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 $Q_s$ 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 $Q_s$ 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.

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高品质因数样品上超声地震波传播和衰减的数值与实验研究

我们提出了一种在实验室规模样品上测量超声波频率地震衰减的方法。我们使用高斯滤波器选择频率带宽来识别小窗口中的衰减，并且通过在数据的频率内容上移动窗口，我们确定与频率相关的衰减函数。我们使用自由表面边界条件，通过不同样本几何形状的地震波传播的三维数值模拟来评估该方法的有效性。我们在各种地震衰减模型下使用粘弹性介质进行模拟。我们的数值结果表明，通过处理体积内或边界处记录的地震信号，无论样本几何形状如何，我们都可以成功恢复介质的代表性粘弹性衰减参数。由于均分现象，地震记录中横波的能量始终高于纵波的能量。因此，我们系统地恢复了介质中横波的衰减特性。我们还对铝和枫丹白露砂岩样本进行了地震波传播实验，以用真实数据验证我们的方法。S波的品质因数${问}_s$铝介质中的 60 kHz 至 1.2 MHz 之间从 300 增加至 7000。枫丹白露砂岩更加细化，表现出${问}_s$从 60 kHz 时的 200 增加到 1.2 MHz 时的 1000。通过我们的方法，我们不仅能够恢复衰减特性，还能识别样本的频率相关衰减模型。我们的方法允许在低衰减介质中以超声波频率进行地震衰减恢复。