In this study, we show that the amplitude radio occultation (RO) method, which employs high-precision global positioning system (GPS) signals, allows one to determine the vertical gradients of refractivity and monitor wave structures in the atmosphere on a global scale at altitudes ranging from 10 to 40 km. We show that the sensitivity of the RO amplitude data to the wave structures in the atmosphere with vertical periods from 0.8 to 4 km exceeds one of the RO phase data by a factor of order 10. As an example of this approach, analytical results of the Challenging Minisatellite Payload's (CHAMP) RO events are presented. Wave clusters were found in the amplitude variations of the RO signals with interior vertical periods from 0.8 to 4 km in the tropopause and lower stratosphere within the heights of 15--24 km (low latitudes) to 10--15 km (moderate latitudes). We demonstrate that the amplitude variations can be considered as a radio-holographic image of the wave structures in the atmosphere. For internal gravity waves (GW), we show that the GW portrait, which consists of the altitude dependence of the GW phase, amplitude and vertical spatial frequency, can be retrieved from the amplitude variations of the RO signal. The GW dispersion and polarization relationships allow one to estimate the vertical profile of the horizontal wind perturbations, its gradient and the GW intrinsic phase speed. In general, when the origin and type of internal waves are not known, the height dependence of the vertical gradient of refractivity can be applied for monitoring the seasonal and geographical distributions of wave activities at different levels in the atmosphere.