A method, comprising: introducing a tool string into a wellbore drilled through a formation, the wellbore at least partially lined with a first casing and a second casing concentrically overlapping a portion of the first casing, wherein a first annulus is defined between the first and second casings (108a,b) and filled with a first annular media, and a second annulus is defined between the second casing and a wall of the wellbore and filled with a second annular media; the method characterized in that it comprises obtaining sonic data of the first and second annular media (110a,b) using a sonic wave emitted from a sonic data tool included in the tool string; performing a first decomposition operation on the sonic data to obtain an amplitude, a frequency, and a phase of the sonic wave as altered by the first and second annular media (110a,b); obtaining ultrasonic data of the first annular media using an ultrasonic wave emitted from an ultrasonic data tool included in the tool string; performing a second decomposition operation on the ultrasonic data to obtain an amplitude, a frequency, and a phase of the ultrasonic wave as altered by the first annular media; obtaining density data of the first annular media using gamma rays emitted by a density tool included in the tool string; performing a third decomposition operation on the density data to obtain far counts, near counts, and an energy spectrum of the first annular media; obtaining cased-hole neutron data using a neutron porosity tool included in the tool string; performing a fourth decomposition operation on the cased-hole neutron data to obtain far counts and near counts of gamma rays generated via neutron scattering due to one or more of the first and second casings (108a,b), the first and second annular media (110a,b), and the formation, and to obtain an energy spectrum of the formation and of the first and second annular media (110a,b); obtaining open-hole neutron porosity log data from measurements performed on the formation prior to casing the wellbore; and performing a fifth decomposition operation on the open-hole neutron porosity log data to obtain far counts and near counts of gamma rays generated due to neutron scattering in the formation, and to obtain an energy spectrum of the formation. introducing a tool string into a wellbore drilled through a formation, the wellbore at least partially lined with a first casing and a second casing concentrically overlapping a portion of the first casing, wherein a first annulus is defined between the first and second casings (108a,b) and filled with a first annular media, and a second annulus is defined between the second casing and a wall of the wellbore and filled with a second annular media; the method characterized in that it comprises obtaining sonic data of the first and second annular media (110a,b) using a sonic wave emitted from a sonic data tool included in the tool string; performing a first decomposition operation on the sonic data to obtain an amplitude, a frequency, and a phase of the sonic wave as altered by the first and second annular media (110a,b); obtaining ultrasonic data of the first annular media using an ultrasonic wave emitted from an ultrasonic data tool included in the tool string; performing a second decomposition operation on the ultrasonic data to obtain an amplitude, a frequency, and a phase of the ultrasonic wave as altered by the first annular media; obtaining density data of the first annular media using gamma rays emitted by a density tool included in the tool string; performing a third decomposition operation on the density data to obtain far counts, near counts, and an energy spectrum of the first annular media; obtaining cased-hole neutron data using a neutron porosity tool included in the tool string; performing a fourth decomposition operation on the cased-hole neutron data to obtain far counts and near counts of gamma rays generated via neutron scattering due to one or more of the first and second casings (108a,b), the first and second annular media (110a,b), and the formation, and to obtain an energy spectrum of the formation and of the first and second annular media (110a,b); obtaining open-hole neutron porosity log data from measurements performed on the formation prior to casing the wellbore; and performing a fifth decomposition operation on the open-hole neutron porosity log data to obtain far counts and near counts of gamma rays generated due to neutron scattering in the formation, and to obtain an energy spectrum of the formation.