Seismic wave propagation analysis in the framework of generalized continuum mechanics theory

Dispersion analysis of generalized wave equations under the single-parameter second-order strain gradient theory

“…Based on the continuum mechanics and wave mechanics, constructing the wave equations that describe the wave propagation in real medium is a key problem to be solved in oil and gas seismic exploration. In recent years, generalized wave equations have been proposed in the framework of the generalized continuum mechanics theory (GCMT), and applied to study wave propagation in the field of seismic exploration, which is of great theoretical and practical significance for the investigation of the relationship between the inherent microstructure of the medium and the seismic response (Wang et al, 2020(Wang et al, , 2021a(Wang et al, , 2021bBai et al, 2023aBai et al, , 2023bWu et al, 2021).…”

“…In an actual medium, the influencing factors that cause physical property changes in the medium are extremely complex, which can cause the medium to exhibit strong spatial variation and heterogeneity. Researches show that microstructural interactions of different scales will trigger the heterogeneous responses of the medium, which in turn has an impact on the mechanical behavior of macro-scales (Roscioli, et al, 2020;Bai et al, 2023aBai et al, , 2023b. In the constitutive relation of the GCMT, the expression of stress contains not only the strain term but also the higher-order gradient term of displacement and the additional parameters of the characteristic length scale of the medium (To simplify expression, it is written as characteristic scale in this paper) (Wang et al, 2021a;Bai et al, 2023a).…”

“…Researches show that microstructural interactions of different scales will trigger the heterogeneous responses of the medium, which in turn has an impact on the mechanical behavior of macro-scales (Roscioli, et al, 2020;Bai et al, 2023aBai et al, , 2023b. In the constitutive relation of the GCMT, the expression of stress contains not only the strain term but also the higher-order gradient term of displacement and the additional parameters of the characteristic length scale of the medium (To simplify expression, it is written as characteristic scale in this paper) (Wang et al, 2021a;Bai et al, 2023a). It is due to the introduction of the higher-order gradient terms and the characteristic scale that the generalized wave equations enhance the ability to reflect the heterogeneity caused by the microstructural interactions, which can provide a reference for the interpretation of the physical information of the reservoir.…”

“…The GCMT includes parameters that reflect the microstructural characteristics of the medium (Voigt, 1987;Toupin, 1962Toupin, , 1964Mindlin, 1964Mindlin, , 1965Eringen, 1966Eringen, , 1972Eringen, , 1990Aifantis, 1999;Yang et al, 2002;Tong, et al, 2016;Wang et al, 2020Wang et al, , 2021aWang et al, , 2021bWang et al, , 2022Bai et al, 2023aBai et al, , 2023b, which is convenient to describe scale effects triggered by the complicated microstructural interactions of the medium and can better express the influence of microstructural characteristics of the medium on macroscopic seismic wavefield (Bonnell, 2003;Jirasek, 2004). In the research of high-speed railway seismology, Wang et al (2020Wang et al ( , 2022 found that when a high-speed train passes through a viaduct, an oscillating motion will be generated by the constrained pier under a huge load, which will lead to a heterogeneous response and localized deformation phenomenon.…”

“…In view of this situation, Wang et al (2020Wang et al ( , 2022 studied the excitation mechanism and the laws of propagation of high-speed rail seismic waves under the framework of GCMT, and the results of numerical modeling show that, when considering the heterogeneous responses triggered by microstructural interactions, the seismograms calculated by the generalized wave equations match well with the field data in both time domain and frequency domain. After that, scholars have further investigated wave propagation under the framework of the GCMT (Wang et al, 2021a(Wang et al, , 2021b(Wang et al, , 2021cWu and Ma, 2022;Bai et al, 2023aBai et al, , 2023b. Wang et al (2021aWang et al ( , 2021b investigated the modified couple stress theory (MCST) and pointed out that scale effects will occur in wave propagation when considering microstructural interactions.…”