Uwe Walzer

Friedrich Schiller University Jena | FSU · Institute of Geosciences, Geodynamics

ABSTRACT We investigated the interactions between continental growth and breakup, inorganic carbonate–silicate cycle, volcanic activity, glaciations, natural climate change, and biotic evolution. As far as volcanism is concerned, the large igneous provinces (LIPs) are proving to be particularly effective. However, this conclusion is not valid with...

This paper presents the computational basis for the study of Walzer and Hendel (2022b), who consider the relationships between continental growth, sedimentary geology, natural climate change, and ice ages. Here we solve the full set of balance equations for mass, energy, momentum, and angular momentum for a 3D spherical-shell mantle. The assumed ra...

This paper presents the computational basis for the study of Walzer and Hendel (2022), who consider the relationships between continental growth, sedimentary geology, natural climate change, and ice ages. Here we solve the full set of balance equations for mass, energy, momentum, and angular momentum for a 3D spherical-shell mantle. The assumed rad...

Oceanic plateaus develop by decompression melting of mantle plumes and have contributed to the growth of the continental crust throughout Earth's evolution. Occasional large-scale partial melting events of parts of the asthenosphere during the Archean produced large domains of precursor crustal material. The fractionation of arc-related crust durin...

Some essential features of Andean orogenesis cannot be explained only by a dynamic regional model since there are essential influences across its vertical boundaries. A dynamic regional model of the Andes should be embedded in a 3-D spherical-shell model. Because of the energy distribution on the poloidal and toroidal parts of the creep velocity an...

[1] We investigate whether the observed zircon age distribution of continental crust (CC) is produced by real crustal growth episodes or is only an artifact of preservation. In connection with the second alternative of this question, other authors proposed that there was little episodicity in the production of new CC and that modeling corroborates...

Section 1 refers to hypotheses on the origin of life. These different hypotheses require distinct geodynamic and structural-geology prerequisites. E.g., in case of chemoautotrophic metabolism-first hypotheses, a plate-tectonic mechanism is necessary that contains sites of reducing volcanic exhalations. It was shown that the mass extinctions of biol...

A dynamic 3-D spherical-shell model for the chemical evolution of the Earth’s mantle is presented. Chemical differentiation, convection, stirring, and thermal evolution constitute an inseparable dynamic system. Our model is based on the solution of the balance equations of mass, momentum, energy, angular momentum, and four sums of the number of ato...

As a model for the Bénard convection in the asthenosphere the problem of the hydrodynamic stability of an infinite horizontal layer is calculated. The layer consists of a micropolar fluid with streich. The field equations for the velocity vector, microrotation vector, microstretch, microinertia, density, temperature, and pressure form a system of e...

The relationships existing between melting temperature and other macroscopic physical quantities are investigated. A new dimensionless quantity Q(1 not containing the Grtineisen parameter proves to be suited for serving in future studies as a tool for the determination of the melting temperature in the outer core of the Earth. The pressure dependen...

We present a dynamic 3-D spherical-shell model of mantle convection and the evolution of the chemical reservoirs of the Earth`s silicate shell. Chemical differentiation, convection, stirring and thermal evolution constitute an inseparable dynamic system. Our model is based on the solution of the balance equations of mass, momentum, energy, angular...

We present the basic conception of a new dynamical model of the thermal and chemical evolution of Mars. Therefore new enlargements of the code Terra are necessary which allow to improve the solutions of the convection differential equations with strongly varying viscosity. These enlargements have been partly tested already. We describe consideratio...

Solid state convection in the rocky mantles is a key to understanding the thermochemical evolution and tectonics of terrestrial planets and moons. It is driven by internal heat and can be described by a system of coupled partial differential equations. There are no analytic solutions for realistic configurations and numerical models are an indispen...

We compute a model of thermal and chemical evolution of the Earth’s mantle by numerically solving the balance equations of mass, momentum, energy, angular momentum and of four sums of the number of atoms of the pairs 238U-206Pb, 235U-207Pb, 232Th-208Pb, and 40K-40Ar. We derive marble-cake distributions of the principal geochemical reservoirs and sh...

