Synthesis of ground backscatter ionograms is a useful technique for studying the structure of the ionosphere. By synthesizing backscatter ionograms from a known ionosphere, knowledge can be obtained on how variations in the ionosphere affect the shape of a backscatter ionogram. A method allowing the rapid synthesis of ground backscatter ionograms is presented. The vertical ionospheric profile is represented by a series of smoothly joined quasi-parabolic segments which can accurately reproduce both measured and model profiles. The ionosphere is, however, restricted to being spherically symmetric. The synthesis includes corrections for geometrical and time delay focusing. The speed of the technique is valuable when ionospheric state is to be determined by seeking a match between measured and synthesized backscatter ionograms. The restriction of the synthesis to spherically symmetric ionospheres means that the best choice can only be made from this class. Residual differences can be a useful indication of the significance of departures from spherical symmetry. The calculations involved in the synthesis are closely related to those necessary to establish coordinate registration in the location of targets for over-the-horizon radar. ¿ 1998 American Geophysical Union