A conservative form of the deep convection equations and the efficiency of heat energy conversion in a polytropic mantle model

A wide class of equations is defined for a high pressure and subcritical temperature range of a fluid state whose thermodynamic properties enable the construction of a polytropic model of the mantle. A variant of deep convection equations of the Ogura and Phillips type is substantiated in terms of the polytropic mantle model. The proposed system of the deep convection equations includes fluctuation of the generalized potential temperature, has a quasi-incompressible form, and is transformed into Mihaljan’s system of shallow convection equations with a decrease in the layer depth. This circumstance is of great importance because it validates the use of the same dimensionless parameters as in the shallow convection model. The advantage of the proposed variant of the deep convection equations is its complete conservatism, which allows one to gain constraints on the efficiency of energy conversion in deep mantle processes and the thermal energy power expended on the generation rate of the convection kinetic energy and associated processes. This power is shown to be of the order of half the geothermal flux measured on the Earth’s surface.     

Temperature and distribution of radioactive matter in the upper mantle

Temperatures of the Earth’s upper mantle, derived from Gutenberg’s seismic velocities, have been revised, using some recent determinations of the clastic constants of dunites. For depths greater than about 50 km the temperature obtained is sufficient to melt the basaltic fraction of a periodotitic mantle (if this low-melting fraction still exists at those depths). The distribution of the radioactive heat sources appears to be fairly uniform down to about 110 km; below this level the radioactive matter is probably absent. This is what would be expected for the upper mantle below the oceans; therefore, Gutenberg’s velocities seem to correspond to oceanic areas, rather than to the mantle below a continental shield.     

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.     

Geoneutrinos and the energy budget of the Earth

The total energy loss of the Earth is well constrained by heat flux measurements on land, the plate cooling model for the oceans, and the buoyancy flux of hotspots. It amounts to 46 ± 2 TW. The main sources that balance the total energy loss are the radioactivity of the Earth's crust and mantle, the secular cooling of the Earth's mantle, and the energy loss from the core. Only the crustal radioactivity is well constrained. The uncertainty on each of the other components is larger than the uncertainty of the total heat loss. The mantle energy budget cannot be balanced by adding the best estimates of mantle radioactivity, secular cooling of the mantle, and heat flux from the core. Neutrino observatories in deep underground mines can detect antineutrinos emitted by the radioactivity of U and Th. Provided that the crustal contribution to the geoneutrino flux can be very precisely calculated, it will be possible to put robust constraints on mantle radioactivity and its contribution to the Earth's energy budget. Equally strong constraints could be obtained from a deep ocean observatory without the need of crustal correction. In the future, it may become possible to obtain directional information on the geoneutrino flux and to resolve radial variations in concentration of heat producing elements in the mantle.     

Effect of hydration on the elasticity of mantle minerals and its geophysical implications

Recent studies have shown that major nominally anhydrous minerals in the Earth’s mantle, such as olivine, pyroxene and garnet, can incorporate considerable amounts of water as structurally bound hydroxyl. Even a small amount of water is present in mantle minerals, it can strongly affect a number of physical properties, including density, sound velocity, melting temperature, and electrical conductivities. The presence of water can also influence the dynamic behavior, lead to lateral velocity heterogeneities, and affect the material circulation of the Earth’s deep interior. In particular, seismic studies have reported the existence of low-velocity zones in various locations of the Earth’s upper mantle and transition zone, which has been expected to be associated with the presence of water in the region. In the past two decades, the effect of water on the elasticity and sound velocities of minerals at relevant pressure-temperature (P-T) conditions of the Earth’s mantle attracted extensive interests. Combining the high P-T experimental and theoretical mineralogical results with seismic observations provides crucial constraints on the distribution of water in the Earth’s mantle. In this study, we summarize recent experimental and theoretical mineral physics results on how water affects the elasticity and sound velocity of nominally anhydrous minerals in the Earth’s mantle, which aims to provide new insights into the effect of hydration on the density and velocity profile of the Earth’s mantle, which are of particular importance in understanding of water distribution in the region.     

On the precession driven geodynamo

Formation of flow structures in the Earth’s liquid core enclosed in a precessing and rotating shell (mantle) is examined within the hydrodynamic approach. The kinematics and energetics of the motions in the Earth’s core initiated by precession allow one to regard these motions as a possible geodynamo mechanism at an early evolutionary stage of the Earth (prior to the formation of the solid core). The influence of the precession driven geodynamo on the stability of the geomagnetic field is discussed.     

