Effective Biot theory and its generalization to poroviscoelastic models

Liu, Xu; Greenhalgh, Stewart; Zhou, Bing; Greenhalgh, Mark

doi:10.1093/gji/ggx460

Cited by 31 publications

(10 citation statements)

References 37 publications

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“…Liu et al. (2018); Liu et al. (2011) represent the moduli of both P and S waves by the relaxation functions based on the generalized fractional Zener model.…”

Section: Anisotropic Poroviscoelastic Models Based On Effective Biot ...mentioning

confidence: 99%

“…Liu et al. (2018) extend their analysis to the fractional Zener model (Bagley & Torvik, 1983; Bartkowska & Ilczuk, 2008; Caputo & Mainardi, 1971; Mainardi, 2010). Yarushina and Podladchikov (2015) and Yarushina et al.…”

Section: Introductionmentioning

confidence: 99%

“…Liu et al (2011) applied the Zener model to approximate the attenuation characteristics and simulate seismic wave propagation. Liu et al (2018) extend their analysis to the fractional Zener model (Bagley & Torvik, 1983;Bartkowska & Ilczuk, 2008;Caputo & Mainardi, 1971;Mainardi, 2010). and ; Yarushina et al (2020) develop nonlinear viscoelastoplastic theory for porous rate-dependent materials.…”

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confidence: 99%

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

et al. 2022

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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.

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“…Liu et al. (2018); Liu et al. (2011) represent the moduli of both P and S waves by the relaxation functions based on the generalized fractional Zener model.…”

Section: Anisotropic Poroviscoelastic Models Based On Effective Biot ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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

et al. 2022

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“…In some previous studies [38,50], attenuation data were used to obtain the viscoelastic parameters by the optimal method. However, this kind of implementation is independent of the mecha-nisms and cannot obtain the analytic expressions of viscoelastic parameters.…”

Section: A New Viscoelastic Modulusmentioning

confidence: 99%

A unified poroviscoelastic model with mesoscopic and microscopic heterogeneities

et al. 2019

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“…Liu et al. (2016, 2018) and Zhao et al. (2015, 2016, 2020) considered these effective poro‐elastic and poro‐viscoelastic equations, respectively.…”

Section: Introductionmentioning

confidence: 99%

Data‐Driven Design of Wave‐Propagation Models for Shale‐Oil Reservoirs Based on Machine Learning

Xiong

Gei

et al. 2021

JGR Solid Earth

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The exploration and exploitation of shale oil is an important aspect in the oil industry. Seismic properties and well‐log data are essential to establish wave‐propagation models. Specifically, the description of wave dispersion and attenuation under complex geological conditions needs proper lithological and petrophysical information. This complex physical mechanism has to be considered if a traditional modeling approach is adopted. In this sense, machine learning (ML) techniques provide new possibilities for this purpose. We compare two deep‐neural‐network (DNN)‐based wave propagation models. In the first (pure data‐driven), a DNN is trained to connect seismic attributes, such as wave velocities, to multivariate functions of rock‐physics properties. By training DNNs with different initial parameters, the uncertainty of the proposed method can be quantified. The second method assumes the form of the wave equations. Then, the elastic constants of the constitutive relations are predicted by DNNs. The resulting dynamical equations describe the dispersion and attenuation and wavefield simulations can be performed to obtain more information. On the basis of a test, the two kinds of wave‐propagation models yield acceptable estimations of the seismic properties, with the second approach showing a broader application because the DNN is trained without S wave data. The methodologies illustrate that the new wave‐propagation model based on ML has high precision and can be general in terms of rheological description.

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Effective Biot theory and its generalization to poroviscoelastic models

Cited by 31 publications

References 37 publications

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

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

A unified poroviscoelastic model with mesoscopic and microscopic heterogeneities

Data‐Driven Design of Wave‐Propagation Models for Shale‐Oil Reservoirs Based on Machine Learning

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