A probe including NE ultrasonic emitters and NR ultrasonic receivers is applied on the medium to be characterized. Each emitter is activated successively and each time signals are detected on the set of receivers during a time window. Each of the NE×NR signals detected is converted by temporal Fourier transformation to a sum of vibrational components each having its temporal frequency. For each frequency, a matrix NE×NR of complex amplitudes of vibrational components having this frequency is extracted. These matrices are decomposed into singular values, the smallest are eliminated, and the singular vectors associated with the singular values retained, a base of the space of the reception signals is formed, for each frequency. The contribution of each plane wave, characterized by its velocity, in this base is calculated. This contribution is represented in the form of a grey level in a frequency-propagation velocity reference system.