the mantle material as a function of temperature, pressure, shear stress, and chemical composition should be taken from the data of laboratory experiments. The aim of this study is to reproduce the generation of the ensemble of the lithospheric plates and to trace their behavior inside the mantle by numerically solving the convection equations with minimum a priori data. The models demonstrate how the rigid lithosphere can break up into the separate plates that dive into the mantle, how the sizes and the number of the plates change during the evolution of the convection, and how the ridges and subduction zones may migrate in this case. The models also demonstrate how the plates may bend and break up when passing the depth boundary of 660 km and how the plates and plumes may affect the structure of the convection. In contrast to the models of convection without lithospheric plates or regional models, the structure of the mantle flows is for the first time calculated in the entire mantle with quite a few plates. This model shows that the mantle material is transported to the mid-oceanic ridges by asthenospheric flows induced by the subducting plates rather than by the main vertical ascending flows rising from the lower mantle.     

Viscosity distribution in the mantle convection models

Viscosity is a fundamental property of the mantle which determines the global geodynamical processes. According to the microscopic theory of defects and laboratory experiments, viscosity exponentially depends on temperature and pressure, with activation energy and activation volume being the parameters. The existing laboratory measurements are conducted with much higher strain rates than in the mantle and have significant uncertainty. The data on postglacial rebound only allow the depth distributions of viscosity to be reconstructed. Therefore, spatial distributions (along the depth and lateral) are as of now determined from the models of mantle convection which are calculated by the numerical solution of the convection equations, together with the viscosity dependences on pressure and temperature (PT-dependences). The PT-dependences of viscosity which are presently used in the numerical modeling of convection give a large scatter in the estimates for the lower mantle, which reaches several orders of magnitude. In this paper, it is shown that it is possible to achieve agreement between the calculated depth distributions of viscosity throughout the entire mantle and the postglacial rebound data. For this purpose, the values of the volume and energy of activation for the upper mantle can be taken from the laboratory experiments, and for the lower mantle, the activation volume should be reduced twice at the 660-km phase transition boundary. Next, the reduction in viscosity by an order of magnitude revealed at the depths below 2000 km by the postglacial rebound data can be accounted for by the presence of heavy hot material at the mantle bottom in the LLSVP zones. The models of viscosity spatial distribution throughout the entire mantle with the lithospheric plates are presented.     

The structure of thermal convection and geotherms beneath a continent and ocean

The formation of the thermal cross section of the lithosphere and mantle upon the interaction between the mantle convection and the immobile continent surrounded by the oceanic lithosphere is studied by numerical modeling. The convective temperature and velocity fields and then the averaged geotherms for subcontinental and suboceanic regions up to the boundary with the core are calculated from the solution of convection equations with a jump in viscosity in the continental zone. Using the experimental data on the solidus temperature in the rocks of the upper mantle, the average thickness of the continental and oceanic lithosphere is estimated at 190 and 30 km, respectively. The effect of a hot spot formed in the subcontinental upper mantle at a depth of 250–500 km, which has not been previously noted, is revealed. Although the temperature in this zone is typically assumed to be close to adiabatic, the calculations show that it is actually higher than adiabatic by up to 200°C. The physical mechanism responsible for this effect is associated with the accumulation of convective heat beneath the thermally insulating layer of the continental lithosphere. The revealed anomalies can be important in studying the phase and mineral transformations at the base of the lithosphere and in the regional geodynamical reconstructions.     

Convective instabilities in a variable viscosity fluid cooled from above

Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν₀ + ν₁ exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 10⁷ and Rayleigh numbers of up to 10⁸ are studied.For intermediate viscosity contrasts (around 10³), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth z_r (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 10¹⁵?5 × 10¹⁶ m² s^?1 for viscosity in the thermal boundary layer below the plate.     

Possible effects of lateral viscosity variations induced by plate-tectonic mechanism on geoid inferred from numerical models of mantle convection

In a traditional analytical method, the convective features of Earth’s mantle have been inferred from surface signatures obtained by the geodynamic model only with depth-dependent viscosity structure. The moving and subducting plates, however, bring lateral viscosity variations in the mantle. To clarify the effects of lateral viscosity variations caused by the plate-tectonic mechanism, I have first studied systematically instantaneous dynamic flow calculations using new density-viscosity models only with vertical viscosity variations in a three-dimensional spherical shell. I find that the geoid high arises over subduction zones only when the vertical viscosity contrast between the upper mantle and the lower mantle is O(10³) to O(10⁴), which seems to be much larger than the viscosity contrast suggested by other studies. I next show that this discrepancy may be removed when I consider the lateral viscosity variation caused by the plate-tectonic mechanism using two-dimensional numerical models of mantle convection with self-consistently moving and subducting plates, and suggest that the observed geoid anomaly on the Earth’s surface is significantly affected by plate-tectonic mechanism as a first-order effect.     

