In this work, we recover physical properties of a material with a focus on the attenuation, using a laboratory-scale sample. We develop a method to accurately invert the attenuation models, illustrating with 3D simulations the seismic wave propagation in the frequency domain considering different rheological viscoelastic models. First, we consider a simplified numerical case where we avoid wave reflections from boundaries. Our analysis allows to characterize the wave behavior and the attenuation properties of the medium. Here, we use a complex wavenumber analysis, to recover a complex-valued mechanical modulus that accounts for the viscoelastic behavior. Secondly, we consider numerically an experimental configuration, with free-surface conditions on the sample boundaries, and measurements restricted to the faces of the sample. In this case, the free-surface boundaries lead to multiple reflections and wave conversions that must be taken into account to analyze both the body waves and surface waves displacements to recover the representative viscoelastic properties. Finally, we carry out laboratory-scale experiments on various rock samples designed to find out their attenuation properties. For this purpose, we run an experimental setup using piezoelectric transmitters acting as a seismic source, and a laser-doppler vibrometer for non-contact time-domain measurements. Then, we have to recover the appropriate attenuation laws and their corresponding parameters, depending on the nature of samples. This eventually serves to build initial models to perform iterative reconstruction with Full Waveform Inversion.