Seismic Wave Propagation in Composite Elastic Media

Abstract

It has been known since the time of Biot-Gassman theory (Biot, J Acoust Soc Am 28: 168-178, 1956, Gassmann, Naturf Ges Zurich 96:1-24, 1951) that additional seismic waves are predicted by a multicomponent theory. It is shown in this article that if the second or third phase is also an elastic medium then multiple p and s waves are predicted. Futhermore, since viscous dissipation no longer appears as an attenuation mechanism and the media are perfectly elastic, these waves propagate without attenuation. As well, these additional elastic waves contain information about the coupling of the elastic solids at the pore scale. Attempts to model such a medium as a single elastic solid causes this additional information to be misinterpreted. In the limit as the shear modulus of one of the solids tends to zero, it is shown that the equations of motion become identical to the equations of motion for a fluid filled porous medium when the viscosity of the fluid becomes zero. In this limit, an additional dilatational wave is predicted, which moves the fluid though the porous matrix much similar to a heart pumping blood through a body. This allows for a connection with studies which have been done on fluid-filled porous media (Spanos, 2002).

Propagation and attenuation of stress waves in heterogeneous elastic rods

“…The thickness of the inclusion is d, and the inclusion divides the bar into three regions, which are marked as Region 1, Region 2, and Region 3 respectively. 1 E and 1 ρ are the elastic modulus and density in Region 1 and Region 3 respectively, and 2 E and 2 ρ are the elastic modulus and density in the inclusion respectively. When the rod end is subjected to an external load ( ) f t , different stress or displacement fields representing wave propagation will be formed inside the rod ( 1R u and 1L u are the right and left traveling waves of Region 1, 2 R u and 2 L u are the right and left traveling waves of Region 2, and 3 R u is the right traveling wave of Region 3).…”

“…The propagation and attenuation of the stress wave have been studied from a long time ago to now, especially in the application of rock mass engineering, such as seismic wave prevention [1][2], engineering blasting [3], impact vibration, and deeper mining protection [4][5]. However, due to the complexity of the actual rock mass environment and the internal structure of the rock mass itself, for example, the characteristics of local continuity or local discontinuity of rock mass, pore cracks, and multiphase media, [6][7][8] it is very difficult to study the propagation and attenuation of the stress waves in this kind of complex rock mass.…”

Scholte Wave Field and Dispersion Curve in Porous Multi-layered Media Filled with Fluid

“…Scholte wave can propagate a long distance with large amplitude and low frequency (Biot, 1962a(Biot, , 1962bSouza and Whitaker, 2003;Liu and Fan, 2012;Pham, 2013). Dispersion phenomenon can be observed when Scholte wave propagates on the seabed, its phase velocity varies with the variation of frequency (Spanos, 2009;Kumar and Saini, 2012;Daniel and Marco, 2019;Chen et al, 2023). In recent years, with the development of marine seismic exploration acquisition equipment, especially the application of efficient seabed surface wave acquisition system with the combination of OBS (Ocean Bottom Seismometer) and air gun source, the Scholte surface wave detection is widely used in seabed engineering geological survey, marine oil and gas exploration and so on (Wu et al, 2021;Qi, 1993;Kugler et al, 2007;Zahra et al, 2016;Krylov et al, 2022a;Liang et al, 2022).…”

A Numerical Study of Elastic Wave Arrival Behavior in a Naturally Fractured Rock Based on a Combined Displacement Discontinuity-Discrete Fracture Network Model

“…These natural fractures, with complicated geometrical and topological patterns, may significantly affect the seismic wave transport in the subsurface leading to scattering and attenuation (Aki 1980 ; Adler and Thovert 1999 ; Sato and Fehler 2009 ). This problem has attracted great attention from different disciplines, such as geophysics, seismology, rock mechanics, and earthquake engineering (Adler and Thovert 1999 ; Toomey et al 2002 ; Spanos 2009 ; Sahimi 2011 ; Khoshhali and Hamzehpour 2015 ; Fan et al 2018 ; Feng et al 2020 ; Zhang et al 2021 ). In addition, natural fractures often dominate the thermo-hydro-mechanical behavior of geological formations, which are highly relevant to many rock engineering applications such as underground excavation, hydrocarbon recovery, and nuclear waste disposal (Tsang 1999 ).…”