High-precision modeling of tide-induced 3-D magnetic field and analysis of geomagnetic satellite orbit requirements

Ground-based magnetic observatories and geomagnetic satellites can observe the induced magnetic field generated by the motion of seawater containing sodium and chlorine ions. Calculating the three-dimensional (3-D) spatial distribution of tide-induced magnetic fields (TIMF) is crucial for inverting the electrical conductivity structure of the oceanic lithosphere. It also serves as an essential basis for designing optimal geomagnetic observatories and satellite orbits. However, existing methods for simulating TIMF suffer from limitations in inaccurately modeling realistic coastlines, heterogeneous land and sea surface properties, and complex deep Earth structures, thereby the interpretational level of TIMF data is reduced. To overcome this issue, we developed a tetrahedral-based finite element method for simulating TIMF, which can efficiently approximate realistic coastlines, heterogeneous land and sea surface properties, and complex deep Earth structures. Firstly, we derived the boundary value problem for the seawater motion-induced electromagnetic field, which was solved using the vector finite element method based on tetrahedral elements. Secondly, using the latest ocean depth and seafloor sediment layer models, we constructed a 3-D conductivity model of the Earth, which includes realistic coastlines, heterogeneous land and sea conductivity distributions. We then computed the TIMF using the M2 tidal source as an example and validated our method by comparing it with results obtained from spherical harmonic finite element and integral equation methods. Finally, utilizing the computed high-precision M2, N2, and O1 TIMF signals, we marked global observatories capable of observing strong M2, N2, and O1 TIMF signals and predicted alternative stations suitable for tide signal observations. Additionally, we calculated TIMF at heights of 450 and 200 km for the Macau Science Satellite 1 and its subsequent satellites. The results indicate that the amplitude of the tidal-induced magnetic field at 200 km is approximately twice that at 450 km. The maximum amplitudes of M2, N2 and O1 TIMF at 200 km are eight, two, and three times the measurement accuracy of the magnetic sensing payload (0.5 nT), respectively. The 200 km orbit has great potential for detecting high-resolution electrical structures of the seafloor lithosphere and asthenosphere in regions such as New Zealand, southern Iceland, the southern Indian Ocean, the Ross Sea region of Antarctica, and the Sea of Okhotsk. It also holds the potential for studying large-scale oceanic dynamic processes and properties.