Ulrich R. Christensen

The influence of trench migration on slab penetration into the lower mantle

Abstract A two-dimensional numerical convection model in cartesian geometry is used to study the influence of trench migration on the ability of subducted slabs to penetrate an endothermic phase boundary at 660 km depth. The transient subduction history of an oceanic plate is modelled by imposing plate and trench motion at the surface. The viscosity depends on temperature and depth. A variety of styles of slab behaviour is found, depending predominantly on the trench velocity. When trench retreat is faster than 2–4 cm/a, the descending slab flattens above the phase boundary. At slower rates it penetrates straight into the lower mantle, although flattening in the transition zone may occur later, leading to a complex slab morphology. The slab can buckle, independent of whether it penetrates or not, especially when there is a localised increase in viscosity at the phase boundary. Flattened slabs are only temporarily arrested in the transition zone and sink ultimately into the lower mantle. The results offer a framework for understanding the variety in slab geometry revealed by seismic tomography.

The role of lithospheric mantle in continental flood volcanism: Thermal and geochemical constraints

Continental flood basalts (CFB) are commonly said to form by direct melting of metasomatized lithospheric mantle, either during major lithospheric extension or when a mantle plume impinges on the base of the lithosphere. We tested these ideas in a thermomechanical model that combines lithospheric dynamics and mantle convection. Dry melting was assumed, and the proportions of melt from different source regions were monitored. In all cases, >96% of melt was found to come from asthenosphere or plume, with minimal amounts from continental lithosphere. During passive lithosphere extension the total amount of melt is small, and the proportion from the lithosphere is 100 km) and have high concentrations of both MgO (>20%) and incompatible trace elements (K2O ∼ 1%). The very low Nb and Ta concentrations in certain CFB cannot, however, be explained by this process. Ratios of Nb to elements such as La or U are lower in many flood basalts and picrites than in all likely source materials: they are almost as low as in most rocks from the continental crust, and they are far lower than in peridotites from the lithospheric or asthenospheric mantle. Another process must therefore fractionate Nb and Ta. We suggest that this takes place during the passage of magma through the lithospheric mantle, perhaps because of differences in the reaction rates of minerals in metasomatized peridotite. The probability that CFB are hybrid magmas containing material from aesthenospheric and lithospheric mantle and in many cases from continental crust, as well as the possibility that some elemental ratios change during magma-lithosphere interaction, casts serious doubt on the reliability of such rocks as probes of the lithospheric mantle.

Dawn at Vesta: Testing the Protoplanetary Paradigm

A New Dawn Since 17 July 2011, NASAs spacecraft Dawn has been orbiting the asteroid Vesta—the second most massive and the third largest asteroid in the solar system (see the cover). Russell et al. (p. 684) use Dawns observations to confirm that Vesta is a small differentiated planetary body with an inner core, and represents a surviving proto-planet from the earliest epoch of solar system formation; Vesta is also confirmed as the source of the howardite-eucrite-diogenite (HED) meteorites. Jaumann et al. (p. 687) report on the asteroids overall geometry and topography, based on global surface mapping. Vestas surface is dominated by numerous impact craters and large troughs around the equatorial region. Marchi et al. (p. 690) report on Vestas complex cratering history and constrain the age of some of its major regions based on crater counts. Schenk et al. (p. 694) describe two giant impact basins located at the asteroids south pole. Both basins are young and excavated enough amounts of material to form the Vestoids—a group of asteroids with a composition similar to that of Vesta—and HED meteorites. De Sanctis et al. (p. 697) present the mineralogical characterization of Vesta, based on data obtained by Dawns visual and infrared spectrometer, revealing that this asteroid underwent a complex magmatic evolution that led to a differentiated crust and mantle. The global color variations detailed by Reddy et al. (p. 700) are unlike those of any other asteroid observed so far and are also indicative of a preserved, differentiated proto-planet. Spacecraft data provide a detailed characterization of the second most massive asteroid in the solar system. The Dawn spacecraft targeted 4 Vesta, believed to be a remnant intact protoplanet from the earliest epoch of solar system formation, based on analyses of howardite-eucrite-diogenite (HED) meteorites that indicate a differentiated parent body. Dawn observations reveal a giant basin at Vesta’s south pole, whose excavation was sufficient to produce Vesta-family asteroids (Vestoids) and HED meteorites. The spatially resolved mineralogy of the surface reflects the composition of the HED meteorites, confirming the formation of Vesta’s crust by melting of a chondritic parent body. Vesta’s mass, volume, and gravitational field are consistent with a core having an average radius of 107 to 113 kilometers, indicating sufficient internal melting to segregate iron. Dawns results confirm predictions that Vesta differentiated and support its identification as the parent body of the HEDs.

