## 2 Data and Methods
### Influence of Ocean  
The C-responses at coastal observatories are significantly influenced by the ocean induction effects caused by the significant electrical conductivity contrasts between conductive oceans and resistive continents, especially for responses with brief durations [21; 36; 37]. Some of our selected observatories are located near the coastline (Figures 1 and 3), so the responses of the stations impacted by the ocean effect must be corrected. The ratio method can be used for ocean effect correction [36; 38], and the specific correction formula is as follows:  
\[C^{\text{corr}}=C^{\text{obs}}.k,\text{ and }k=C^{\text{1D}}/C^{\text{1D+shell}} \tag{11}\]  
\begin{table}
\begin{tabular}{c c c c c c|c c c c c} \hline \hline
**Code** & **Long** & **Lat** & **GM-** & **GM-** & **Data** & **Code** & **Long** & **Lat** & **GM-** & **GM-** & **Data** \\ \hline AQU & 42.38 & 13.32 & 42.39 & 94.65 & 1960-2009 & K2N & 55.83 & 48.85 & 49.8 & 131.71 & 1957-2016 \\ ARS & 56.43 & 58.57 & 49.2 & 140.05 & 1973-2018 & LVV & 49.9 & 23.75 & 47.87 & 107.22 & 1957-2019 \\ ASH & 37.95 & 58.11 & 31.06 & 135.3 & 1959-1990 & MAB & 50.3 & 5.68 & 51.39 & 90.15 & 1995-2021 \\ BDV & 49.08 & 14.02 & 48.75 & 97.73 & 1994-2020 & MBO & 14.38 & 343.03 & 20.03 & 57.51 & 1952-2020 \\ BEL & 51.84 & 20.79 & 50.24 & 105.27 & 1966-2021 & MNK & 54.5 & 27.88 & 51.62 & 112.91 & 1961-2019 \\ BFE & 55.62 & 11.67 & 55.43 & 98.54 & 1981-2008 & MOS & 55.47 & 37.32 & 51.08 & 121.68 & 1957-2020 \\ BFO & 48.33 & 8.32 & 49.03 & 91.91 & 2006-2021 & NCK & 47.63 & 16.72 & 46.88 & 99.74 & 1993-2021 \\ BGY & 31.72 & 35.09 & 28.27 & 112.66 & 1989-2019 & NNK & 52.07 & 12.68 & 51.86 & 97.73 & 1932-2021 \\ BOX & 58.07 & 38.23 & 53.45 & 123.61 & 1977-2020 & ODE & 46.78 & 30.88 & 43.67 & 112.69 & 1957-1991 \\ CLF & 48.02 & 2.26 & 49.79 & 85.79 & 1936-2021 & PAG & 42.52 & 24.18 & 40.64 & 105.09 & 1956-2020 \\ CIG  
Here, \(C^{\rm corr}\) is the corrected response, and \(C^{\rm obs}\) is the observed response at the station; \(k\) is the correction coefficient, which can be calculated from the response (\(C^{\rm 1D}\)) of the one-dimensional (1D) model and the response (\(C^{\rm 1D+shell}\)) of a 1D model with a covering shell comprised of oceans and continents. Obviously, the correction coefficient changes with the 1D model. This makes it difficult to search for a perfect 1D model that is suitable for all the oceans and continents.  
Figure 3: Electrical conductivity of the shell comprised of oceans and continents used to correct the ocean effect on C-responses and drawn in a geomagnetic coordinate system. White circles represent the used observatories in the geomagnetic coordinate system. The outlines of oceans and continents in a geographic coordinate system are also depicted.  
Figure 2: C-responses at 50 selected observatories; (**a,b**) are the real and imaginary components of C-responses.  
stations, because the electrical structure of Earth is undiscovered and in three dimensions. Therefore, in our 3D inversion of GDS, the conductivity of the shell with ocean and land is treated as a surface layer of Earth (Figure 3). A lateral grid of \(1^{\circ}\times 1^{\circ}\) with a thickness of 12.65 km is considered in order to describe the shell more finely [17] and to ensure sufficiently accurate accounting for OIE [36]. The shell will be incorporated in forward numerical but fixed throughout the inversion [3; 15].