Abstract: The invention provides a method for estimating an impedance of a material behind a casing wall, wherein the casing is disposed in a borehole drilled in a geological formation, and wherein a borehole fluid is filling said casing, the material being disposed in an annulus between said casing and said geological formation, said method using a logging tool positionable inside the casing and said method comprising: exciting a first acoustic wave in said casing by insonifying said casing with a first pulse, the first acoustic wave having a first mode that may be one of flexural mode or extensional mode; receiving one or more echoes from said first acoustic wave, and producing a first signal; extracting from said first signal a first equation with two acoustic properties unknowns for respectively said material and said borehole fluid; exciting a second acoustic wave in said casing by insonifying said casing with a second pulse, the second acoustic wave having a thickness mode; receiving one or more echoes from said