We present a numerical method of simulating at any location in the magnetosphere, the observed frequency versus time (f-t) spectrogram resulting from a lightning strike at any given latitude on Earth. Using a two-dimensional ray tracing code, we calculate the trajectories of 5330 whistler rays that effectively sample the lightning strike's frequency spectrum and latitudinal spread about the source and then use these so-called sample rays to create ~120 million interpolated rays, each weighted with a measure of energy according to its frequency and injection latitude. This energy is progressively attenuated along the ray's trajectory using a Landau damping calculation with realistic suprathermal electron fluxes. A detection area is defined in the plasmasphere, and rays that cross this area are used to construct the f-t spectrogram representative of what would be observed on a satellite located in that region. We investigate the role that the lightning source latitude, observation location, and plasmaspheric electron density structures have on the appearance of the simulated f-t spectrograms and show that all three parameters exhibit distinct and well-defined effects. In particular, we focus on plasmaspheric electron density structures and explain the connection between these structures and the appearance of specific observed features in the spectrograms. Using this analysis, it may be possible to crudely infer certain features of the source and plasmasphere from observed magnetospherically reflecting whistler spectrograms.