Station Displacements Research Articles

Ionospheric Current Structure as Determined from Ground-based Magnetometer Data

Summary The magnetic perturbations from a three-dimensional current system commonly used to describe magnetospheric substorm variations have been inverted, by using the linear inverse theory of Backus and Gilbert, to obtain estimates of the (height-integrated) ionospheric current density producing the observations. Under the assumption that electrojet intensity is not a function of longitude it has been found that displacement of stations from the central meridian yields no significant change in resolution of the current density so long as the observation sites remain within the longitudinal limits of the ionospheric current; hence a linear array can provide as much resolution as a two-dimensional one. The maximum resolution possible is shown to be ∼ 1° latitude or about one ionospheric height unit. An investigation of the dependence of resolution (of a linear array) on station spacing shows that the optimum spacing is dependent upon the number of stations and the desired standard deviation of the estimate of the current density; nevertheless, the rule of thumb that stations should be separated by 1° of latitude is shown to be a good compromise between maximizing resolution and simultaneously minimizing the number of stations. Inversion results using data from a polar magnetic substorm of 1970 June 15 indicate that the magnitude of the westward current density was at least 0·90 ± 0·15 A m−1 and that the current density cannot be approximated by a constant value over widths much greater than 1° of latitude. Published magnetic data from the equatorial region have also been inverted to obtain estimates of the current density in the equatorial electrojet.

High-Resolution Imaging of Tropospheric Radio Scatterers

A two-dimensional matched filter technique is described for processing ing the signal from a pulsed coherent troposcatter link to obtain high crosspath resolution "maps" showing the relative positions of individual scatterers. For a typical tropolink (station displacement 200 km; midpath beam halfwidth 2 km; wavelength 0.3 meters) crosspath resolution is about 4.5 meters under perfect conditions. Vertical resolution is inversely proportional to scatterer height, but even for wide bandwidth signals is never better than hundreds of meters. Slight velocity mismatches between the signal and filter degrade crosspath resolution considerably so that the scatterers' velocity must be known accurately a priori. Crosspath resolution is relatively insensitive to mismatch in signal and filter record lengths. Random fluctuations of the velocity of a scatterer seriously degrade crosspath resolution. For the typical tropolink parameters and with a 10 m/s scatterer crosspath velocity and a 0.2 m/s standard deviation ion fluctuation the crosspath resolution degrades by an order of magnitude. It is concluded that the matched filter imaging scheme will produce images of individual scatterers if specific atmospheric conditions ions exist. The best results are obtained if the received signal comes from a single scattering layer at a known height, with scatterers moving at a known constant horizontal velocity, with no along-path or vertical components. Such a layer would be observed during night time or early morning when convective and mixing processes are at a minimum.

REDUCTION OF UNEVENLY SPACED POTENTIAL FIELD DATA TO A HORIZONTAL PLANE BY MEANS OF FINITE HARMONIC SERIES

Conventional reductions of gravity and magnetic data do not lead to values that are effectively on the same horizontal plane, although it is common practice to regard them so. In regions of high topographic relief, failure to take into account local differences in vertical gradients can result in appreciable error. In this study a method is developed for reducing to a common level gravity or magnetic anomaly data observed at unevenly spaced stations at various elevations above a reference plane. The reduction is effected by means of finite harmonic series approximations in which the coefficients are determined by matrix methods and least squares. Traditional Fourier methods are not applicable because uneven station spacing and relative vertical displacement of stations preclude the use of the orthogonality properties of the trigonometric functions. The number of terms required to represent the data adequately is discussed in terms of “cutoff” wavenumbers empirically determined from residual variance estimates. The method is illustrated by application to theoretical and field data.