Generalized Effective Biot Theory and Seismic Wave Propagation in Anisotropic, Poroviscoelastic Media

Abstract

The interior of the Earth is quite complex due to the actual geometrical structure and the presence of complex rheological materials, including viscoelastic rocks, porous sediments and the presence of anisotropy. Seismic wavefield forward modeling in such media forms the basis of most wave equation‐based methods for investigating the structure of the Earth and processing and imaging of seismic data, e.g., seismic full waveform inversion. Numerical modeling using Biot's equations that describe the physics of poroelasticity provides a useful framework to investigate wave attenuation and dispersion. Poroelasticity describes the interaction between the deformation of an elastic porous solid and the fluid flow in the porous structure. We present a time‐domain finite‐difference method for seismic wavefield modeling, taking into account both attenuation and anisotropy of poroviscoelastic Earth structure. The mathematical formulations and modeling methods are based on (a) the linear Biot's poroelastic theory and double porosity models in anisotropic media and (b) a relaxation function that uses the generalized standard linear solid model with anisotropic τ parameter for magnitude of attenuation and nearly constant Q model. Using a modified relaxation function that is suggested to describe the anisotropy attenuation, we develop a generalized anisotropic Biot model in the anisotropic, viscoelastic media. In addition to the anisotropic poroelasticity based on Biot theory, we implement the generalized anisotropic Biot model with complex moduli for an effective Biot's model in which the attenuative anisotropic viscoelastic model with the generalized standard linear solid model is used to approximate the attenuation factor function. The method generalizes the linear poroviscoelastic model based on effective Biot theory for seismic wave modeling to the attenuative, anisotropic case. In the anisotropic, poroviscoelastic model, we represent the bulk modulus and shear modulus of the solid frame by the modified relaxation function. We present time‐domain finite‐difference modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical, tilted or horizontal symmetry axis (VTI, TTI, and HTI). We also consider the extension of the two new models to nearly constant Q viscoelastic anisotropy.

Wireless Underground Sensor Communication Using Acoustic Technology

“…Biot's [29] theory characterises acoustic wave propagation through porous media including soil. The theory states the existence of two primary waves (Type I and Type II) and one shear wave when sound propagates through porous media.…”

Improved numerical solution of anisotropic poroelastic wave equation in microseismicity: Graphic process unit acceleration and moment tensor implementation

“…The rotated‐staggered‐grid (RSG) finite difference method is an exceptional solution for addressing the Biot poroelastic wave equations in a homogeneous half space (O'Brien, 2010). A seismic wavefield modelling method, taking into account both attenuation and anisotropy of poro‐viscoelastic earth structure, is presented (Huang et al., 2022). The first‐and second‐order nearly constant Q models capable of describing the attenuation of the solid skeleton were introduced, thereby extending the Boit and BISQ models to poro‐viscoelastic media (Han et al., 2023).…”

Propagation and attenuation of stress waves in heterogeneous elastic rods

“…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.…”