A wave propagation model with the Biot and the fractional viscoelastic mechanisms

• Published in: Science China. Earth sciences Vol. 64; no. 3; pp. 364 - 376
• Main Authors: Yang, Jiaming, Yang, Dinghui, Han, Hongwei, Qiu, Lingyun, Cheng, Yuanfeng
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01-03-2021; Springer Nature B.V
• Subjects: Attenuation; Computational fluid dynamics; Dispersion; Dynamic models; Earth and Environmental Science; Earth Sciences; Energy dissipation; Energy loss; Fluids; Frequency ranges; Low frequencies; Low frequency; Numerical experiments; Order parameters; P waves; Porous media; Propagation; Research Paper; S waves; Seismic waves; Solid phases; Viscoelasticity; Wave attenuation; Wave propagation; Dispersion and attenuation; Wave propagation; Poroviscoelasticity; Fractional derivative
• ISSN: 1674-7313; 1869-1897
• DOI: 10.1007/s11430-020-9668-5

Energy loss in porous media containing fluids is typically caused by a variety of dynamic mechanisms. In the Biot theory, energy loss only includes the frictional dissipation between the solid phase and the fluid phase, resulting in underestimation of the dispersion and attenuation of the waves in the low frequency range. To develop a dynamic model that can predict the high dispersion and strong attenuation of waves at the seismic band, we introduce viscoelasticity into the Biot model and use fractional derivatives to describe the viscoelastic mechanism, and finally propose a new wave propagation model. Unlike the Biot model, the proposed model includes the intrinsic dissipation of the solid frame. We investigate the effects of the fractional order parameters on the dispersion and attenuation of the P- and S-waves using several numerical experiments. Furthermore, we use several groups of experimental data from different fluid-saturated rocks to testify the validity of the new model. The results demonstrate that the new model provides more accurate predictions of high dispersion and strong attenuation of different waves in the low frequency range.