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Modeling of Mantle Electrical Conductivity Anomalies Associated with an Upwelling Hot Plume

Fumiko Tajima

Anomalies Associated with Hot Plumes

Recent 3-D global seismic tomography studies have captured stunning features of low velocity anomalies, which are almost continuous from the core mantle boundary into the upper mantle beneath Africa and the South Pacific (Ritsema et al., 1999; Mégnin and Romanowicz, 2000). The blurred image of low velocity anomaly with a lateral extent of over 2000 km may indicate a hot plume which is, however, assumed to be upwelling in a much narrower column. As seismic wave velocities are not very sensitive to tempereture, partial melt, or chemical compositions that could distinguish hot plumes, the resolution of seismological approaches alone may be ultimately limited to constrain the structure of upwelling hot plumes.

On the other hand electrical conductivity ($\sigma$) is sensitive to such properties. Here we focus on the temperature difference between a plume and the surrounding mantle to estimate the conductivity anomaly using in situ conductivity data measured for various mantle minerals in recent laboratory experiments (Xu et al., 1998, 2000; Xu and Shankland, 1999). Electrical conductivity is expressed as:


\begin{displaymath}
\sigma = \sigma_0 \cdot exp(-\displaystyle\frac {\Delta H}{k T})
\end{displaymath} (24.1)

where $\sigma_{0}$ is a pre-exponential factor, $T$ is temperature, $k$ is the Boltzmann constant (in electron volt per kelvin), and the activation enthalpy $\Delta H = \Delta U + P\Delta V$ (where $\Delta U$ is activation energy, $\Delta V$ is activation volume, and P is pressure). Then the contrast of electrical conductivities across a mantle convection cell can be estimated as follows:
\begin{displaymath}
ln\displaystyle\frac {\sigma '}{\sigma} = 11.605 \cdot \Delt...
...cdot (\displaystyle\frac {1}{T}
- \displaystyle\frac {1}{T'})
\end{displaymath} (24.2)

where $\sigma '$ is the conductivity in a hot plume, and 11.605 is from $\displaystyle\frac {1}{k}$. $\Delta H$ can be measured such as $\sim $1.29 ev for wadsleyite and $\Delta H \sim 1.16 ev$ for ringwoodite in the transition zone depths. The temperature contrast $\Delta T$ is assumed to be $\sim $500 K. Then, $\displaystyle\frac {\sigma '}{\sigma }\sim 5.7$ for pyrolite, and $\sim 10.2$ for eclogite composition (410 to 660 km). $\displaystyle\frac {\sigma '}{\sigma }\sim$15 for upper mantle (200 to 410 km), and $\sim $2.5 for lower mantle (800 to 900 lm), respectively.

Figure 24.1: Illustration of a hot plume upwelling in a narrow, vertical column of a $\sim $100 to 400 km diameter with an overlying broader layer in a multi-layered mantle structure. The shaded area is meant a hot plume in which the conductivity ($\sigma ^{'}$) is larger. The depth range between $d_{1}$ and $d_{2}$ in which the upwelling plume flattens is uncertain.
\begin{figure}\vspace{2pc}
\begin{center}
\epsfig{file=fumiko01_2.fig1.ps, width=7cm}\end{center}\end{figure}

Simulation of Magnetic Induction

We carried out high performance computer simulations of electromagnetic (EM) responses induced by the coupling of external EM fields with the Earth's mantle using a newly developed time-domain 3-D finite difference code (Chou et al., 2000). The time-domain code has considerable advantages in dealing with transient EM fields.

Figure 24.1 illustrates a hot plume in a multi-layered structure (see the caption). An input plane electric field in the x-direction (or a vector potential ${\bf A}$ differentiated by time) that oscillates with a period of 50000 to 130000 sec ($\sim $14 hours to 1.5 days) represented the external field. After sufficient computation time (3 to 5 times as long as the oscillation period of the external field), the induced magnetic fields (IMF's) at the surface were evaluated. Results show an observable difference of EM responses for different conductivity distributions, and that the plume tail with high conductivity can be detected given an appropriate frequency band of the external field for skin depths (see Figure 24.2).

Figure 24.2: Example of induced magnetic field in y-direction ($B_{y}$) associated with a plume like anomaly of mantle conductivity. The size of the plume tail in the lower mantle is 400 x 400 $km^2$ and the head 1000x1000 $km^2$ in the uppermantle. The conductivity anomaly contrast is given $\sim $5 for the tail, 10 for the transition zone, and 15 for the upper mantle, respectively. The input field is a plane sinusoidal electric field that oscillates with $T_0$=100,000 sec in x-direction. The snap shots were made with an interval of two hours during the 3rd cicle starting at 200,800 sec after the onset. The amplification (or reduction) of the $B_{y}$ above the conductivity anomaly is visible. Note that without the 3-D anomaly the induced field should be a plane wave oscillating only in y-direction, and there will be no induction in z-direction (Tajima, 2001).

Discussion

The conductivity variation can be contrasted with the equivalent P- and S-wave velocity variation, which is in the range of within several percent. Combining electrical conductivity of deep-seated rocks with seismic models would provide a more powerful probe of mantle composition and state than would either property separately. Although we are using a simplified EM field imposed on the surface at present, the codes are flexible and have capability to incorporate with data.

Acknowledgements

The author thanks W. Chou and R. Matsumoto at Chiba University for collaboration at an early stage of the code development, and T. Shankland at Los Alamos National Laboratory for providing her with experimental results of electrical conductivity measurements and discussion. She also appreciates T. Ebisuzaki at RIKEN, who provided with access to the Fujitsu VPP700 computer.

References

Chou, W., R. Matsumoto, and F. Tajima, Simulational modeling of time-domain magnetic induction using parallel computational schemes: (I) in the Cartesian coordinates, Comp. Phys. Comm., 131, 26-40, 2000.

Mégnin, C., and B. Romanowicz, The three-dimensional shear velocity structure of the mantle from the inversion of body, surface, and higher mode waveforms, Geophys. J. Int., 143, 709-728, 2000.

Ritsema, J., H. J. van Hijist, and J. H. Woodhouse, Complex shear wave velocity structure imaged beneath Africa and Iceland, Science, 286, 1925-1928, 1999.

Shankland, T. J., J. Peyronneau, and J.-P. Poirier, Electrical conductivity of the Earth's lower mantle, Nature, 366, 453-455, 1993.

Schulz, A., R. D. Kurz, A. D. Chave, and A. G. Jones, Conductivity discontinuities in the upper mantle beneath a stable craton, Geophys. Res. Lett., 20, 2941-2944, 1993.

Tajima, Time-domain simulation of magnetic induction for modeling electrical conductivity anomalies in the Earth's mantle, RIKEN Review, 40: Focused on High Performance Computing in RIKEN, in press, 2001.

Xu, Y., B. T. Poe, T. J. Shankland, and D. C. Rubie, Electrical conductivity of olivine, wadsleyite, and Ringwoodite under upper-mantle conditions, Science, 280, 1415-1418, 1998.

Xu, Y., and T. J. Shankland, Electrical conductivity of orthopyroxene and its high pressure phases, Geophys. Res. Lett., 26, 2645-2648, 1999

Xu, Y., T. J. Shankland, and B. T. Poe, Laboratory-Based Electrical Conductivity in the Earth's Mantle, J. Geophys. Res., 105, B12, 27,865-27,875, 2000.


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