Mantle effect

The Earth's lithosphere and mantle are not perfectly electrical insulators and, consequently, external changes in the Earth's magnetic field -- which are primarily caused by the solar-wind interaction with the ionosphere and magnetosphere at periods much shorter than the eleven-year sunspot cycle -- can induce electric currents in the Earth's lithosphere and mantle and, then, produce a secondary magnetic field that is measurable by ground magnetic observatories and high-accuracy geomagnetic satellites. The profile and magnitude of the secondary magnetic field open up a means of probing three-dimensional conductivity and heterogeneity of the Earth's mantle that is closely connected with its physical and chemical properties, such as porosity, the amount and distribution of water, temperature and composition. Consequently, studies of the electromagnetic induction in the Earth's lithosphere and mantle of lateral heterogeneity complement those of seismic tomography that is mainly associated with the mechanical properties of the Earth's lithosphere and mantle. The problem of the global electromagnetic induction in the Earth's lithosphere and mantle can be mathematically formulated via a perturbation approach by assuming, for example, that the ionospheric dynamo is totally decoupled from the core geodynamo. A powerful combination of the seismological and geomagnetic studies of the Earth's mantle can lead to our better understanding of the dynamics and evolution of the deep Earth, offering a unique constraint between geomagnetism and seismic tomography on the physical and chemical heterogeneity in the upper mantle that is unattainable alone via the seismological studies.

Below is a brief description of our progress on the forward modeling of the global electromagnetic (EM) induction. A key ingredient of the conductivity inversion is the forward modeling solver of global EM induction, which focuses on the numerical solution of Maxwell’s equations on a global scale and strongly affects the accuracy of the conductivity determination. A number of forward modeling solvers have been proposed with acceptable accuracies, in which various numerical approaches are applied, such as spherical harmonics, integral equation methods, finite difference methods, and finite element methods. Each approach owns its advantages and disadvantages in terms of accuracy, efficiency, applicability and robustness. Considering the sparse and irregular distribution of geomagnetic data and large lateral conductivity variations (especially ocean-continent contrasts), the finite element methods, which can deal with arbitrary conductivity distributions and has a flexible grid adaptability, show potential advantages. In particular, the computational cost of such methods can be greatly alleviated with the aid of modern supercomputers and parallel computational algorithms, such as domain decomposition, Krylov subspace iterative methods and multigrid preconditioning. Besides finite element methods, finite volume methods also have capability of handling arbitrary geometries and unstructured grids but draw little attention to date in global EM induction forward modeling. In addition to the geometric flexibility, another important advantage of the finite volume methods is that the numerical schemes are related to the physical meaning and conservation principles. Therefore, it is attractive to apply such methods to the global EM induction forward modeling, which constitutes one part of our recent progress. Based on cell-centered collocated unstructured grids, we develop a first finite volume solver for global EM induction forward modeling. The proposed algorithm is validated by two synthetic cases, i.e. an Earth model approximated by concentric homogeneous spherical shells with an analytical solution available (case 0) and a case of thin shell conductance contrast NS (case 1), as shown in Figure 1 and 2.

Figure 1. Comparison of the magnetic field components of the case 0 along the colatitude direction at satellite altitude (400 km) and longitude ϕ=42.2° for the period T =4.64×10^5 s.

Figure 2. The magnetic field components of the case 1 along the colatitude direction at the Earth surface and longitude ϕ=0° for the period T = 4 days (a, b) and T = 6 hours (c, d).

In the forward modeling, the large conductivity contrasts between oceans and continents can significantly distort the global EM induction fields measured by both coastal geomagnetic observatories and geomagnetic satellites. To accurately account for these ocean induction effects, we have developed a new global EM forward modeling solver based on a finite element method. Our solver employs multi-resolution tetrahedral grids to efficiently approximate the mantle and the heterogeneous crust regions. Both the goal-oriented mesh refinement approach and high-order Nedelec elements are adopted to improve the accuracy of simulated EM fields. Fully parallel implementation at both the frequency and mesh decomposition levels using MPI is employed to accelerate the computations. Figure 3 shows the large ocean induction effects at three Chinese coastal geomagnetic observatories. Figure 4 illustrates the ocean induction effects at two satellite altitudes (450 and 200 km, which are the planned flying altitudes of Macau’s geomagnetic satellites).

Figure 3. Real (left) and imaginary (right) parts of local C-responses simulated by multi-resolution finite-element approach for (a) (b) Quanzhou (QZH); (c) (d) Guangzhou (GZH); and (e) (f) Yongning (YON) observatories. The differences between 1D and 3D responses illustrate the large ocean induction effects.

Figure 4. Real and imaginary parts of the vertical component of the magnetic induction vector at 450 and 200 km altitudes. From top to bottom: 1D model responses, 3D model responses and the ocean induction responses (3D-1D). The testing period is 2 days.

For more details, please see:

[1] Hongbo Yao, Zhengyong Ren*, Jingtian Tang*, Yufeng Lin, Changchun Yin, Xiangxun Hu, Qinghua Huang, Keke Zhang. 3D finite-element modeling of Earth induced electromagnetic field and its potential applications for geomagnetic satellites. Science China Earth Sciences, 2021, 64, 1798–1812. https://doi.org/10.1007/s11430-020-9786-9

[2] Hongbo Yao, Zhengyong Ren*, Jingtian Tang, Keke Zhang. A multi-resolution finite-element approach for global electromagnetic induction modeling with application to southeast China coastal geomagnetic observatory studies. Journal of Geophysical Research: Solid Earth, 2022, 127(8), e2022JB024659. https://doi.org/10.1029/2022JB024659