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Modeling Electrical Conductivity in the Mantle

Fumiko Tajima

Significance of this Simulation Project

Over the past decade seismology has made significant progress in using tomographic techniques for 3-D imaging of the elastic properties in the crust, mantle and core, that dominates our present view of the Earth's interior. Although seismic waves provide good representations of elastic properties, they are not unambiguously sensitive to temperature, partial melt, chemical compositions, or presence of volatiles within the Earth. The gap between the conjecture based on large-scale tomographic images and the reality of mantle property measurements based on mineral physics is enormous.

In comparison, electrical conductivity (EC) is sensitive to such properties and can be measured by studying the frequency-dependent electromagnetic (EM) response in the Earth [Roberts, 1986]. The lateral temperature contrast across a mantle convection cell is estimated to be in the range 102 to 103 K. For a dry crystalline mantle this contrast can map into approximately an order-of-magnitude lateral variation in EC, and thus it presents a good prospect for 3-D image modeling. This order of magnitude of conductivity variation can be contrasted with the equivalent P- and S-wave velocity variation, which is in the range of approximately several percent. The somewhat poorer resolving power of EM imaging techniques (diffusion equation) relative to seismic techniques (wave equation) is counterbalanced by the intense material property contrasts [Schultz et al., 1993].

The distribution of permanent observation sites of EM fields is extremely sparse, which has impeded efforts to construct detailed 3-D images of EC distribution in the mantle. Supplying a different approach, recent laboratory experiments provide EC data measured for various mantle minerals, and temperature (T) and pressure (P) conditions in the depth range from upper mantle transition zone to $\sim $1500 km [Shankland et al., 1993; Xu et al., 1998a, b; Xu and Shankland, 1999], and conductivities can be extrapolated to greater depths without gross uncertainty [Shankland et al., 1993; Xu et al., 2000]. Chemical composition and temperature in this depth range are fundamentally important for understanding mantle dynamics, while their characterization is still a matter of debate. Combining EC of deep-seated rocks with seismic models would provide a more powerful probe of mantle composition and state than would either property separately. We are thus carrying out high performance computer simulations of EM response induced by the coupling of external magnetic fields with mantle EC, first for layered models, and then for a laterally heterogeneous 3-D Earth.

As an example of the significance of this approach, seismic wave velocity and EC in the mantle depend on how melt is distributed around mineral grains [Shankland, et al., 1981]. Experimental investigation of water-containing rocks [Olhoeft, 1981] has revealed a pronounced increase of EC in the temperature range from 500o to 700o which may be attributed to the beginning of fractional melting, and hence, anomalies of EC may be helpful in identifying zones of possible melting or hydration. The combination of electrical conductivity of deep-seated rocks with seismic models can be a more powerful probe of mantle composition and state than either separately.

Thus this simulation study aims to test if the magnetotelluric (MT) modeling for a suite of EC distributions has sufficient resolution and sensitivity for improving the mantle structural model developed by seismology. Results from this simulational study will provide valuable assessments for integration of Earth models by using different approaches from seismology, mineral physics and EM investigations.

Code Development and Feasibility Study

We are carrying out computer simulations of EM responses using recently developed codes by Chou et al. [2000]. The codes are written to solve the EM induction equations in the time domain both in Cartesian and spherical coordinates, and are designed to run on high performance supercomputers with parallel processing. There are a number of published papers that attempted to develop this kind of computer simulations. To our knowledge, however, simulations presented in those papers were carried out in the frequency domain, and none of such efforts has successfully parallelized the computations. The codes developed in the time-domain with parallel processing have considerable advantages in dealing with data. Although we are using a simplified EM field imposed on the surface of the Earth at present, the codes have capability to incorporate observed data and expand to deal with naturally occurring powerful, low-frequency EM fields whose primary sources are located in the magnetosphere and ionosphere.

We tested the resolution and sensitivity of EM modeling for layered structures using different EC values. We are going to test the anomalous low velocities determined in recent 3-D seismic tomography models [Mégnin and Romanowicz, 2000], which show almost continuous reduced velocities from the core mantle boundary to the upper mantle transition zone beneath Africa and the South Pacific. The anomalies may suggest hot superplumes (see the illustration in Fig. 33.1). The features and behavior of hot plumes in the mantle transition zone have been controversial.


  
Figure 33.1: Illustration of a model associated with a plume like feature, and three cases of electrical conductivity anomalies
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\epsfig{file=fumiko00_3_1.ps, width=7cm}\end{center}\end{figure}


  
Figure: [Case 1] Time evolution of the induced magnetic field Bz on the surface of the Earth with anomaly at the center in the third layer. The numbers for the colored lines correspond to the number of grid ny where the sampling was taken place relative to the center. [Case 1'] The anomaly in Case 1 was extended to 1000km. As a result the amplitude of the induced field is $\sim $4 times larger than that in case 1. [Case 2] The anomaly in the fourth layer is in a thinner column than in Case 1', and the amplitudes are between those in Case 1 and Case1'. [Case 3] The anomaly in the fourth layer is in a thinner column than in Case 2.
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\epsfig{file=fumiko00_3_2.ps, width=7cm}\end{center}\end{figure}

We have already tested the codes for performance speed and stability/convergence as well as the sensitivity of "skin depth" using simplified models of the upper mantle and transition zone structure. Here skin depth defines the sampling depth of EM waves as a function of frequency and conductivity. We are testing the EM responses for a variety of EC distributions using different conductivity values measured in the laboratory experiments focusing on the sensitivity of magnetic induction observable on the surface for the mantle materials and P and T conditions in the depth range from $\sim $400 km to 1500 km. Figure 33.1 illustrates three cases with high EC anomalies associated with hot plume around the transition zone, and Figure 33.2 the results of simulations. We will test the EM induction observable on the surface for layered as well as 3-D structures having lateral heterogeneity using EC data provided by Dr. Shankland. To test laterally anomalous structure we will use the recent global P model by Fukao and his co-workers, and SH model by Romanowicz and co-workers as an initial model.

Acknowledgements

We acknowledge the following scientists whose collaboration was essential for expanding this project: W. Chou at RIST/Japan and R. Matsumoto at Chiba University in code development, and T. Shankland at Los Alamos National Laboratory in coordination of EC experimental results for the simulation. We also appreciate T. Ebisuzaki at RIKEN, who generously provided us with access to Fujitsu VPP700, a powerful supercomputer.

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., in press, 2000a.

Chou, W., R. Matsumoto, and F. Tajima, Simulational modeling of time-domain magnetic induction using parallel computational schemes: (II) in the spherical coordinates, Comp. Phys. Comm., accepted, 2000b.

Mégnin, C., and B. Romanowicz, The 3D shear velocity structure of the mantle from the inversion of body, surface, and higher mode waveforms, Geophys. J. Int., in press, 2000.

Olhoeft, G. R., Electrical properties of granite with implications for the lower crust, J. Geophys. Res., 86, 931-936, 1981.

Roberts, R. G., The deep electrical structure of the Earth, Geophys. J. R. Astr. Soc., 85, 583-600, 1986.

Roberts, J. J., and J. A. Tyburczy, Partial-melt electrical conductivity: Influence of melt composition, J. Geophys. Res., 104, 7055-7065, 1999

Shankland, T. J., and R. J. O'Connell, and H. S. Waff, Geophysical Consequences of Partial Melting in the Upper Mantle, Revs. Geophys. Space Phys., 19, 394-406, 1981.

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.

Xu, Y., C. McCammon, and B. T. Poe, The effect of Alumina on the electrical conductivity of silicate perovskite, Science, 282, 922-924, 1998.

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., submitted, 2000.


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