On Earth’s Mantle Constitution and Structure from Joint Analysis of Geophysical and Laboratory-Based Data: An Example

Determining Earth’s structure is a fundamental goal of Earth science, and geophysical methods play a prominent role in investigating Earth’s interior. Geochemical, cosmochemical, and petrological analyses of terrestrial samples and meteoritic material provide equally important insights. Complementary information comes from high-pressure mineral physics and chemistry, i.e., use of sophisticated experimental techniques and numerical methods that are capable of attaining or simulating physical properties at very high pressures and temperatures, thereby allowing recovered samples from Earth’s crust and mantle to be analyzed in the laboratory or simulated computationally at the conditions that prevail in Earth’s mantle and core. This is particularly important given that the vast bulk of Earth’s interior is geochemically unsampled. This paper describes a quantitative approach that combines data and results from mineral physics, petrological analyses of mantle minerals, and geophysical inverse calculations, in order to map geophysical data directly for mantle composition (major element chemistry and water content) and thermal state. We illustrate the methodology by inverting a set of long-period electromagnetic response functions beneath six geomagnetic stations that cover a range of geological settings for major element chemistry, water content, and thermal state of the mantle. The results indicate that interior structure and constitution of the mantle can be well-retrieved given a specific set of measurements describing (1) the conductivity of mantle minerals, (2) the partitioning behavior of water between major upper mantle and transition-zone minerals, and (3) the ability of nominally anhydrous minerals to store water in their crystal structures. Specifically, upper mantle water contents determined here bracket the ranges obtained from analyses of natural samples, whereas transition-zone water concentration is an order-of-magnitude greater than that of the upper mantle and appears to vary laterally underneath the investigated locations.     

Deep electrical conductivity features in the transition zone from the Pacific to Eurasia

Understanding the processes that occur in the transition from the Pacific Ocean to Eurasia is key to constructing the tectonic models of the Earth’s shells and the convection models of the upper mantle. The electromagnetic methods permit estimating the temperature and fluid content (and/or carbon (graphite) content) in the Earth’s interior. These estimates are independent of the traditionally used estimates based on seismic methods because the dependence of electrical conductivity on the physical properties of the rock is based on different principles than the behavior of the elastic waves. The region is characterized by a complicated geological structure with intense three-dimensional (3D) surface heterogeneities, which significantly aggravate the retrieval of the information about the deep horizons in the structure of the Earth’s mantle from the observed electromagnetic (EM) fields. The detailed analysis of the nature of the deep electrical conductivity and structural features of the transition from the Pacific to Eurasia included numerical modeling of the typical two- and three-dimensional models has been carried out. Based on this analysis, the approaches that increase the reliability of the interpretation of the results of the EM studies are suggested.     

On the admissible range of the radial temperature gradient and Brünt-Väisäla frequency in the mantle and core: I. Main relations

The question of ambiguity in the solution of the inverse problem for determining the Brünt-Väisäla frequency in the Earth’s mantle from the entire set of the up-to-date data on seismicity, free oscillations, and forced nutations of the Earth, as well as the data on the Earth’s total mass and total moment of inertia, is considered. Based on the results of a series of numerical experiments, the band of admissible distributions of the Brünt-Väisäla frequency and mantle density with depth is calculated. This estimate is used for investigating the convective and gravitational stability of the different regions of the mantle against relatively small adiabatic and nonadiabatic perturbations. The generalization of the known Rayleigh criterion of convective stability of homogeneous and a nonself-gravitating incompressible viscous fluid for the case of a compressible self-gravitating fluid is given. A system of the ordinary eight-order differential equations with complex coefficients and homogeneous boundary conditions, whose eigenvalues determine the transition from the stable state to instability, is obtained. Examples of the numerical determination of these eignevalues are presented. For interpreting the data about the band of the admissible distributions of the Brünt-Väisäla frequency with depth, the notion of the effective bulk modulus of the medium at different depths is introduced. This quantity governs the depth changes in temperature in a convecting mantle and allows us to make a conclusion about the role of heat conduction and the radial heterogeneity of the mantle composition without imposing any constraints on the convection mechanism. It is shown that within the present-day observation errors in the frequencies of the Earth’s free oscillations, the simplest reasonable model is that in which the ratio of the effective bulk modulus to its adiabatic value in the lower and middle mantle is 1.043 ± 0.05. The closeness of this value to unity indicates that convection in the lower and middle mantle is fairly close to adiabatic. At the same time, when the analysis only relies on seismic data and on the information about the periods of the free oscillations of the Earth, there is a significant uncertainty in the models of the effective bulk modulus distribution in the upper mantle and crust. This uncertainty precludes us from making purely empirically derived conclusions that reliably and unambiguously describe the role of the effects of heat conduction and radially heterogeneous material composition in the convection in the upper mantle.     