We present the basic conception of a new fluid-dynamic and geodynamic project on the Andean orogeny. We start with a kinematic analysis of the entire orogeny and test different numerical options to explain these systematized observations by a physical model. Therefore we consider partly kinematic, partly dynamic regional models as well as purely dy...

We present a three-dimensional spherical shell numerical model for chemical differentiation and redistribution of incompatible elements in a convective Earth's mantle heated mostly from within by U, Th, and K and slightly from below. The evolution-model equations guarantee conservation of mass, momentum, energy, angular momentum, and four sums of t...

The focus of this paper is numerical modeling of crust-mantle differentiation. We begin by surveying the observational constraints of this process. The present-time distribution of incompatible elements are described and discussed. The mentioned differentiation causes formation and growth of continents and, as a complement, the generation and incre...

This is a report on first steps for a combination of two numerical models of the evolution of the Earth’s mantle: The first one, K3, is a new 2-D convection-fractionation model that simulates the growth of continents and of the geochemically complementary depleted mantle reservoir. The second model shows the 3-D generation of oceanic lithospheric p...

The thermal evolution of the Earth is controlled by radioactive elements whose heat production rate decays with time and whose spatial distribution depends on chemical segregation processes. We present a 2-D and finite-difference Boussinesq convection model with temperature-dependent viscosity and time- and space-dependent radioactive heat sources....

The main subject of this paper is the numerical simulation of the chemical differentiation of the Earth’s mantle. This differentiation induces the generation and growth of the continents and, as a complement, the formation and augmentation of the depleted MORB mantle. Here, we present for the first time a solution of this problem by an integrated t...

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convecti...

At first, we develop the theory and show numerical simulations of solid-state convection of the Martian mantle. Available structural models of Mars have been studied in order to receive a basic model for our dynamical calculations of the Martian spherical- shell mantle. We newly derived thermal expansivity, activation volume and energy, Grüneisen p...

Compared to [33], the model of the thermal evolution of the Earth’s mantle is considerably improved. The temporal development of the radial viscosity profile due to cooling of the Earth could substantially be taken into account by numerical progress using a new variant of the temperature- and pressure-dependence of the shear viscosity of the mantle...

The first part of this investigation refers to the theory and numerical simulations of solid-state convection of the Martian mantle. Available structural models of Mars have been critically studied to receive a basic model for our dynamical calculations of the Martian spherical-shell mantle. We newly derived thermal expansivity, activation volume,...

The present paper describes a set of numerical experiments on the mantle's thermal evolution with an infinite Prandtl number fluid in a compressible spherical shell heated mainly from within. We used the anelastic liquid approximation with Earth-like material parameters. The usual variable-viscosity approach in mantle-convection models is the assum...

The viscosity stratification has a strong influence on the thermal evolution of a compressible Earth’s mantle with time-dependent internal heating. The differential equations for infinite Prandtl-number convection are solved using a three-dimensional finite-element spherical-shell method on a computational mesh derived from a regular icosahedron wi...

Extraction of partial melt and degassing produce geochemical heterogeneities near the Earth's surface, which are exposed to stirring by mantle convection than. Here we investigate stirring properties of time-dependent velocity fields, obtained from numerical mantle-convection models. Common features of all model mantles are 3-d spherical geometry,...

We present two investigations of the evolution of the Earth's mantle with variable viscosity and time-dependent internal heating. In the first model,the differential equations for infinite Prandtl-number convection are solved using a 3D FE spherical-shell method for a compressible mantle.In the second model,we developed a 2D FD convection model wit...

A 3-D compressible spherical-shell model of the thermal convection in the Earth’s mantle has been investigated with respect to its long-range behavior. In this way, it is possible to describe the thermal evolution of the Earth more realistically than by parameterized convection models. The model is heated mainly from within by a temporally declinin...

U. Walzer, R. Hendel, and J. Baumgardner. Generation of plate-tectonic behavior and a new viscosity profile of the Earth's mantle. In D. Wolf, G. Münster, and M. Kremer, editors, NIC Symposium, volume 20 in NIC Series, pages 419-428, Jülich, 2003b. Generation of Plate-Tectonic Behavior and a New Viscosity Profile of the Earth's Mantle Uwe Walzer1,...

