Sonic data, ultrasonic data, and density data of the annulus are obtained using a sonic tool, an ultrasonic tool, and a density tool, respectively, included in a tool string. A first deconvolution operation is performed to obtain an amplitude, a frequency, and a phase of the modified sonic wave. A first inverse modeling operation results in a first density value of the annular media. A second deconvolution operation is performed to obtain an amplitude, a frequency, and a phase of the modified ultrasonic wave. A second inverse modeling operation results in a second density value of the annular media. A third deconvolution operation is performed to obtain far counts, near counts, and an energy spectrum of gamma rays. A third inverse modeling operation results in a third density value of the annular media.