Correlation of variations in the thermal neutron flux from the Earth’s crust with the Moon’s phases and with seismic activity

The results of the long-term recording of thermal neutron flux near the Earth’s surface with the use of an unshielded scintillation thermal-neutron detector are presented. The data obtained indicate the presence of periodic variations in the thermal neutron flux with the lunar diurnal and the lunar monthly periods. A hypothesis about the existence in the Earth’s crust of radon-neutron tidal variations in the concentration of thermal neutrons, correlated with the Moon’s phases and which have the gravitational origin, is formulated and confirmed experimentally. A simple mathematical model is proposed, which satisfactorily describes the observed variations. The case of the anomalous behavior of thermal neutrons is presented, which correlates with the high local seismic activity.     

Theory of EM monitoring of sea bottom geothermal areas

Monitoring of geophysical conditions of marine sedimentary basins is necessary for predicting seismic events and for adaptation of geothermal technologies for seismically active (as a rule) sea bottom geothermal areas. These conditions are characterized by seismo-hydro-electromagnetic (EM) geophysical field interaction in the presence of gravity. Based on the main physical principles, geophysical and petrophysical data, we formulate a mathematical model of seismo-hydro-EM interaction in a basin of a marginal sea and calculate the transformation of a seismic excitation in the upper mantle under the central part of the sea of Japan into the low-frequency (0.1 to 10 Hz) EM signals at the top of the sea bottom sedimentary layer, at the sea surface and in the atmosphere up to the lower boundary of the ionosphere. Physics of the EM generation and propagation process is shown including: generation of EM waves in the upper mantle layer M by a seismic wave from under M, spatial modulation of diffusive EM waves by a seismic wave, stopping of the EM wave arrived (before the seismic P wave) from the upper mantle at the top of the sediments because of the high electric conductivity of seawater (3.5 S/m), immediate penetration of the EM wave through the seawater thickness after the delayed seismic P wave shock into the sea bottom, and EM emission from the sea surface into the atmosphere. Let us note that the EM signal in the sea bottom sediments is the first measurable signal of a seismic activation of geological structures beneath the seafloor and this signal is protected by seawater from the influence ionosphere disturbances. Amplitude of the computed magnetic signals (300, 200, 50, and 30 pT at the ocean–atmosphere interface and at the height of 10, 30 and 50 km, respectively), their predominant frequency (0.25 Hz), the delay of the seismic P wave in regard to the magnetic signal for the receivers at the shore (20 s), the amplitude of temperature disturbances in sediments (up to 0.02 K), the parameters of the long (150 km) tsunami wave of a small (up to 20 cm) amplitude far from the shore and other values that characterize the seismo-hydro-EM process are of the orders observed. Recommendations for the EM monitoring of dynamic processes beneath seafloor geothermal areas are given.     

Formalization of assessing radioactive waste burial site seismic regime parameters from seismological and geological data

A model is proposed that shows the relation of the block structure of the crust and earthquake sources (Sadovskii, 1979; Rodionov, 1979, 1984, 1994; Bugaev, 1999, 2011, 2014, 2015). The model can formalize how to assess the prediction of seismic regime parameters depending on the elastic limit and conditions and rate of deformation of the Earth’s crust. The spent nuclear fuel repository site in Olkiluoto (Finland) and a site in the area of the Krasnoyarsk Mining and Chemical Combine are considered as examples. It is demonstrated that the parameters of the prediction graphs limit the location of the points of magnitude repeatability graphs calculated for a site based on samples of earthquakes in the area according to different authors. This makes it possible to recommend predictive assessment of seismic regime parameters for stability monitoring of the seismic regime and safety analysis of a geological environment’s insulation properties for waste sites from the results of seismological monitoring and high-precision observations of modern movements of the Earth’s crust.     

