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:
- (i) 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;
- (ii) receiving one or more echoes from said first acoustic wave, and producing a first signal;
- (iii) extracting from said first signal a first equation with two unknowns, where first unknown is an acoustic property of said material and second unknown is an acoustic property of said borehole fluid;
- (iv) exciting a second acoustic wave in said casing by insonifying said casing with a second pulse, the second acoustic wave having a thickness mode;
- (v) receiving one or more echoes from said second acoustic wave, and producing a second signal;
- (vi) extracting from said second signal a second equation with said two unknowns;
- (vii) extracting said acoustic property of said material from said first and said second equations.