U. Walzer and R. Hendel. Convection and the formation of the principal reservoirs of the Earth's silicate mantle. EOS, 80, no. 46, F1171, 2000. 1999 Fall Meeting Search Results: V41E-01 Convection and the Formation of the Principal Reservoirs of the Earth's Silicate Mantle * Walzer, U. uwe@kokopelli.lanl.gov Inst.Geowiss., Univ.Jena, Burgweg 11,...

There are geochemical reservoirs (CC, DM, PM, EM1, EM2, HIMU) in the Earth's mantle and crust. They are distinguished by their isotopic and chemical abundance ratios and they arise from the combination of partial melting, segregation, ascent of the melt, differentiation of the melt, and lateral transport. The fractionation generates the chemical an...

The evolution of the Earth is characterized by irreversible processes: radioactive decay of the major heat-producing elements, thermal convection and chemical segregation. The prevailing heating from within and the temperature dependence of the viscosity are essential for thermal convection. In the present paper, the chemical and thermal evolution...

U. Walzer. Melting temperature systematics of binary intermetallic compounds. High Temp. - High Pressures, 24:35-44, 1992 Melting temperature systematics of binary infermetallic compounds U. Walzer Institut für Geowissenschaften, Universität Jena Burgweg 11, 6900 Jena, Germany Abstract The melting temperature of pure metals is calculated as a fun...

U. Walzer. The application of a pseudopotential approach to the physics of binary intermetallic compounds. High Temp. - High Pressures, 24:23-34, 1992. The application of a pseudopotential approach to the physics of binary intermetallic compounds U. Walzer Institut für Geowissenschaften, Universität Jena Burgweg 11, 6900 Jena, Germany Abstract A...

First, a survey is given of semiempirical approaches designed for predicting physical and chemical properties of binary alloy systems from the properties of the elements. The same goal is pursued with the help of a pseudopotential theory with optimum transferability derived from relativistic quantum mechanics. The curves of the l-dependent bare-ion...

At first, a review is given on how structure maps for the prediction of the space group and structure type of AB-type binary compounds can be designed with the help of semiempirical theories. Then, two ab-initio pseudopotential theories are compared in detail. The all-electron single-particle equation and the spin-density-functional formalism form...

Norm-conserving pseudopotentials derived from the Dirac equation serve for the derivation of new characteristic quantities. For each chemical element and each electron shell, two characteristic energy and two characteristic spacing quantities are calculated. Therefrom, functions are formed for binary compounds and alloys of type AB. If two each of...

U. Walzer. Cohesion in transition metals under high pressures. Preceedings XXV. Annual Meeting of the European High Pressure Research Group. In H. Vollstädt (Ed.), High Pressure Geosciences and Material Synthesis. Akademie-Verlag Berlin, 110-113, 1988. Cohesion in transition metals under high pressures U. Walzer Key words: high-pressure physics, s...

A description of the d-band structure in which the pseudopotential theory is combined with the muffin-tin orbital theory serves for the calculation of the cohesive properties of d-state metals. The coupling of free-electron states and local, non-overlapping d-states is also taken into account. On this basis, two new models are developed. In both th...

Elements considered include Fe and Ni.-C.M.B.H.

A theory linking the nearly-free-electron theory to d-band broadening and hybridization effects is further developed in such a way that a model, called MA, for the energy, the pressure p, the bulk modulus and its derivatives with respect to pressure as a function of the relative volume x is created. The theoretical values of MA are compared with al...

A new equation of state for the interatomic bonding forces of metals is developed for applications in geophysics. A formulation is made for the free energy, including expressions for the lattice energy and for the Fermi energy, in order to adequately describe the bonding forces of metals in a planetary interior. The resultant equations of state are...

The present paper deals primarily with convection in the Earth's mantle. But it includes also considerations about the possibility of thermal convection in the outer core of the Earth and about the pressure dependence of significant material parameters, with a close relationship between the subjects considered becoming apparent. In Section 1, we gi...

