A logging method and apparatus are provided for the acoustic inspection of a borehole fitted with a casing wherein obtained measurements which are representative respectively of one or more data items relating to the casing and to the material which surrounds it are corrected for the effects of the environment. The method comprises: emitting a first acoustic pulse through the medium present in the casing and directed at a substantially normal incidence towards a sector of the wall of the casing; obtaining a first reflected acoustic signal corresponding to said emitted pulse; emitting through said medium a second acoustic pulse directed at a substantially normal incidence towards a reference reflector whose nominal characteristics are substantially similar to those of said sector of the casing being investigated; obtaining a second reflected acoustic signal corresponding to said second emitted pulse; and from at least a selected portion of said first obtained signal and a selected portion of said second obtained signal, forming one or more corrected signals representative respectively of one or more data items relating to at least said casing. This correction eliminates effects due to the medium inside the casing and to the geometry of the casing. The data items relating to the casing and to the materials which surround it generally include the quality of the connection between the casing and the cement disposed behind the casing, the roughness of the inside wall of the casing, and the thickness of the casing.