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Related Experiment Videos

Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector

Qiwei Zhan1,2, Mingwei Zhuang3, Yuan Fang1

  • 1Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 15, 2019
PubMed
Summary

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A novel Green's function for dispersive anisotropic poroelastic media is developed, simplifying complex 3D equations into solvable 1D scalar equations for accurate analysis.

Area of Science:

  • Geophysics
  • Solid Mechanics
  • Wave Propagation

Background:

  • Poroelastic media exhibit complex behavior due to fluid-solid interaction and anisotropy.
  • Analyzing these media in a full-frequency regime requires advanced mathematical techniques.
  • Existing methods often struggle with incorporating dispersion and anisotropy simultaneously.

Purpose of the Study:

  • To derive a compact Green's function for general dispersive anisotropic poroelastic media.
  • To develop a method applicable in the full-frequency domain.
  • To provide a foundation for analyzing wave propagation and responses in such complex materials.

Main Methods:

  • Exact incorporation of anisotropic dispersion in the frequency domain.
  • Reduction of 3D differential equations to a 1D system using the Radon transform.
Keywords:
Green's functionRadontransformanisotropydispersionporoelasticityviscoelasticity

Related Experiment Videos

  • Decoupling of 1D vector problems into scalar equations via eigenvector diagonalization.

    • Main Results:

    • A novel Green's function is presented for the first time.
    • The Green's function decomposes into static and transient response components.
    • The methodology is adaptable to other multi-physics coupling problems.

    Conclusions:

    • The derived Green's function offers a computationally efficient and accurate tool.
    • The method successfully handles dispersion and anisotropy in poroelasticity.
    • The approach is validated against existing solutions and numerical solvers.