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Fig. 2

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Local geographic coordinate system, O-xyɀ, and geomagnetic coordinates, O-xy′ɀ′. In O-xyɀ coordinates, the positive x-axis and y-axis point toward geographic east and north, respectively; the positive z-axis points upwards. In the geomagnetic coordinate system, obtained by clockwise rotation of the geographic coordinates by an angle of π/2 + I around the y-axis and an angle of π/2 – D around the ɀ-axis, the positive x′- and y′-axis are toward Pedersen and Hall directions, respectively; the ɀ′-axis is a magnetic field-aligned axis and completes the right-handed system. φ is the wave azimuth angle defined by the incidence of the wavenumber vector (k) with respect to the geographic north. θ is the angle of incidence between the xy plane and wavenum-ber vector. I refers to the geomagnetic dip angle. The declination angle, marked by D, defined by the incidence of the magnetic field with respect to the geographic north, is assumed to equal 90° in this study, suggesting that the magnetic field lines are located in the xz plane and the Hall direction is toward the north.

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