大陆岩石圈、地幔底部异常体与地幔对流相互作用的数值模拟

在地球表层存在着占地表面积约30%的具有低固有密度、高黏度的大陆岩石圈.由于其特殊的物理化学性质,大陆岩石圈通常不直接参与下方的地幔对流,但其与地幔对流格局有着重要的相互影响.大量研究显示,在中太平洋和非洲的下地幔底部,存在着两块占核幔边界（CMB）面积约20%的高密度热化学异常体（由于其剪切波速度较低,常称作低剪切波速度省（LSVPs））.LSVPs的演化既受地幔对流的影响,同时也影响地幔物质运动的格局和动力学过程.本文系统研究了存在大陆岩石圈,下地幔LSVPs的地幔对流模型.模拟结果显示：（1）当大陆体积较小时,其边缘常伴随着俯冲,大陆区域地幔常处于下涌状态,其上地幔温度较低,大陆岩石圈在水平方向处于压应力状态.随着大陆体积的增大,大陆边缘的俯冲逐渐减弱,大陆区域地幔由下涌转为上涌,其上地幔温度较高,大陆岩石圈水平方向处于拉应力状态.（2） 岩石圈与软流圈边界（LAB）在大陆下方较深,温度较低;在海洋区域较浅,温度较高.随着大陆体积的增大,陆洋之间LAB深度、温度的差异逐渐减小.（3）大陆区域地幔底部LSVPs物质的丰度与大陆的体积呈正相关.当大陆体积较小时,大陆下方的LSVPs丰度比海洋区域少.随着大陆体积的增大,大陆下方LSVPs的丰度逐渐增大.（4）海洋地区地表热流高,且随时间波动大,大陆地区地表热流低,随时间波动较小;LSVPs区域的核幔边界热流低.     

Signatures of downgoing plate-buoyancy driven subduction in Cenozoic plate motions

The dynamics of plate tectonics are strongly related to those of subduction. To obtain a better understanding of the driving forces of subduction, we compare relations between Cenozoic subduction motions at major trenches with the trends expected for the simplest form of subduction. i.e., free subduction, driven solely by the buoyancy of the downgoing plate. In models with an Earth-like plate stiffness (corresponding to a plate–mantle viscosity contrast of 2–3 orders of magnitude), free plates subduct by a combination of downgoing plate motion and trench retreat, while the slab is draped and folded on top of the upper-lower mantle viscosity transition. In these models, the slabs sink according to their Stokes’ velocities. Observed downgoing-plate motion–plate-age trends are compatible with >80% of the Cenozoic slabs sinking according to their upper-mantle Stokes’ velocity, i.e., subducting-plate motion is largely driven by upper-mantle slab pull. Only in a few cases, do young plates move at velocities that require a higher driving force (possibly supplied by lower-mantle–slab induced flow). About 80% of the Cenozoic trenches retreat, with retreat accounting for about 10% of the total convergence. The few advancing trench sections are likely affected by regional factors. The low trench motions are likely encouraged by low asthenospheric drag (equivalent to that for effective asthenospheric viscosity 2–3 orders below the upper-mantle average), and low lithospheric strength (effective bending viscosity ～2 orders of magnitude above the upper-mantle average). Total Cenozoic trench motions are often very oblique to the direction of downgoing-plate motion (mean angle of 73°). This indicates that other forces than slab buoyancy exert the main control on upper-plate/trench motion. However, the component of trench retreat in the direction of downgoing plate motion (≈ slab pull) correlates with downgoing-plate motion, and this component of retreat generally does not exceed the amount expected for free buoyancy-driven subduction. High present-day slab dips (on average about 70°) are compatible with largely upper-mantle slab-pull driven subduction of relatively weak plates, where motion partitioning and slab geometry adjust to external constraints/forces on trench motion.     

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.     

