<p>A stationary medium containing inhomogeneities of the sound speed, density, and frequency-dependent absorption coefficient is considered. These inhomogeneous acoustic characteristics, including the power index of frequency dependence of the absorption coefficient, are unknown and should be reconstructed based on scattering data at many frequencies. First, the complex scatterer function, which contains the contributions from various types of the inhomogeneities, is reconstructed by solving the inverse problem. Then, the method for extracting the individual spatial distributions of all the sought acoustic characteristics from the scatterer function is proposed. Numerical modeling results are presented, which illustrate the capabilities and limitations of the method for various noise levels in the initial data. It is shown that the result of reconstructing the power index of the frequency dependence of the absorption coefficient has the lowest noise resistance. At the same time, the sound speed, density, and absorption coefficient are reconstructed with acceptable accuracy and high resolution.</p>