In the modeling procedure, the conductivity of land and seabed is set to a typical value of 0.01 S/m up to 100km below the surface since both land and seabed belong to the lithosphere. Taking into account the skin effect of the electromagnetic field, the skin depth is calculated for a surface current of frequency of 0.003 Hz and current density 100 A/m2 in the ground with a conductivity of 0.01 S/m. The calculation results show that the electromagnetic field at a depth of 400km is ~1% of the surface electromagnetic field. Therefore, the lower boundary of the model is set at a depth of 400km. In order to avoid the influence of the lateral boundary conditions on the IGF, the left and right boundaries are set at 500km from the center. At the lateral tion boundaries, the electromagnetic wave is complteley absorbed though theoretically the boundary can extend to infinity.
The ocean depth is set at 4 km considering the average global ocean depth of 3688 m, and the ocean conductivity is set at 4 S/m, the average conductivity of sea water. Since geomagnetic disturbances arise mainly from the changes in the storm-time ionospheric current, these disturbances are simulated by assuming the current. Following Pulkkinen et al. (2007), the current is considered as a thin uniform current sheet at a height of 100 km above the earth's surface. Assuming that the ionospheric current frequency is 0.003 Hz, the surface current density is set at 100 A/m2. The surface current in the model starts from the boundary on one side to the boundary on the corresponding side, which is a continuous current that runs through the entire model. The ionospheric current generates magnetic waves propagating down to the earth and induces the geoelectric field. To simulate the attenuation effect of air on the waves, the atmospheric conductivity is set at 1.8×10−4 S/m in the region between the ionospheric current and earth surface. The upper boundary of the model is set 50km above the sheet current, and electromagnetic waves are completely absorbed at the boundary. Figure 2(a) shows the ground conductivity model of the land-sea boundary area. Figures 2(b) and 2(c) display the calculated underground (X-Z plane with Y=0) magnetic field and IGF, and Figures 2(d) and 2(e) display the calculated surface (X-Y plane with Z=0) magnetic field and IGF, respectively.
As shown by Figures 2b and 2d, the magnetic field in the ocean area is concentrated on the ocean surface (reddish-yellow strip in Figure 2b) and does not extend much below the surface; the magnetic field in the land area, though weak at the surface, extends well below the surface. The IGF (Figures 2c and 2e) is concentrated within a small distance on the land side of the land-sea interface, with amplitude up to 115 mV/km at the center of the interface; beyond the small distance, IGF gradually decreases to nearly uniform value laterally. In the sea side there is almost no IGF. The main point in Figure 2 is the illustration of the ‘coastal effect’. That is, IGF gets concentrated within a small area on the land side of the land-sea interface. The coastal effect therefore should be considered seriously in GIC risk assessment.
Comparing (a) and (b), it can be found that the distribution of IGF in the two figures is basically the same without considering the size and frequency of the sheet current. It shows that using this model to analyze the distribution of IGF is effective.
3.1 Effects of different factors on IGF
As mentioned in section 1, IGF is affected by many factors such as conductivity, ionospheric current (frequency, magnitude and direction), ocean depth, etc. The effects of these factors on IGF are investigated in this section.
3.1.1 Effect of conductivity
The conductivity of slate in common sedimentary rocks and metamorphic rocks are found to be in ~0.001-0.1 S/m range and quartzite in magmatic rocks and metamorphic rocks are in ~0.0001-0.01 S/m range. To cover these ranges, in the model (Figure 2a), we use the lithospheric conductivity in ~0.0001-0.1 S/m range. Other conditions are same as in the model. As shown in Figures 4-5, when the conductivity increases from 0.0001 to 0.1 S/m, in the land side the maximum IGF (IGFmax) at the center of the land-sea interface decreases from 368.3 mV/km to 24 mV/km. For all conductivity values, IGF decreases rapidly within a short distance and stabilizes gradually at a long distance from the interface (Figure 5). The stars indicate the distances (~20-30 km) where IGF becomes 50% of IGFmax and dots indicate the distances (~150-90 km) where IGF nearly stabilizes when conductivity increases from 0.0001 to 0.01 S/m. In the sea side, IGF suddenly decreases to a value of zero for all conductivities.
The fact that IGFmax decreases from high to low values (368 mV/km to 24 mV/km) with the increase of lithospheric conductivity (0.0001 to 0.01 S/m) indicates that the conductivity is a major factor influencing the IGF in coastal areas. The greater the difference in electrical conductivity between land and ocean, the greater the magnitude of IGF generated in the land-sea boundary area, and the more severe the impact of the coastal effect.
3.1.2 Effects of ionospheric current
The ionospheric current during geomagnetic storms can affect IGF through changes in frequency, magnitude and direction. The effects of these aspects are studied here. The storm-time ionospheric current is found to have periodic variations with periods ~100-1000s (Xu, 2000). We use current of frequency 0.001-0.01 Hz; all other conditions remain the same as in the model (Figure 2a).
The simulation results (Figures 6-7) show that IGFmax decreases rapidly from 153 mV/km to 52 mV/km when the current frequency increases from 0.001 Hz to 0.01 Hz. The decrease of IGF with distance from the interface (Figure 7) is similar to that for the conductivity (Figure 5) though IGFmax for the current case is only about half. Stars and dots indicate the distance where IGF becomes 50% of IGFmax (~25-65 km) and nearly stabilizes (~125-60 km), respectively, for frequency 0.001-0.006 Hz. Like conductivity, the ionospheric current frequency is a major factor influencing the strength IGF in coastal areas.
The effect of ionospheric current density on IGF is shown in Figure 8; (a), (b) and (c) are surface IGF for current density 50 A/m2, 100 A/m2 and 200 A/m2 with all other conditions same as in the model (Figure 2a). As shown, magnitude of IGFmax at the interface is nearly equal to that of current density indicting that the severity of IGF (and GIC) depends directly on the severity of storm-time ionospheric current. To study the effect of ionospheric current direction, the current (100 A/m2) is changed to be parallel to the land-sea interface; all other conditions are same as for Figure 8b. In this case (Figure 8d), there is no IGF at the interface and IGF in inland areas is slightly decreased compared to when the current is perpendicular to the interface (Figure 8b). The results (Figure 8) indicate that IGF (and GIC) are strong in coastal areas where the current is perpendicular to the sea-land interface.
3.1.3 Effect of ocean depth
The ocean is generally considered to have two parts, the sea and ocean. The ocean is the main body which has a depth of ~3-100 km and sea is the shallow ocean-land boundary having depth up to 3 km. The coastal area includes the coastal land area and the adjacent sea-ocean boundary area. Considering that there is rarely any deep ocean in the sea-land boundary area, the ocean depth is set to vary from 1 to 3 km. All other conditions remain the same as in the model (Figure 2a). There is only a small change in IGF (Figure 9) when ocean depth increases from 1 to 3 km.
The corresponding IGFmax at the interface is found to decrease by a small amount from 139.2 mV/km to 100 mV/km. With distance from the interface, the IGF rapidly decreases and becomes nearly constant at ~50 km away from the interface for all ocean depths (line curves not shown). The results indicate that the ocean depth has only a minor effect on IGF.