A viscoelastic model for seismic attenuation using fractal mechanical networks
A viscoelastic model for seismic attenuation using fractal mechanical networks
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DOI：
10.1093/gji/ggaa549
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发表时间：
2020-12
影响因子：
2.8
通讯作者：
G. Xing;T. Zhu
中科院分区：
文献类型：
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作者：
G. Xing;T. Zhu
地震衰减（用质量因子Q量化）对地震波形有显著影响，特别是在流体饱和岩石中。这种耗散过程可以用粘弹性模型现象学地表示。以往的地震学研究表明，在地震频率范围内，大地介质的Q值表现出几乎与频率无关的特性（文献中常称为常数Q）。这种衰减可以用数学Kjartansson常数- q模型来描述，该模型缺乏粘弹性意义上的物理表示。受斑片状饱和岩石孔隙流体分布的分形特性的启发，本文提出了分形力学网络（FMN）模型，即分形树模型和准分形阶梯模型，以现象学方式表征频率无关的Q行为。与经典的粘弹性模型一样，FMN模型由以不同层次模式排列的机械元件（弹簧和阻尼器）组成。每个模型的特定参数化可以产生与Kjartansson模型相同的复模量，从而导致常数q。将该理论应用于几个典型岩石样品，我们发现这些岩石的地震衰减特征可以用任意一种FMN模型准确地表示。此外，我们还证明阶梯式模型更能真实地反映饱和岩石的多尺度分形结构。因此，FMN模型可以为从宏观地震衰减观测中估计岩石微观结构特性提供一种新的方法。
Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.