• attenuation
• granular media
• quality factor
• signal analysis
• spectral ratio method
• Stockwell transform
• wave propagation

The energy loss of elastic waves propagating through the earth is a physical phenomenon called attenuation. The total energy of the wave is redistributed according with the anelastic nature of real earth materials. Because of the extrinsic mechanism of the earth (geometrical spreading, layering effects, like interference and scattering effects) the total energy is conserved (apparent attenuation). On the other hand, internal mechanisms of earth materials, like presence of fluids in the pore space of rocks, absolute local motion of the particles, solid and liquid, the atomic and molecular structures of crystal minerals, the presence of small cracks and fractures do not offer a purely elastically behaviour under transient conditions. This mean that the elastic energy of the wavefield is dissipated or also converted into internal energy (intrinsic attenuation). Is precisely the last one to cause a major impact in the seismic wave propagation.
In terms of exploration geophysics, the seismic energy loss can be translated into impoverishment of the frequency bandwidth, where higher frequencies components are faster attenuated than shorter frequencies components causing shape changes in transient waveforms that accompanied with velocity dispersion, causing delay and stretch of seismic waves signals. Thus, attenuation is a key factor in exploration geophysics and its evaluation can be quantified by the amount of dissipated energy of elastic waves over a given frequency range, and by the extraction the quality factor (Q).
There are diverse categories to experimentally obtain quality factors (free vibration, forced vibration, observational of stress-strain curves and wave propagation). Excepting for the latter, all the others are mainly employed for laboratory studies and cannot be applied in situ. For the scope of this thesis the wave propagation phenomena will be exploited to estimate attenuation. For that, some numerical methods have been developed and tested on a suitable synthetic attenuated models to extract the elastic quality factor (Q) from ultrasonic waves propagating in unconsolidated media.
In the first part of this thesis, numerical methods have been developed to extract attenuation information from ultrasonic signal: frequency domain (Spectral Ratio Method) and time-frequency domain (Stockwell transform - Spectral ratio) techniques were implemented and tested on a suitable synthetic attenuated model. The aim of this test is to assess the reliability and robustness of the methods in diverse signal noise condition and absorption levels. Additionally, the test helps to identify frequency ranges that obey the assumption of constant seismic quality factor, and to assess the influence of the windowing effect to provide accurate seismic quality factor.
As the final part of this thesis work, methodologies have been implemented in a laboratory data set of ultrasonic measurement on a model granular system, i.e. glass beads. Compressional and shear wave quality factors have been estimated from ultrasonic signals propagating through a packing of glass beads under the execution of isotropic, oedometric and triaxial tests. The application of proposed numerical methods have provided some interest results. The analysis based on time-frequency domain appears the best, over those tested, to extract reliable values for Q even in very noisy traces. Final results allow us to comprehend some attenuation relationship, to validate some previous approximation, and to extract information that can be related to the rock physics properties of the media under certain stress and pressure conditions.