Exploring the Earth's lowermost mantle by Schrodinger equation
Abstract: The seismic velocities propagating in the post-perovskite, a new mineral phase discovered recently in the laboratory experiment, were calculated by using the first principles electronic structure calculation. The results can explain many strange features of the Earth's lowermost mantle (D" layer) consistently. This gives a solid ground for the model that the post-perovskite is the main component of the D" layer. (Iitaka et al., Nature 430, 442-445 (2004).) <free pdf file>
| Background:
The Earth's structure are studied mainly by the propagation of earthquakes: The Earth is covered by the crust and lithosphere, below which and down to 2,900 km in depth is called mantle. Below the mantle and down to the center of the earth is called core. Mantle has layers called upper mantle, transition layer, lower mantle, and the D" layer. The core consist of the outer core (liquid) below the D" layer down to 5,150 km and the inner core (solid) from there to the center of the Earth. The main component of the lower mantle and the D" layer has been assumed to be a mineral called MgSiO3 perovskite (Fig.2 (a)). However the model with MgSiO3 perovskite only could not explain the discontinuity of seismic velocity at the top of the D" layer and the polarization anisotropy of the share waves in the D" layer. Therefore the question of what is the main component of the D" layer has remained as a one of the most important problem in the earth science.
Prof. Kei Hirose at Tokyo Institute of Technology has been developing technique that realize the high temperature and high pressure at the bottom of the mantle in the laboratory to measure the crystal structure under such conditions by using X-ray diffraction method (see Kei and Motohiko on RealPlayer 56K/512K). By using the state of art synchrotron facility, SP-ring8 at RIKEN, he has recently discovered a new mineral named "MgSiO3 post-perovskite" (Science 304, 855–858). In the experiment, the crystal structure of the MgSiO3 post-perovskite (Fig.2 (b)) was determined by in situ X-ray diffraction measurement, but the elastic stiffness tensor of the MgSiO3 post-perovskite is not measurable with the present day technique. The elastic stiffness tensor, the constant of proportionality between the applied strain and the reacting stress, represents the stiffness of the mineral and determines the velocity of seismic waves propagating in the mineral.
 
Results:
I have been studying, by using the large scale first principle electronic state calculation with super computers, the properties of materials under pressures as high as in the planets. This time I calculated the elastic stiffness tensors of the MgSiO3 perovskite and the MgSiO3 post-perovskite. The result tells us that the existence of the MgSiO3 post-perovskite can consistently explain many seismic observations such as the discontinuity and anisotropy of the seismic velocities (Table 1). For example, VSH > VSV in the post-perovskite as well as in seismic observations though
Table 1.
| seismic observation
| with post-perovskite
| with perovskite
| seismic discontinuity atop of D" layer
| ~ 3%
| 4~7%
| cannot explain with simple model
| share wave polarization anisotropy
| 1~3%
| 4 %
| minus 4%
| correlation between bulk sound velocity and share wave velocity
| negative
| negative
| cannot explain with simple model |
View:
Today's models of seismic propagation and mantle convection in the earth does not take into account the existence of MgSi3 post-perovskite. They should be reconstructed by taking into account the effects of MgSiO3 post-perovskite as well as our present results. In fact the layer has been an absolute condition for the existence of development of the life on earth.
 | Thank you, John ... very interesting |
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