Dislocation-mediated melting of iron and the temperature of the Earth's core

Summary . Dislocation theories of melting provide a possibility of calculating the melting temperature, from first principles, as the temperature at which the free energy of a crystal saturated with dislocations becomes equal to that of the dislocation-free crystal. After a brief review of the physical bases of the dislocation melting theories, Ninomiya's theory is used to determine the melting temperature as well as the volume and entropy of melting and the slope of the melting curve for iron at atmospheric pressure and under conditions prevailing at the Earth's inner core boundary. The necessary parameters (elastic moduli, Grüneisen parameter) are drawn from seismological earth models. We find a melting temperature of the material of the inner core of about 6150 K, independent of shock-wave experiments but in good agreement with them and with extrapolations using Lindemann's law. With usually accepted values of the melting point depression due to light elements in solution, the temperature at the inner core boundary is found to be T _ICB≅ 5000 K. This temperature is compatible with a temperature of the outer core at the core-mantle boundary T _CMB≅ 3800 K. Dislocation melting theories can thus help constrain the temperature profile in the Earth's core.     

On imperfection of elasticity in the Earth's interior

Summary. Attempts are made to estimate the distribution of damping with depth, based on the observed damping of P waves, of free vibrations, and of surface waves and partly on a discussion by D. L. Anderson and R. S. Hart. Results are consistent in order of magnitude, but could easily be wrong by a factor of 2. Comments are added on the need for further work. Stress is laid on the damping of the free nutation, which indicates that α in the modified Lomnitz law is about 0.2 on an average.     

Observational constraints on the chemical and thermal structure of the Earth's deep interior

Summary. The observations of the periods of free oscillation of the Earth provide direct constraints on the density distribution in the Earth. These in turn allow constraints to be placed on the size of departures from a state of adiabaticity and chemical homogeneity. These departures are quantified in terms of a stratification parameter '8' first introduced as an index of chemical homogeneity. The resolving power theory of Backus & Gilbert is used to determine the ability of the observed free oscillations to constrain η in the lower mantle and outer core. The results suggest that the outer core is not strongly chemically stratified although a significantly thermally stable core cannot be excluded. The free oscillations also apparently require a compositional difference between the inner and outer cores.     

Determination and analysis of long-wavelength transition zone structure using SS precursors

Global mapping of 410 and 660 km discontinuity topography and transition zone thickness has proven to be a powerful tool for constraining mantle chemistry, dynamics and mineralogy. Numerous seismic and mineral physics studies suggest that the 410 km discontinuity results from the phase change of olivine to wadsleyite and the 660 km discontinuity results from the phase change of ringwoodite to perovskite and magnesiowustite. Underside reflections of the 410 and 660 km discontinuities arrive as precursors to SS . With the recent development of a semi-automated method of determining SS arrivals, we have more than tripled the Flanagan and Shearer (1998a) data set of handpicked SS waveforms. We are able to increase resolution by stacking waveforms in 5° rather than 10° radius bins as well as increasing data coverage significantly in the southern hemisphere. The resulting SS-S410S and SS-S660S times are heavily influenced by upper-mantle velocity structure. We perform a joint inversion for discontinuity topography and velocity heterogeneity as well as performing a simple velocity correction to the precursor differential times and find little difference between the two methods. The 660 km discontinuity topography and transition zone thickness are correlated with velocities in the transition zone whereas the 410 km discontinuity topography is not. In addition, the 410 km discontinuity topography is not correlated with the 660 km discontinuity topography, rather anticorrelated, as expected due to the opposite signs of the Clapeyron slopes of their respective phase changes. These results suggest that, whereas the topography of 660 km discontinuity could be dominated by thermal effects, the topography of the 410 km discontinuity is likely dominated by compositional effects. In addition, unlike previous studies which find less topography on the 410 km discontinuity than on the 660 km discontinuity, our 410 and 660 km topography have similar amplitudes.     

Which is the correct stress strain relation for the anelasticity of the Earth's interior?

Summary. The effect of anelasticity on the periods of the Earth's free oscillation (toroidal modes) is examined in the light of several different studies leading to different results. The possibility of discrimination between the different analytic models for the anelasticity of the Earth's interior is discussed. A splitting of the spectral lines caused by Q is also suggested.     

The melting of floating ice raises the ocean level

It is shown that the melting of ice floating on the ocean will introduce a volume of water about 2.6 per cent greater than that of the originally displaced sea water. The melting of floating ice in a global warming will cause the ocean to rise. If all the extant sea ice and floating shelf ice melted, the global sea level would rise about 4 cm. The sliding of grounded ice into the sea, however, produces a mean water level rise in two parts ; some of the rise is delayed. The first part, while the ice floats, is equal to the volume of displaced sea water. The second part, equal to 2.6 per cent of the first, is contributed as it melts. These effects result from the difference in volume of equal weights of fresh and salt water. This component of sea rise is apparently unrecognized in the literature to date, although it can be interpreted as a form of halosteric sea level change by regarding the displaced salt water and the meltwater (even before melting) as a unit. Although salinity changes are known to affect sea level, all existing analyses omit our calculated volume change. We present a protocol that can be used to calculate global sea level rise on the basis of the addition of meltwater from grounded and floating ice; of course thermosteric volume change must be added.     

Vertical structure of the head of a cylindrical mantle plume from a model of two-phase flow with melting

Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.     

Hydrological processes of glacier and snow melting and runoff in the Urumqi River source region,eastern Tianshan Mountains,China

Hydrological processes were compared, with and without the influence of precipitation on discharge, to identify the differences between glacierized and non-glacierized catchments in the Urumqi River source region, on the northern slope of the eastern Tianshan Mountains, during the melting season (May-September) in 2011. The study was based on hydrological data observed at 10-min intervals, meteorological data observed at 15-min intervals, and glacier melting and snow observations from the Empty Cirque, Zongkong, and Urumqi Glacier No.1 gauging stations. The results indicated that the discharge differed markedly among the three gauging stations. The daily discharge was more than the nightly discharge at the Glacier No.1 gauging station, which contrasted with the patterns observed at the Zongkong and Empty Cirque gauging stations. There was a clear daily variation in the discharge at the three gauging stations, with differences in the magnitude and duration of the peak discharge. When precipitation was not considered, the time-lags between the maximum discharge and the highest temperature were 1-3 h, 10-16 h, and 5-11 h at the Glacier No.1, Empty Cirque, and Zongkong gauging stations, respectively. When precipitation was taken into consideration, the corresponding time-lags were 0-1 h, 13 h, and 6-7 h, respectively. Therefore, the duration from the generation of discharge to confluence was the shortest in the glacierized catchment and the longest in the catchment where was mainly covered by snow. It was also shown that the hydrological process from the generation of discharge to confluence shortened when precipitation was considered. The factors influencing changes in the discharge among the three gauging stations were different. For Glacier No.1 station, the discharge was mainly controlled by heat conditions in the glacierized region, and the discharge displayed an accelerated growth when the temperature exceeded 5°C in the melt season. It was found that the englacial and subglacial drainage channel of Glacier No.1 had become simpler during the past 20 years. Its weaker retardance and storage of glacier melting water resulted in rapid discharge confluence. It was also shown that the discharge curve and the time-lag between the maximum discharge and the highest temperature could be used to reveal the evolution of the drainage system and the process of glacier and snow melting at different levels of glacier coverage.