A thermochemical boundary layer at the base of Earth's outer core and independent estimate of core heat flux

SUMMARY Recent seismological observations suggest the existence of a ≈150-km-thick density-stratified layer with a P-wave velocity gradient that differs slightly from PREM. Such a structure can only be caused by a compositional gradient, effects of a slurry or temperature being too small and probably the wrong sign. We propose a stably stratified, variable concentration layer on the liquidus. Heat is transported by conduction down the liquidus while the light and heavy components migrate through the layer by a process akin to zone refining, similar to the one originally proposed by Braginsky. The layer remains static in a frame of reference moving upwards with the expanding inner core boundary. We determine the gradient using estimates of co, the concentration in the main body of the outer core, and cb, the concentration of the liquid at the inner core boundary. We determine the depression of the melting point and concentrations using ideal solution theory and seismologically determined density jumps at the inner core boundary. We suppose that co determines �ρ mod, the jump from normal mode eigenfrequencies that have long resolution lengths straddling the entire layer, and that cb determines �ρ bod, the jump determined from body waves, which have fine resolution. A simple calculation then yields the seismic, temperature, and concentration profiles within the layer. Comparison with the distance to the C-cusp of PKP and normal mode eigenfrequencies constrain the model. We explore a wide range of possible input parameters; many fail to predict sensible seismic properties and heat fluxes. A model with �ρ mod = 0.8 gm cc −1 , �ρ bod = 0.6 gm cc −1 , and layer thickness 200 km is consistent with the seismic observations and can power the geodynamo with a reasonable inner core heat flux of ≈2 TW and nominal inner core age of ≈1 Ga. It is quite remarkable and encouraging that a model based on direct seismic observations and simple chemistry can predict heat fluxes that are comparable with those derived from recent core thermal history calculations. The model also provides plausible explanations of the observed seismic layer and accounts for the discrepancy between estimates of the inner core density jumps derived from body waves and normal modes.

[1]  J. C. Slater.  Introduction to chemical physics , 1933 .

[2]  E. J. Öpik,et al.  Physics of the Earth's Interior , 1959 .

[3]  K. E. Bullen,et al.  An Introduction to the Theory of Seismology , 1964 .

[4]  E. S. Husebye,et al.  Array analysis of PKP phases and their precursors , 1972 .

[5]  W. Malkus.  Convection at the melting point: A thermal history of the earth's core , 1973 .

[6]  J. Cleary,et al.  Evidence for scattering of seismic PKP waves near the mantle-core boundary , 1974 .

[7]  P. Roberts,et al.  On the motion of an iron-alloy core containing a slurry: I. general theory , 1977 .

[8]  P. Roberts,et al.  On the motion of an iron-alloy core containing a slurry. II. A simple model , 1980 .

[9]  P. Roberts,et al.  A study of conditions at the inner core boundary of the earth , 1981 .

[10]  D. Loper,et al.  The evolution of an iron-poor core I. Constraints on the growth of the inner core , 1983 .

[11]  D. L. Anderson.  Theory of Earth , 2014 .

[12]  G. Poupinet,et al.  The velocity profile at the base of the liquid core from PKP(BC+Cdiff) data: An argument in favour of radial inhomogeneity , 1991 .

[13]  Xiaodong Song,et al.  Velocity structure near the inner core boundary from waveform modeling , 1992 .

[14]  K. Hirahara,et al.  Seismic structure near the inner core‐outer core boundary , 1994 .

[15]  Paul H. Roberts,et al.  Equations governing convection in earth's core and the geodynamo , 1995 .

[16]  E. R. Engdahl,et al.  Constraints on seismic velocities in the Earth from traveltimes , 1995 .

[17]  Xiaodong Song,et al.  A P wave velocity model of Earth's core , 1995 .

[18]  T. Lay,et al.  Modern Global Seismology , 1995 .

[19]  UK,et al.  First-principles simulations of liquid Fe-S under Earth's core conditions , 1998 .

[20]  M. Gillan,et al.  The melting curve of iron at the pressures of the Earth's core from ab initio calculations , 1999, Nature.

[21]  London,et al.  Oxygen in the Earth's core: a first-principles study , 1999 .

[22]  UK,et al.  Structure and dynamics of liquid iron under Earth’s core conditions , 2000 .

[23]  E. M. Lifshitz,et al.  Course in Theoretical Physics , 2013 .

[24]  Thermodynamic Stability of Fe/O Solid Solution at Inner‐Core Conditions , 2000, cond-mat/0002208.

[25]  Jean-Paul Poirier,et al.  The age of the inner core , 2001 .

[26]  M. Gillan,et al.  Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data , 2002 .

[27]  Geoffrey D. Price,et al.  The influence of potassium on core and geodynamo evolution , 2003 .

[28]  M. Roberts,et al.  Convective Instability of a Mushy Layer - I: Uniform Permeability , 2003 .

[29]  M. Gillan,et al.  Can the Earth's dynamo run on heat alone? , 2003 .

[30]  G. Masters,et al.  On the resolution of density within the Earth , 2003 .

[31]  K. Koper,et al.  Observations of PKiKP/PcP amplitude ratios and implications for Earth structure at the boundaries of the liquid core , 2004 .

[32]  B. Romanowicz,et al.  FAST TRACK PAPER: Constraints on density and shear velocity contrasts at the inner core boundary , 2004 .

[33]  M. Gillan,et al.  Gross thermodynamics of two-component core convection , 2004 .

[34]  K. Koper,et al.  Seismic properties of the inner core boundary from PKiKP / P amplitude ratios , 2005 .

[35]  H. Shimizua,et al.  On crystallization at the inner core boundary , 2005 .

[36]  K. Koper,et al.  The structure of the base of the outer core inferred from seismic waves diffracted around the inner core , 2008 .