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.     

The structure of convection in the spherical mantle with internal heating

Thermal convection in the mantle is caused by the heat transported upwards from the core and by the heat produced by the internal radioactive sources. According to the data on the heat transfer by the mantle plumes and geochemical evidence, only 20% of the total heat of the Earth is supplied to the mantle from the core, whereas most of the heat is generated by the internal sources. Along with the models that correctly allow for the internal heat sources, there are also many publications (including monographs) on the models of mantle convection that completely ignore the internal heating or the heat flux from below. In this study, we analyze to what extent these approximations could be correct. The analytical distributions of temperature and heat flux in the case of internal heating without convection and the results of the numerical modeling for convection with different intensity are presented. It is shown that the structure of thermal convection is governed by the distribution of the heat flux in the mantle but not by the heat balance, as it is typically implicitly assumed in most works. Heat production by the internal sources causes the growth of the heat flux as a function of radius. However, in the spherical mantle of the Earth, the heat flux decreases with radius due to the geometry. It turned out that with the parameters of the present Earth, both these effects compensate each other to a considerable extent, and the resulting heat flux turns out to be nearly constant as a function of radius. Since the structure of the convective flows in the mantle is determined by the distributions of heat flux and total heat flux, in the Cartesian models of the mantle convection the effective contribution of internal heating is small, and ignoring the heat flux from the core significantly distorts the structure of the convective currents and temperature distributions in the mantle.     

On the modified Taylor constraint

A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe magnetic field generation in Earth’s core well, a magnetostrophic dynamo has not yet been found even though Taylor [Proc. R. Soc. Lond. A 1963, 274, 274–283] devised an apparently viable method of finding one. His method for determining the fluid velocity from the magnetic field and the energy source involved only the evaluation of integrals along lines parallel to the Earth’s axis of rotation and the solution of a second-order ordinary differential equation. It is demonstrated below that an approximate solution of this equation for a broad family of magnetic fields is immediate. Furthermore inertia, which was neglected in Taylor’s theory, is restored here, so that the modified theory includes torsional waves, whose existence in the Earth’s core has been inferred from observations of the length of day. Their theory is reconsidered.     

Comparative analysis of the characteristics of global seismic wave propagation excited by the Mw9.0 Tohoku earthquake using numerical simulation

Giant earthquakes generate rich signals that can be used to explore the characteristics of the hierarchical structure of the Earth’s interior associated with the eigenfrequencies of the Earth.We employ the spectral element method,incorporated with large-scale parallel computing technology,to investigate the characteristics of global seismic wave propagation excited by the2011 Mw9.0 Tohoku earthquake.The transversely isotropic PREM model is employed as a prototype of our numerical global Earth model.Topographic data and the effect of the oceans are taken into consideration.Wave propagation processes are simulated by solving three-dimensional elastic wave governing equations with the seismic moment tensor obtained from the Global Centroid Moment Tensor Catalog.Three-dimensional visualization of our computing results displays the nature of the global seismic wave propagation.Comparative analysis of our calculations with observations obtained from the Incorporated Research Institutions for Seismology demonstrates the reliability and feasibility of our numerical results.We compare synthetic seismograms with incorporated and unincorporated ocean models.First results show that the oceans have obvious effects on the characteristics of seismic wave propagation.The peak displacement and peak velocity of P waves become relatively small under the effect of the ocean.However,the effect of the ocean on S-waves is complex.The displacement and velocity of S waves decrease rapidly over time using an unincorporated ocean model.Therefore,the effects of the ocean should be incorporated when undertaking quantitative earthquake hazard assessments on coastal areas.In addition,we undertake comparative analysis on the characteristics of the Earth’s oscillation excited by the 2004 Sumatra-Andaman,2008 Wenchuan,and 2011Tohoku earthquakes that incorporate the effect of the Earth’s gravitational potential.A comparison of the amplitude spectra of the numerical records indicates that energy released by the three big earthquakes is different.Our comparative analysis realizes that the computing results can accurately reproduce some eigenfrequencies of the Earth,such as toroidal modes 0T2 to 0T13and spheroidal modes 0S7 to 0S31.These results demonstrate that numerical simulations can be successfully used to investigate the Earth’s oscillations.We propose that numerical simulations can be used as one of the major tools to further reveal how the Earth’s lateral heterogeneities affect the Earth’s oscillations.     

