Frequency Domain Biot--Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting
Abstract
We present a frequency-domain formulation of Biot's dynamic poroelastic equations with frequency-dependent dissipation (Biot--Allard) for anisotropic, heterogeneous media with memory effects. Two equivalent two-field representations--a displacement-pressure and a velocity-pressure-rate formulation--enable stabilized iterative splitting. While coupling operators generally lack an adjoint or skew-adjoint relationship at finite frequencies, the velocity--pressure-rate representation restores a skew-adjoint structure in the quasi-static limit. We prove continuity of the coupling operators and coercivity of the diagonal blocks, essential for convergence of the L-stabilized splitting scheme. The frequency-domain setting eliminates convolutional memory terms, incorporates attenuation and dispersion via complex-valued parameters, and reduces the time-dependent problem to a family of elliptic boundary-value problems suited for parallel computation and multi-frequency inversion. A conforming Galerkin finite element discretization preserves block structure, and numerical experiments confirm robustness and capture frequency-dependent attenuation. To illustrate discretization independence, we include a large-scale wave simulation using a pseudo-spectral method. This work provides a rigorous and efficient framework for modeling wave phenomena in complex porous media.
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BibTeX
@misc{jakobsen2026frequency,
title = {{Frequency Domain Biot--Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting}},
author = {Morten Jakobsen and Jakob Seierstad Stokke and Kundan Kumar and Florin Adrian Radu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07388},
eprint = {2609.07388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07388},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frequency Domain Biot--Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting
AU - Morten Jakobsen
AU - Jakob Seierstad Stokke
AU - Kundan Kumar
AU - Florin Adrian Radu
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07388
UR - https://arxiv.org/abs/2609.07388
AB - We present a frequency-domain formulation of Biot's dynamic poroelastic equations with frequency-dependent dissipation (Biot--Allard) for anisotropic, heterogeneous media with memory effects. Two equivalent two-field representations--a displacement-pressure and a velocity-pressure-rate formulation--enable stabilized iterative splitting. While coupling operators generally lack an adjoint or skew-adjoint relationship at finite frequencies, the velocity--pressure-rate representation restores a skew-adjoint structure in the quasi-static limit. We prove continuity of the coupling operators and coercivity of the diagonal blocks, essential for convergence of the L-stabilized splitting scheme. The frequency-domain setting eliminates convolutional memory terms, incorporates attenuation and dispersion via complex-valued parameters, and reduces the time-dependent problem to a family of elliptic boundary-value problems suited for parallel computation and multi-frequency inversion. A conforming Galerkin finite element discretization preserves block structure, and numerical experiments confirm robustness and capture frequency-dependent attenuation. To illustrate discretization independence, we include a large-scale wave simulation using a pseudo-spectral method. This work provides a rigorous and efficient framework for modeling wave phenomena in complex porous media.
ER -