Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: part II—numerical investigations

In this paper, numerical computations are carried out to investigate the seismo-electromagnetic signals arising from the motional induction effect due to an earthquake source embedded in 3-D multi-layered media. First, our numerical computation approach that combines discrete wavenumber method, peak-trough averaging method, and point source stacking method is introduced in detail. The peak-trough averaging method helps overcome the slow convergence problem, which occurs when the source–receiver depth difference is small, allowing us to consider any focus depth. The point source stacking method is used to deal with a finite fault. Later, an excellent agreement between our method and the curvilinear grid finite-difference method for the seismic wave solutions is found, which to a certain degree verifies the validity of our method. Thereafter, numerical computation results of an air–solid two-layer model show that both a receiver below and another one above the ground surface will record electromagnetic (EM) signals showing up at the same time as seismic waves, that is, the so-called coseismic EM signals. These results suggest that the in-air coseismic magnetic signals reported previously, which were recorded by induction coils hung on trees, can be explained by the motional induction effect or maybe other seismo-electromagnetic coupling mechanisms. Further investigations of wave-field snapshots and theoretical analysis suggest that the seismic-to-EM conversion caused by the motional induction effect will give birth to evanescent EM waves when seismic waves arrive at an interface with an incident angle greater than the critical angle θc = arcsin(Vsei/Vem), where Vsei and Vem are seismic wave velocity and EM wave velocity, respectively. The computed EM signals in air are found to have an excellent agreement with the theoretically predicted amplitude decay characteristic for a single frequency and single wavenumber. The evanescent EM waves originating from a subsurface interface of conductivity contrast will contribute to the coseismic EM signals. Thus, the conductivity at depth will affect the coseismic EM signals recorded nearby the ground surface. Finally, a fault rupture spreading to the ground surface, an unexamined case in previous numerical computations of seismo-electromagnetic signals, is considered. The computation results once again indicate the motional induction effect can contribute to the coseismic EM signals.

Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: part I—theoretical formulations

Taking into account the motional induction effect, in which the Earth crust that has finite electrical conductivity vibrates in the ambient geomagnetic field resulting in motionally induced electric current, we derive semi-analytical solutions of seismo-electromagnetic signals generated by an earthquake source in 3-D multi-layered media, which consists of an air half-space and multiple solid layers. First, both the elastic and electromagnetic (EM) wave-fields involved in the governing equations, which have the form of Maxwell’s equations coupled with elastodynamic equations, are expanded by a set of vector basis functions in cylindrical coordinate system. Then, we reorganize the transformed governing equations expressed by expansion coefficients and obtain corresponding first-order ordinary differential equations for the wave-fields in air and solid media. The expansion of the motionally induced electric current and the reorganization of Maxwell’s equations are the most important part, and also the most complicated and tedious part of this work. Thereafter, we solve the first-order ordinary differential equations through the Luco–Apsel–Chen generalized reflection and transmission method gaining solutions of the expansion coefficients. Finally, we obtain the frequency–space-domain semi-analytical solutions written as integrations of corresponding expansion coefficients over wavenumber domain, which can be numerically calculated by the discrete wavenumber method. The time-domain solutions can be achieved by further applying the discrete inverse Fourier transform. To have a numerical stability at any high frequency, we adopt the analytical regularization approach in the derivation process by introducing two artificial interfaces with infinitely small distance from the source. On the basis of the semi-analytical solutions, we can tell that only EM fields of TM mode (in which magnetic fields are transversely polarized) will be induced by SH waves, whereas EM fields of both TE mode (in which magnetic fields are transversely polarized) and TM mode will be induced by P and SV waves. The derived semi-analytical solutions can be used to calculate seismo-electromagnetic signals either below or above the free surface.

Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call plesio-geostrophy , which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.

