Global Navigation Satellite System radio occultation (GNSS-RO) is an important technique used to sound the Earth's atmosphere and provide data products to numerical weather prediction (NWP) systems as well as to climate research. It provides a high vertical resolution and SI-traceability that are both valuable complements to other Earth observation systems. In addition to direct components refracted in the atmosphere, many received RO signals contain reflected components thanks to the specular and relatively smooth characteristics of the ocean. These reflected components can interfere the retrieval of the direct part of the signal, and can also contain meteorological information of their own, e.g., information about the refractivity at the Earth's surface. While the conventional method to detect such reflections is by using radio-holographic methods, it has been shown that it is possible to see reflections using wave optics inversion, specifically while inspecting the amplitude of the output of phase matching (PM). The primary objective of this paper is to analyze the appearance of these reflections in the amplitude output from another wave optics algorithm, namely the much faster full spectrum inversion (FSI). PM and FSI are closely related algorithms - they both use the method of stationary phase to derive the bending angle from a measured signal. We apply our own implementation of FSI to the same GNSS-RO measurements that PM was previously applied to and show that the amplitudes of the outputs again indicate reflection in the surface of the ocean. Our results show that the amplitudes output from the FSI and PM algorithms are practically identical and that the reflection signatures thus appear equally well.