On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

The effect of spatial variations in viscosity on the structure of mantle flows

According to an opinion widespread in the literature, high viscosity regions (HVRs) in the mantle always affect the structure of mantle flows, changing it in both the HVR itself and the entire mantle. Moreover, a simplified relation is often adopted according to which the flow velocity in the HVR decreases in inverse proportion to viscosity. Therefore, in order to treat a smoother value, some authors introduce a new variable equal to the product of the flow velocity and the viscosity value in a given place. On the basis of numerical modeling, this paper shows that HVRs of two types should be distinguished in the mantle. If an HVR is immobile, mantle flows actually do not penetrate it. If the viscosity increase is more than five orders, the HVR behaves as a solid and flow velocities within it almost vanish. However, if an HVR is free, it moves together with the mantle flow. Then, the general structure of flows changes weakly and flow velocities within the HVR become approximately equal to the average velocity of flows in the absence of the HVR. Horizontal layers and vertical columns differing in viscosity from the mantle behave as regions of the first type, whose flow velocities can differ by a few orders. However, even such large-scale regions as the continental lithosphere, whose viscosity is four to five orders higher than in the surrounding mantle, float together with continents at velocities comparable to mantle flows, i.e., behave as regions of the second type.     

Edge-driven convection

We consider a series of simple calculations with a step-function change in thickness of the lithosphere and imposed, far-field boundary conditions to illustrate the influence of the lithosphere on mantle flow. We consider the effect of aspect ratio and far-field boundary conditions on the small-scale flow driven by a discontinuity in the thickness of the lithosphere. In an isothermal mantle, with no other outside influences, the basic small-scale flow aligns with the lithosphere such that there is a downwelling at the lithospheric discontinuity (edge-driven flow); however, the pattern of the small-scale flow is strongly dependent on the large-scale thermal structure of a much broader area of the upper mantle. Long-wavelength temperature anomalies in the upper mantle can overwhelm edge-driven flow on a short timescale; however, convective motions work to homogenize these anomalies on the order of 100 million years while cratonic roots can remain stable for longer time periods. A systematic study of the effect of the boundary conditions and aspect ratio of the domain shows that small-scale, and large-scale flows are driven by the lithosphere. Edge-driven flow produces velocities on the order of 20 mm/yr. This is comparable to calculations by others and we can expect an increase in this rate as the mantle viscosity is decreased.     

Small-scale convection induced by passive rifting: the cause for uplift of rift shoulders

Areas adjacent to rifts, or rift shoulders, are often observed to be uplifted as much as a kilometer or more. In some of these regions geologic data indicate a passive origin for the rifting itself (i.e. there was no anomalous heating of the regions before rifting). Purely conductive heat transport between the rift, where the lithosphere has been thinned, and the rift flanks cannot account for the magnitude of the uplift. Small-scale convection will be induced in the mantle beneath a rift due to the lateral temperature gradients there. Numerical experiments show that convection increases the amount of heat transported vertically into the rift and laterally out of it. In these calculations, the viscosity is taken to be dependent on temperature and pressure and, in some cases, stress. The mantle flow results in thinning of the adjacent lithosphere causing flanking uplift as well as slowing of the subsidence of the middle of the rift. The magnitude of the uplift is dependent on the geometry of the rift and the importance of stress-dependence in the rheology of the mantle. For viscosity parameters which are consistent with the pre-rift temperature structure small-scale convection can produce uplift at least twice as great as would be produced by lateral conduction alone.     

Small-scale upper mantle convection and orogeny of Tianshan Mountains in China

In this study, from the travel time data recorded in the Tianshan passive seismic array experiment, we present the P-wave velocity structure of the upper mantle down to 660 km along the Kuqa-Kuitun pro-file in terms of seismic tomography technique. Based on the P-wave velocity model, we derive the corresponding 2D upper mantle density model. The 2D small-scale convection of the upper mantle underneath the Tianshan Mountains in China driven by the density anomalies is simulated using the hybrid finite element method combining with the marker-in-cell technique. The main features of the upper mantle convection and the reciprocation between the convection and mountain building are in-vestigated. The results manifest that (1) in the upper mantle underneath the Junggar basin and North Tianshan exists a counterclockwise convection, which scale is ~ 500 km; (2) underneath the Tarim ba-sin and South Tianshan exists a clockwise northward convection, which is relatively weak; (3) the convective velocity at the top of the upper mantle underneath the Tianshan Mountains in China should not be less than 20 mm/a, while considering the dependent of convective velocity on the viscosity; (4) the northward extrusion of the Tarim block plays a key role in the Cenozoic Tianshan mountain building and the present-day tectonic deformation of the Tianshan range is related closely to the upper mantle convection; and (5) the northward subduction of the Tarim block does not influence obviously the up-per mantle convection.     