First-principles calculations of elasticity of minerals at high temperature and pressure

The elasticity of minerals at high temperature and pressure(PT) is critical for constraining the composition and temperature of the Earth's interior and understand better the deep water cycle and the dynamic Earth. First-principles calculations without introducing any adjustable parameters, whose results can be comparable to experimental data, play a more and more important role in investigating the elasticity of minerals at high PT mainly because of(1) the quick increasing of computational powers and(2) advances in method. For example, the new method reduces the computation loads to one-tenth of the traditional method with the comparable precise as the traditional method. This is extraordinarily helpful because first-principles calculations of the elasticity of minerals at high PT are extremely time-consuming. So far the elasticity of most of lower mantle minerals has been investigated in detail. We have good idea on the effect of temperature, pressure, and iron concentration on elasticity of main minerals of the lower mantle and the unusual softening in bulk modulus by the spin crossover of iron in ferropericlase. With these elastic data the lower mantle has been constrained to have 10–15 wt% ferropericlase, which is sufficient to generate some visible effects of spin crossover in seismic tomography. For example, the spin crossover causes that the temperature sensitivity of P wave at the depth of ~1700 km is only a fraction of that at the depth of ~2300 km. The disruptions of global P wave structure and of P wave image below hotspots such as Hawaii and Iceland at similar depth are in consistence with the spin crossover effect of iron in ferropericlase. The spin crossover, which causes anomalous thermodynamic properties of ferropericlase, has also been found to play a control role for the two features of the large low shear velocity provinces(LLSVPs): the sharp edge and high elevation up to 1000 km above core-mantle boundary. All these results clearly suggest the spin crossover of iron in the lower mantle. The theoretical investigations for the elasticity of minerals at the upper mantle and water effect on elasticity of minerals at the mantle transition zone and subducting slab have also been conducted extensively. These researches are critical for understanding better the composition of the upper mantle and water distribution and transport in the Earth's mantle. Most of these were static calculations, which did not include the vibrational(temperature) effect on elasticity, although temperature effect on elasticity is basic because of high temperature at the Earth's interior and huge temperature difference between the ambient mantle and the subducting slab. Including temperature effect on elasticity of minerals should be important future work. New method developed is helpful for these directions. The elasticity of iron and iron-alloy with various light elements has also been calculated extensively. However, more work is necessary in order to meet the demand for constraining the types and amount of light elements at the Earth's core.     

The study of the radiation characteristics and propagation of seismic waves in the North Caucasus by modeling the accelerograms of the recorded earthquakes

For evaluating the parameters of the vibrations of the Earth’s surface in the case of strong earthquakes, which are possible in the future, the regular patterns of the emission and propagation of seismic waves in the North Caucasus regions are investigated. The regional parameters of emission and propagation of seismic waves are evaluated by solution of the inverse problems of stochastic modeling of the accelerograms of the earthquakes, recorded by the seismic station in Sochi. The horizontal components of the strongest earthquakes (M _w ～ 3.9?5.6), that occurred in 2002–2006 within a radius of ～300 km from the seismic station, with source depths up to 60 km are modeled. For calculations of accelerograms, estimates of the quality are used, obtained earlier for this region in the form: Q(f) ～ 80 ～ f ^0.9. The parameter settings are carried out, which determine the shapes of the source spectra, the amplification of the seismic waves in the Earth’s crust, the weakening of the waves at high frequencies (κ), the parameters that determine the shape and duration of accelerograms, etc. Sufficiently good agreement of the calculated and recorded accelerograms is obtained, the regional characteristics of emission and propagation of seismic waves, which can be used for prediction of the parameters of strong motions in the North Caucasus, are evaluated; however, in the future these characteristics should be studied in more detail.     

地气耦合研究进展简介

简要介绍了近十多年来地气相互作用研究领域所取得的成果,并从整体地球系统的角度探索自然灾害(气象灾害和地震灾害)的成因.在总结和评述过去工作的基础上,提出了地幔对流节律性假说,并利用这一假说解释了板缘地震、地球自转和厄尼诺之间的关系;利用地幔中存在中小尺度对流这一设想并结合绝对涡度守恒原理讨论了板内地震、地热流和旱涝分布之间的联系.最后提出了对今后地气耦合研究工作的一些看法.