Lower hybrid wave cavities detected by the Freja satellite are analyzed. On the basis of simple statistical arguments by use of signals from two density probes, it is possible to obtain rather general results concerning the individual shapes of these cavities. In particular, it is demonstrated that a cylindrically symmetric Gaussian density depletion seems to give a very good fit for a vast majority of cases. The validity of this model is shown to give a great simplification in the interpretation of the data. As a result, a number of well-defined characteristics are obtained which have to be accommodated within an ultimate theory describing the observed wave phenomena. ¿ 2000 American Geophysical Union