Empirical models of the average magnetospheric magnetic field, plasma density, and temperature distributions are used to construct a model of the distribution of MHD wave mode speeds within the magnetosphere. Although the MHD wave speeds in general have a smaller dynamic range than the magnetic field intensity or the plasma properties, considerable structure and variability is found which will lead to interesting ''optical'' effects on the propagation of low frequency waves. A persistent feature of the derived optical structure, which is qualitatively insensitive to known variability of the field or plasma, is a pronounced minimum of the wave speeds in the outer plasmasphere, i.e., a magnetospheric ''shoal.'' This feature does not map along magnetic field lines, but is confined to the equatorial region, leading to a positive radial gradient of wave speeds near synchronous orbit. The breaking of earthward propagating disturbances in this region may play an essential role in the formation of the substorm injection boundary and in the creation of equatorially trapped warm ion distributions. ¿ American Geophysical Union 1987