Seismic Oceanography is coming of age as an established technique of observation of the thermohaline structure of the ocean. The present paper deals with the seismic reflectivity of the Armorican Shelf seasonal thermocline, west of France, based on two seismic experiments performed with a sparker source. The peak frequency was 500 Hz for the ASPEX experiment, where the thermocline was located at 27 m water depth, and reduced to 400 Hz associated to a higher source level for the IFOSISMO experiment, where the thermocline was 12 m deeper. Despite this settings, only the first experiment could clearly highlight the thermocline reflector, providing the first seismic observation of a shallow oceanic structure. To better understand the limitation of high-resolution seismic devices in detecting weak oceanic features, we develop a wavelet-based seismic analysis and consider, as a first approximation, a simple thermocline modelled by a Gauss Error function, allowing an analytical expression for the associated seismic reflectivity. We show that the acoustic impedance profile of the thermocline is mainly controlled by a sound velocity proportional to the temperature. We show that the seismic reflectivity is controlled by the reflection coefficient of the large-scale structure of the thermocline and by an attenuation factor which depends on the ratio between the seismic wavelength and the characteristic size of the thermocline. Depending on this ratio, the strength of the thermocline-related reflection may be too weak to be detected by seismic measurement.