V. P. Trubitsyn

Geodynamic model of the evolution of the Pacific Ocean

The present Pacific Ocean differs significantly in its structure and evolution from the expanding Atlantic Ocean. The Pacific is asymmetric. Its mid-ocean ridge is located not along its median line but is closer to South America and adjoins North America. The Pacific is surrounded by a ring of subduction zones but has marginal seas only at its Eurasian margins. After the breakup of Pangea, the Atlantic began to open and the Pacific began to close. This paper examines the evolution of the Pacific Ocean and, in particular, the formation mechanisms of its present structures. Numerical modeling of the long-term drift of a large continent is performed, with the initial position of the continent corresponding to the state after the breakup of the supercontinent. At first the continent, driven by the nearest descending mantle flow, begins to approach a subduction zone. Since the mantle flows beneath a large continent have different directions, its velocity is a few times lower than that of the mantle flows near the subduction zone. As a result, a zone of extension arises at the active continental margin and a fragment is broken off from the continent; this fragment rapidly moves away and stops above the descending mantle flow as in a trap. A marginal sea forms at the active continental margin. The continent continues its slow movement toward the subduction zone. The oceanic lithosphere, which earlier sank vertically, begins to descend obliquely. This evolutionary stage corresponds to the present position of Eurasia. The modeling shows how the interaction of the continent with the mantle causes the subduction zone to roll back toward the ocean. Subsequently, the continent nevertheless catches up with the subduction zone, and they move together for a while. The marginal sea then closes and high compressive stresses arise at the active continental margin. This state corresponds to the present position of South America. During the subsequent drift, the continent together with the subduction zone reaches the mid-ocean ridge and partially overrides it. This state corresponds to North America, which was the first to break off from Pangea and passed through the stages of both Eurasia and South America. The large and slowly moving Eurasia, which formed only at the time of Pangea, is still in the first evolutionary stage of the Pacific Ocean closure.

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.

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.

Exact analytical solutions of the stokes equation for testing the equations of mantle convection with a variable viscosity

Presently, the study of the mantle flow structure is mainly based on numerical modeling. The most important stage of the development of a computer program is its testing. For this purpose, results of various test models of convection flows with a given set of parameters are compared. The solution of the Stokes equation, involving the derivative of viscous stresses, is most difficult. Exact analytical solutions of the Stokes equation are obtained in this work for various cases of special loads. These solutions can be used as benchmarks for testing programs of numerical calculation of viscous flows in both geophysics and engineering. The advantage of this testing technique is the exceptional simplicity of the solution form, the admissibility of any spatial viscosity variations, and the fact that solutions can be compared not for a narrow set of the solution parameters but for any distributions of velocities, viscous stresses, and pressures at all points of the space.

Numerical models of subduction of the oceanic crust with basaltic plateaus

Light continents and islands characterized by a crustal thickness of more than 30 km float over a convective mantle, while the thin basaltic oceanic crust sinks completely in subduction zones. The normal oceanic crust is 7 km thick. However, anomalously thick basaltic plateaus forming as a result of emplacement of mantle plumes into moving oceanic lithospheric plates are also pulled into the mantle. One of the largest basaltic plateaus is the Ontong Java plateau on the Pacific plate, which arose during the intrusion of a giant superplume into the plate ∼100 Myr ago. Notwithstanding its large thickness (averaging ∼30 km), the Ontong Java plateau is still experiencing slow subduction. On the basis of numerical modeling, the paper analyzes the oceanic crust subduction process as a function of the mantle convection vigorousness and the density, thickness, viscosity, and shape of the crust. Even a simplified model of thermocompositional convection in the upper mantle is capable of explaining the observed facts indicating that the oceanic crust and sediments are pulled into the mantle and the continental crust is floating on the mantle.

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.

Seismic tomography and continental drift

Based on data of seismic tomography, the structure of the mantle flows of the contemporary Earth and the continental drift are calculated. Results of calculation of the contemporary motion of continents and their future drift for 150 Myr are presented. The present-day positions of six continents and the nine largest islands are taken as an initial state. The contemporary temperature distribution in the mantle is calculated according to the data of seismic tomography. The 3-D distribution of seismic wave velocities is converted into the density distribution and then into the temperature distribution. The Stokes equation is numerically solved for flows in a viscous mantle with floating continents for the given initial temperature distribution. In this way, the velocities of convective flows are determined in the entire present-day mantle and the surface distribution for the Earth’s heat flux is obtained. The reliability of the calculated flows in the mantle is estimated by the comparison of the calculated velocities of the contemporary continents and oceanic lithosphere with data of satellite measurements. Further, evolutionary equations of convection with floating continents were numerically solved. The calculated structure of mantle flows, temperature distribution, and position of continents are presented for a time moment 150 Myr in the future. The resulting successive changes in the position of continents in time show how islands (in particular, Japan and Indonesia) will be attached to continents and how continents will converge, exhibiting a tendency toward the formation of a new supercontinent in the southern hemisphere of the Earth.

Phase Transition Zone Width Implications for Convection Structure

A temperature and pressure increase in the mantle causes phase transitions and related density changes in its material. The transition boundary in the pressure-temperature phase diagram is determined by the curve of phase equilibrium with the slope γ = dp/dT. If the slope is nonzero, a phase transition in hot ascending and cold descending mantle flows occurs at different depths and, therefore, either enhances (γ > 0) or slows down convection (γ < 0). The mantle material has a multicomponent composition. Therefore, phase transitions in the mantle are distributed over an interval of pressures and depths. In this interval, the concentration of one phase smoothly decreases and the concentration of the other increases. The widths of phase transition zones in the Earth’s mantle vary from 3 km for the endothermic transition in olivine at a depth of 660 km to 500 km for the exothermic transition in perovskite, and the high-to-low spin change in the atomic state of iron takes place at a depth of about 1500 km. This work presents results of calculations demonstrating the convection effect of phase transitions as a function of the transition zone width. Transitions of both types with different slopes of the phase curve and different intensities of mantle convection are examined. For the first time, the convection enhancement and an increase in the mass transfer across the phase boundary are quantitatively investigated in the presence of an exothermic phase transition as a function of the slope of the phase curve. The mixing of material under conditions of partially layered convection is examined with the help of markers.

Convection in the Mantle with an Endothermic Phase Transition

An endothermic phase transition at a depth of 660 km in the mantle partially slows down mantle flows. Many models considering the possibility of temporary layering of flows with separation of convection in the upper and lower mantle have been constructed over the past two decades. The slowing-down effect of the endothermic phase transition is very sensitive to the slope of the phase-equilibrium curve. However, laboratory measurements contain considerable uncertainties admitting both a partial convection layering and only an insignificant slowing down of a part of downgoing mantle flows. In this work, we present results of calculations of mantle flows within a wide range of phase-transition parameter values, determine ranges of one-and two-layer convection, and derive dependences of the amplitude and period of oscillations on phase-transition parameters.

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.