Propagation and Attenuation of Elastic Wave in a Fluid-Saturated Triple-Porosity Medium

Triple-porosity models provide a possibility to investigate the significant problem in some natural sciences and engineering fields. These media often consist of different scale fractures/cracks with different permeability embedded in a matrix with low-permeability pores. In this paper, the phenomenological equation for the elastic wave propagating in a fluid-saturated triple-porosity medium is developed based on the Lagrangian method. The mass coefficients in kinetic energy and drag coefficients in dissipation energy are obtained by reducing them to single- and double-porosity cases. The plane wave analysis shows that there are four compressional waves and one shear wave, namely, one more compressional wave is generated comparing with the double-porosity model. The dispersion and attenuation of the compressional and shear waves at multiple frequencies are analyzed based on the numerical results. It is observed that the first compressional wave has two attenuation peaks, namely, one more attenuation peak is observed comparing with the double-porosity case.