Using a new theory of the volume dependence of Grüneisen's parameter we have reconsidered the core paradox. If the melting-point curve according to Higgins and Kennedy (1971) applies, and if the inner and outer cores are chemically equal, thermo-convective dynamos are impossible throughout the outer core. Thermal convection would be prevented even...

First an introduction into the dynamo problem and the core paradox is given. A novel theory of the volume dependence of Grneisen''s parameter is used for calculating the adiabatic temperatures on the assumption that the melting temperature of the material is reached at the boundary between the inner and outer cores of the Earth (IOB). On this condi...

Three theories that are of importance for planetary physics are examined by establishing whether the curves in the pressure-density diagram which have been calculated from the appropriate equations of state satisfactorily describe the dynamic and static data obtained for cubic solids. For this purpose, the fourth-order anharmonic theory derived fro...

The hydrodynamic problem of stability of a plane, horizontal fluid layer is solved both for the free-free and the rigid-rigid case of the boundary conditions. A Newtonian fluid with spatial heat sources is assumed. The present study differs from previous inquiries in that it takes into account, in the problem of convection considered, the following...

The question is discussed to which areas of geophysics the mechanics of micropolar fluids can be applied. As a model for the partly molten Gutenberg low-velocity layer a horizontal layer consisting of a micropolar fluid is introduced. An analytical solution is deduced for the problem of hydrodynamic stability. The assumption is made that the bounda...

The hypothesis is developed that convection takes place continuously in the upper mantle and episodically also in the lower mantle. The reason for the latter assumption is seen in the temperature dependence of the viscosity. By radioactive heating of the lower mantle the viscosity gradually decreases until the critical Rayleigh number is achieved....

The differential equations of convection are linearized and in this form solved for the following case: The lower and upper boundaries of a plane layer standing vertically in a homogeneous field of gravity and consisting of a Newtonian fluid are kept at constant temperaturesT 0 andT 1, respectively, withT 0>T 1. Moreover, the fluid contains a heat-...

First of all it is shown that the nine fundamental suppositions of the kinematic theory of the mantle convection fit well into the image which is obtained from the mantle by other geophysical results. The question of episodicity of the orogenesis is dealt with in connection with the questions of steadiness and unsteadiness of the convection. Moreov...

Based on a system of structurally simple postulations the kinematics of mantle convection is derived. With regard to the strain-stress relations valid in the mantle and the energy source of the convection the theory is without any presumptions. In compliance with recent hydrodynamic investigations the flow is introduced rather as roll currents than...

Oscillatory paths of microseisms and special characteristics of these paths at Central European and Cuban stations have been examined and compared. The question of the origin of the microseisms is also discussed.

A system of simple principles concerning the kinematics of the convection currents in the Earth''s mantle was postulated as the starting point. The mantle is supposed to become more and more homogeneous downward. Here it is essential, for the reason of symmetry, that the current system has a degree of regularity as high as possible and is modified...

A way is shown for the improvement of seismic signal-to-noise ratio in the period range of 2–10 sec using a polarization filter system. For this method only a homogeneous three-component set of seismographs in the interior of a continent is necessary. The basis of the procedure is the found polarization of the planes of microseismic oscillations, w...

The surface wave magnitudes determined at one seismic station are dependent of azimuthal receiving characteristics of this station.

Viscosity in the Earth's mantle varies by several orders of magnitude, dependent on temper-ature, pressure, grain size and phase transformations. Modeling these variations realistically in three-dimensional mantle convection simulations has been a long-standing problem. We present various approaches to increase the robustness and efficiency of the...

Analysis of microseisms observed at the German stations Moxa and Berggiesshübel was performed and the result was utilized to improve the signal-to-noise ratio for the observation of the real seismic events.

Дается предварительное краткое изложение более детальной работы по свойствам длиннопериодических микросейсм (с 2сек до 10сек) станции г. Берггиссхюбель в Саксонии (50°52,5′ сев. ш., 13°57,0′ вост. д.; грунт: роговообманковый сланец). В табл. 1 приведены постоянные почти однородного комплекта использованных 20-секундных сейсмографов с постоянным уве...