A viscoelastic model for seismic attenuation using fractal mechanical networks

Journal Article · 17 November 2020 · Geophysical Journal International

DOI: https://doi.org/10.1093/gji/ggaa549 · OSTI ID:1735385

Xing, Guangchi  ^[1]; Zhu, Tieyuan  ^[2]

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1. Department of Geosciences, The Pennsylvania State University, University Park, PA 16802, USA
2. Department of Geosciences, The Pennsylvania State University, University Park, PA 16802, USA, EMS Energy Institute, The Pennsylvania State University, University Park, PA 16802, USA

SUMMARY 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.

• Research Organization: Pennsylvania State Univ., University Park, PA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Fossil Energy (FE)
• Grant/Contract Number: FE0031544
• OSTI ID: 1735385
• Alternate ID(s): OSTI ID: 1849252
• Journal Information: Geophysical Journal International, Journal Name: Geophysical Journal International Vol. 224 Journal Issue: 3; ISSN 0956-540X
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United Kingdom
• Language: English