Моделирование ионосферного отклика на процесс подготовки землетрясений

Fig. 1. Magnetic maps of model TEC deviations (%) relative to the quiet conditions for "straight" currents located at 5° lat. (from top to bottom): "return" currents spread out over the globe except points with "straight" currents; without "return" currents; the same as at top but currents flow from the ionosphere to the Earth; "return" currents are located at the grid nodes nearest to the "straight" currents. Stars – grid points with "straight" currents. Diamonds – the magnetically conjugated points. Orange circle – the subsolar point. Black curves – terminator lines

Fig. 2. Magnetic maps of model TEC deviations (%) relative to the quiet conditions for "straight" currents located at 15° lat.

Fig. 3. Magnetic maps of model TEC deviations (%) relative to the quiet conditions for "straight" currents located at 30° lat.

Fig. 4. Magnetic maps of model TEC deviations (%) relative to the quiet conditions for "straight" currents located at 45° lat.

Previous numerical simulations ( Namgaladze , 2010; Namgaladze et al. , 2011; Namgaladze, Zolotov , 2011) showed that point electric current sources larger than 10^-6A/m² generated too strong TEC disturbances. Similar point sources but with densities less than 10^-9-10^-8 A/m² generated TEC disturbances not exceeding 10-20 %. Those values were smaller than ones usually taken into consideration in pre-earthquake TEC modifications studies. The vertical electric current with density of about 2∙10^-8 A/m2 flowing between the fault and the ionosphere set at the area of about ~200 km X ~4000 km may create electric fields generating the TEC increases up to ~50 % at night-time as observed before the Haiti Jan. 12, 2010 earthquake. Appearance of the terminator and subsolar point caused depression down to full destruction of electric potential generated by external electric current. TEC disturbances were also modified: "escaped" from terminator to dark-side of the ionosphere with following full destruction, but with time lag relative to the electric potential. Next night the electric potential and corresponding TEC disturbances restored.

The principle goal of this paper is to present the results of numerical simulations of ionosphere electric fields and corresponding TEC disturbances depending on various parameters of electric currents between the Earth and ionosphere: (1) latitudinal position, (2) general spatial orientation of the vertical electric currents' distribution and (3) direction (to or from the ionosphere).

2. Simulation methods

Model experiments were carried out using the Upper Atmosphere Model – global numerical model of the Earth's upper atmosphere (thermosphere, ionosphere, plasmasphere and inner magnetosphere). The model calculates main physical parameters of upper atmosphere such as densities, temperatures and velocities of the neutral (O, O 2 , N 2 , H) and charged (O 2 ⁺, NO⁺, O⁺, H⁺ and electrons) species by numerical integration of the continuity, momentum and heat balance equations as well as the equation of the electric field potential ( Namgaladze et al. , 1988; 1991; 1998a; 1998b).

To build model difference maps of the TEC we first performed a regular calculation without any additional electric current sources to use those results as quiet background values. Then, an external electric current ("straight" current) flowing between the lower atmosphere and the ionosphere presumably of seismogenic origin was used as a model input for the calculations of the ionospheric field and the corresponding TEC variations. These additional sources of the electric current with the magnitude of 4∙10-8 A/m2 were switched on at the lower boundary (80 km) in the UAM electric potential equation, which was solved numerically jointly with all other UAM equations for neutral and ionized gases.

Currents sources were switched on at five numerical grid nodes which correspond to the size of the area about 200 km along the parallel and about 3000 km along the meridian depending on latitude. The latitudinal position (5°, 15°, 30° and 45° mag. lat.) and direction of the currents (to or from the ionosphere) were varied in. The grid nodes with vertical electric currents ("straight" currents) were surrounded by boundary grid points with currents of the opposite direction ("return" currents) so that the total current in the global electric circuit didn't change. In other investigated configuration "return" currents were spread out over the globe except the points with "straight" current. The configuration without "return" currents were studied as well.

strong disturbances by magnitude. Sources for latitudes less than 30° generate pronounced modification of the Appleton anomaly.

It should be noted that similar numerical calculations were performed by ( Kuo et al. , 2011). The difference is that their currents flow the over area 200 km X 30 km that is much smaller than in our case. "Rock currents" were switched on near ground surface (not at the lower boarder of the ionosphere). Then they used the empirical model of the atmosphere's conductivity modified from some considerations. They simulated only TEC response at the epicenter region and did not consider magnetically conjugated ones. The simulations were local (not for the globe as in our case) with "single" point sources. According to their simulations using SAMI2 model the current density of 0.2-10 µA/m² in the earthquake fault zone can cause TEC variations of up to 2-25 % in the daytime ionosphere and the density of 0.01-1 µA/m² can lead to nighttime TEC variations of 1-30 %. Such huge currents are required due to a too small area of the current generation in their simulation. Beside of this, our and their model results do not contradict each other.