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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
Summary
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.
- 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.
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