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The ellipsoidal surface with semi-axes a, b, c, is the surface of the constant autocorrelation function of refractive index fluctuations. For expressing the equation of the surface in local geographic coordinates, the transformation from North–East-Down coordinate system x,y,z to the Singleton coordinates is used. The transformation consists of: (a) the rotation on the magnetic declination angle ϕ followed by the rotation on the magnetic inclination or dip angle ψ; (b) the rotation on angle that characterizes the tilt of the ionospheric layer relative to the observer plane. In order to visualize the orientation of the plane within which the geomagnetic field has constant magnitude the multiple field lines are shown in the sketch (b).
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