Numerical and experimental study of ultrasonic seismic waves propagation and attenuation on high-quality factor samples

We propose an approach for measuring seismic attenuation at ultrasonic frequencies on laboratory-scale samples. We use a Gaussian filter to select a bandwidth of frequencies to identify the attenuation in a small window and, by moving the window across the frequency content of the data, we determine the frequency-dependent attenuation function. We assess the validity of the method with three-dimensional numerical simulations of seismic wave propagation across different sample geometries, using free surface boundary conditions. We perform the simulations using viscoelastic media under various seismic attenuation models. Our numerical results indicate that we can successfully recover the representative viscoelastic attenuation parameters of the media, regardless of the sample geometry, by processing the seismic signal recorded either within the volume or at the boundaries. Due to the equipartition phenomenon, the energy of S-waves is consistently higher in seismic records than that of P-waves. Therefore, we systematically recover the attenuating properties of S-waves in the medium. We also conduct experiments of seismic wave propagation on samples of aluminum and Fontainebleau sandstone to validate our approach with real data. The quality factor of the S-wave Qs$Q_s$ in the aluminum medium increases from 300 to 7000 between 60 kHz and 1.2 MHz. The Fontainebleau sandstone, which is more attenuating, exhibits a Qs$Q_s$ that increases from 200 at 60 kHz to 1000 at 1.2 MHz. With our approach, we are not only able to recover the attenuation property but also identify the frequency-dependent attenuation model of the samples. Our method allows for seismic attenuation recovery at ultrasonic frequencies in low-attenuating media.