Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different frequencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that establishes a relation between the wave properties at different frequency bands considering a size range of heterogeneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10⁻⁶, 10^−1.5] m and [10⁻⁶, 10^−3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band.

了解多尺度非均质性对岩石在不同频率下的波响应的影响对于解释地震数据至关重要。事实上，超声波和地震波的行为不同，因为实验涉及不同的空间尺度。然后，一个解决方案是应用一种理论，该理论在考虑异质性大小范围的情况下建立不同频带的波特性之间的关系。为了研究这个问题，我们测量了致密储层岩石在超声波、声波和地震频率下的压缩波（P 波）滞弹性（速度和衰减）。作为孔隙度或粘土含量函数的波行为显示出一致的趋势。随着围压的增加，孔隙率对衰减的影响减小，而粘土含量逐渐变得重要。为了解释数据，我们通过结合裂缝和粘土矿物的自相似特征提出了双分形孔隙弹性模型。实验数据与模型结果的对比揭示了粘土包裹体和裂纹的分形性，半径范围为[10^-6 , 10 ^-1.5 ] m 和[10 ^-6 , 10 ^-3.1 ] m，它们分别是波在宽频带上的滞弹性行为的原因。