Coseismic electric and magnetic signals observed during 2017 Jiuzhaigou Mw 6.5 earthquake and explained by electrokinetics and magnetometer rotation

SUMMARY Very clear coseismic electric and magnetic signals accompanying seismic waves were observed during the 2017 Mw 6.5 Jiuzhaigou earthquake, which took place in western China. In order to understand the generation mechanism of these observed signals, we simulate electric and magnetic responses to this specific earthquake based on three mechanisms, namely, the electrokinetic effect, the motional induction effect and the rotation effect of the coil-type magnetometer. We conduct the simulations using a point source model and a realistic layered earth model and compare to the observed data in the frequency band 0.05–0.3 Hz. Our results show that the electrokinetic effect can explain the observed electric fields in both waveform and amplitude, but it cannot explain the magnetic signals accompanying the Rayleigh wave. The motional induction effect cannot explain either the coseismic electric or magnetic data because it predicts much weaker coseismic electric and magnetic fields than the observed data. The magnetic fields resulting from the rotation of the magnetometer agree with the observed data in the waveforms though their amplitudes are two to four times smaller than the observed data. Our simulations suggest that the electrokinetic effect is responsible for the generation of coseismic electric fields and that rotation of the coil magnetometer is likely the main cause of coseismic magnetic fields. The results improve our interpretation of the coseismic electromagnetic (EM) phenomenon and are useful for understanding other kinds of earthquake-associated EM phenomena.

Electromagnetic responses to an earthquake source due to the motional induction effect in a 2-D layered model

Summary Movement of the conductive earth medium in the ambient geomagnetic field can generate an electromotive force and a motional induction current, which further cause the disturbances of the electromagnetic (EM) fields. Such a mechanoelectric coupling is known as the motional induction (MI) effect and has been proposed to be a possible mechanism for the generation of the observed EM signals during earthquakes. In this paper, we study the EM responses to an earthquake source due to such a MI effect in a 2-D horizontally layered model. First we transform the governing equations that couple the elastodynamic equations and Maxwell equations into a set of first-order ordinary depth-dependent differential equations. Then we solve the seismic and EM responses to a moment tensor source. Finally, we transform the 2-D seismic and EM responses to 3-D responses using a simple amplitude correction method. We conduct several numerical examples to investigate the properties of the EM signals generated by the earthquake source. The results show that two types of EM signals can be observed. The first one is the coseismic electric/magnetic field that accompanies the seismic P and S waves as well as the Rayleigh wave. The second one is the early EM signal which arrives before the P wave. The numerical results show that the EM signals change with the inclination angle of the geomagnetic field, the azimuth angle between the wave propagation plane and the geomagnetic vertical plane, and the medium conductivity. Increase in the conductivity can enhance the coseismic electric and magnetic signals. Our simulation also shows that an EM wave can be generated by a seismic wave at the interface separating two different media. The radiation pattern of the interface EM wave generated by a P wave is similar to that of a horizontal electric dipole located on the interface.

Depth of origin of ocean-circulation-induced magnetic signals

As the world ocean moves through the ambient geomagnetic core field, electric currents are generated in the entire ocean basin. These oceanic electric currents induce weak magnetic signals that are principally observable outside of the ocean and allow inferences about large-scale oceanic transports of water, heat, and salinity. The ocean-induced magnetic field is an integral quantity and, to first order, it is proportional to depth-integrated and conductivity-weighted ocean currents. However, the specific contribution of oceanic transports at different depths to the motional induction process remains unclear and is examined in this study. We show that large-scale motional induction due to the general ocean circulation is dominantly generated by ocean currents in the upper 2000 m of the ocean basin. In particular, our findings allow relating regional patterns of the oceanic magnetic field to corresponding oceanic transports at different depths. Ocean currents below 3000 m, in contrast, only contribute a small fraction to the ocean-induced magnetic signal strength with values up to 0.2 nT at sea surface and less than 0.1 nT at the Swarm satellite altitude. Thereby, potential satellite observations of ocean-circulation-induced magnetic signals are found to be likely insensitive to deep ocean currents. Furthermore, it is shown that annual temporal variations of the ocean-induced magnetic field in the region of the Antarctic Circumpolar Current contain information about sub-surface ocean currents below 1000 m with intra-annual periods. Specifically, ocean currents with sub-monthly periods dominate the annual temporal variability of the ocean-induced magnetic field. Keywords. Electromagnetics (numerical methods) – geomagnetism and paleomagnetism (geomagnetic induction) – history of geophysics (transport)