Three‐dimensional modeling of plume‐lithosphere interaction

In order to understand better the dynamics of hot spots such as Hawaii, we present a three-dimensional numerical model for the interaction of a thermal plume with a moving lithosphere. The model domain is a rectangular box filled with fluid whose viscosity depends upon temperature and pressure. The lithosphere is represented by a layer of cold, highly viscous fluid moving with an imposed horizontal velocity U in the x direction, and a thermal plume is generated by a circular temperature anomaly on the bottom of the box. The steady flow is determined numerically using a hybrid spectral/finite difference technique. The flow is characterized by a “stagnation streamline” of width y ∼ x1/5 that represents the edge of the spreading plume material. We illustrate the detailed behavior of the model using the example of the Hawaiian plume. Our best fitting Hawaiian model is obtained by adjusting the plume buoyancy flux B until the predicted topography anomaly matches the observed Hawaiian swell topography; we find B = 4100 kg s−1, which implies a plume radius of 90 km for an assumed plume/mantle temperature contrast of 300°C. The predicted topography is supported primarily by density anomalies beneath the lithosphere and cannot be explained by lithospheric erosion. We therefore conclude that the classical “lithospheric reheating” model is unable to account for hotspot swells. The horizontal flux of buoyancy associated with the swell exceeds B by up to 80%, suggesting that current estimates of B for mantle plumes are too high. Empirically derived scaling laws for the width of the stagnation streamline and for the topography anomaly exhibit power law dependencies on B and U that agree well with those predicted by the “refracted plume” model of Olson (1990). The principal weakness of the model is that the predicted geoid/topography ratio of 0.010 for the Hawaiian swell is about twice the observed value of 0.004–0.006.

A mantle plume below the Eifel volcanic fields, Germany

Abstract We present seismic images of the upper mantle below the Quaternary Eifel volcanic fields, Germany, determined by teleseismic travel time tomography. The data were measured at a dedicated network of more than 200 stations. Our results show a columnar low P-velocity anomaly in the upper mantle with a lateral contrast of up to 2%. The 100 km wide structure extends to at least 400 km depth and is equivalent to about 150–200 K excess temperature. This clear evidence for a plume below a region of comparatively minor volcanism suggests that deep mantle plumes could be more numerous than commonly assumed. They may often be associated with small volcanic fields or may have no volcanic surface expression at all.

Numerical modeling of the geodynamo: Mechanisms of field generation and equilibration

Numerical calculations of fluid dynamos powered by thermal convection in a rotating, electrically conducting spherical shell are analyzed. We find two regimes of nonreversing, strong field dynamos at Ekman number 10 -4 and Rayleigh numbers up to 11 times critical. In the strongly columnar regime, convection occurs only in the fluid exterior to the inner core tangent cylinder, in the form of narrow columnar vortices elongated parallel to the spin axis. Columnar convection contains large amounts of negative helicity in the northern hemisphere and positive helicity in the southern hemisphere and results in dynamo action above a certain Rayleigh number, through a macroscopic α 2 mechanism. These dynamos equilibrate by generating concentrated magnetic flux bundles that limit the kinetic energy of the convection columns. The dipole-dominated external field is formed by superposition of several flux bundles at middle and high latitudes. At low latitudes a pattern of reversed flux patches propagates in the retrograde direction, resulting in an apparent westward drift of the field in the equatorial region. At higher Rayleigh number we find a fully developed regime with convection inside the tangent cylinder consisting of polar upwelling and azimuthal thermal wind flows. These motions modify the dynamo by expelling poloidal flux from the poles and generating intense toroidal fields in the polar regions near the inner core. Convective dynamos in the fully developed regime exhibit characteristics that can be compared with the geomagnetic field, including concentrated flux bundles on the core-mantle boundary, polar minima in field intensity, and episodes of westward drift.

A comparison of methods for the modeling of thermochemical convection

We have compared several methods of studying thermochemical convection in a Boussinesq fluid at infinite Prandtl number. For the representation of chemical heterogeneity tracer, marker chain, and field methods are employed. In the case of an isothermal Rayleigh-Taylor instability, good agreement is found for the initial rise of the unstable lower layer; however, the timing and location of the later smaller-scale instabilities may differ between methods. For a simulation of entrainment by thermal convection of a dense layer at the bottom of the mantle we found good agreement for a few overturn times. After this, differences between the results can be large. We propose intrinsic differences between the methods and possibly chaotic mixing effects may be the cause of the lack of detailed agreement. The comparison shows that high resolution is necessary for a reasonable thermochemical study. This will pose severe restrictions on the applicability of these methods to three-dimensional situations.

A numerical dynamo benchmark

We present the results of a benchmark study for a convection-driven magnetohydrodynamic dynamo problem in a rotating spherical shell. The solutions are stationary aside from azimuthal drift. One case of non-magnetic convection and two dynamos that differ in the assumptions concerning the inner core are studied. Six groups contributed numerical solutions which show good agreement. This provides an accurate reference standard with high confidence.

Energy flux determines magnetic field strength of planets and stars

The magnetic fields of Earth and Jupiter, along with those of rapidly rotating, low-mass stars, are generated by convection-driven dynamos that may operate similarly (the slowly rotating Sun generates its field through a different dynamo mechanism). The field strengths of planets and stars vary over three orders of magnitude, but the critical factor causing that variation has hitherto been unclear. Here we report an extension of a scaling law derived from geodynamo models to rapidly rotating stars that have strong density stratification. The unifying principle in the scaling law is that the energy flux available for generating the magnetic field sets the field strength. Our scaling law fits the observed field strengths of Earth, Jupiter, young contracting stars and rapidly rotating low-mass stars, despite vast differences in the physical conditions of the objects. We predict that the field strengths of rapidly rotating brown dwarfs and massive extrasolar planets are high enough to make them observable.

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.