Multi-oriented and layered structures of lith osphere in orogenic belt and their effects on Cenozoic magmatism

Integrating the surface structures with the reinterpretations of 3-D velocity images, this paper puts forward a kind of multi-oriented and layered structure for those of the upper and mid-lower crust, lithospheric and asthenospheric mantle in Tethyan orogenic belt of western Yunnan and Sichuan, China (Sanjiang belt). There exists a detachment between upper and mid-lower crust. The lithospheric mantle is a rigid and competent body unable to be deformed which preserved the older tectonic framework. The asthenosphere is an imcompetent layer that is easy to be deformed, and behaves as an initiation region of deformation, and its structural patterns reflect younger tectonics. The Cenozoic intracontinental magmatism of this region is controlled by: (i) sub-meridional and NNE trending asthenospheric upwelling around the western margin of Yangtze block; (ii) crust-mantle transitional layer formed by underplating of ascending melts; and (iii) intersection or transformation of regional structures such as major faults.     

U-Pb isotopic geochemistry of the post-collisional mafic-ultramafic rocks from the Dabie Mountains——Crust-mantle interaction and LOMU component

Geochronological studies of mafic-ultramafic intrusions occurrence in the northern Dabie zone (NDZ) suggest that these pyroxenite-gabbro intrusions formed 120—130 Ma ago should be post-collisional magmatic rocks[1—4]. These mafic-ultramafic rocks provid…     

Geophysical observations pertaining to solid-state convection in the terrestrial planets

We present a broad-based review of the observational evidence that pertains to or otherwise implies solid-state convection to be occurring (or have occurred) in the interiors of the terrestrial planets.For the Earth, the motion of the plates is prima facie evidence of large-scale mantle convection. Provided we understand upper-mantle thermal conductivity correctly, heat flow beneath the old ocean basins may be too high to be transported conductively from the upper mantle through the base of the lithosphere and therefore convection on a second smaller scale might be operative. The horizontal scale of plate dimensions implies, due to typical cell aspect ratios observed in convection, that the motion extends to the core-mantle boundary. Improved global data coverage and viscoelastic modeling of isostatic rebound due to Pleistocene deglaciation imply a uniform mantle viscosity, and thus indicate that whole-mantle convection could exist. Additionally, there is some seismic evidence of lithospheric penetration to depths deeper than 700 km. We discuss some salient features and assumption boundedness of arguments for convection confined to the upper mantle and for convection which acts throughout the mantle since the vertical length scale has a profound effect upon the relevance of geophysical observations. The horizontal form of mantle convection may be fully three-dimensional with complex planform and, therefore, searching for correlative gravity patterns in the ocean basins may not be useful without additional geophysical constraints. Many long-wavelength gravity anomalies may arise from beneath the lithosphere and must be supported dynamically, although thermal convection is not a unique explanation. Topography is an additional geophysical constraint, but for wavelengths greater than a few hundred kilometers, a general lack of correlation exists between oceanic residual gravity and topography, except at specific locations such as Hawaii. Theoretical calculations predict a complex relationship between these two observational types. Oceanic gravity data alone shows no regular planform and there is no correlation with any small-scale convective pattern predicted by laboratory experiments.All of the observational evidence argues against Martian plate tectonics occurring now or over much of the history of this planet, but lack of plate tectonics is not an argument against interior convection. The Tharsis uplift on Mars may have resulted from convective processes in the mantle, and the present-day gravity anomaly associated with Tharsis must be supported by the finite strength of the lithosphere or by mantle convection. Stresses imparted by the present topographic load would be greater than a kilobar, in excess of long-term finite strength. Observed fracture patterns are probably a direct result of this load, and the key question concerns the level of resultant strain relief. The global topographic and geomorphic dichotomy between the northern and southern hemisphere required a solid-state flow process to create the accompanying center-of-figure to center-of-mass offset.Lunar heat flow values, in analogy with oceanic heat flow on the Earth, strongly imply a convective mechanism of heat transport in the interior which, based on seismic Q values, is limited to the lower mantle. The presence of moonquakes in this region does not preclude solid-state convective processes. Lunar conductivity profiles provide no information on convection because of the difficulty in conductivity modeling, uniqueness of models, and the uncertainty in the conductivity-temperature relationship. The excess oblateness of the lunar figure over the hydrostatic value does not require convective support; in fact, such a mechanism is unlikely.The presence of a dipole magnetic field on Mercury does not provide a constraint on mantle convection unless its existence can be inextricably linked to a molten core. The non-hydrostatic shape of the equatorial figure, required for the observed $\text{3}\text{2}$ resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The $\text{3n}\text{2}$ resonance implies escape from a 2n resonance and, therefore, is related to the question of a molten core. Further dynamical data is needed to constrain interior models.Interpretation of limited radar imagery for the surface of Venus is enigmatic in terms of plate tectonics and therefore interior convection. Linear tensional and possibly compressional features are observed, but there are also crustal regions which appear to show large impact structures and are thus geologically old and may not have been recycled.