Frequency domain spectral element method for modelling poroelastic waves in 3-D anisotropic, heterogeneous and attenuative porous media
- 15 July 2021
- journal article
- research article
- Published by Oxford University Press (OUP) in Geophysical Journal International
- Vol. 227 (2), 1339-1353
- https://doi.org/10.1093/gji/ggab269
Abstract
Simulating poroelastic waves in large-scale 3D problems having porous media coupled with elastic solids and fluids is computationally challenging for traditional methods. It is well established that the spectral element method (SEM) is more effective than the traditional methods like the finite element method (FEM) when dealing with complex geophysical problems, for its high-order accuracy with exponential convergence. However, at present, little research has been done for SEM in the frequency domain, which will be more efficient than the time-domain SEM for narrowband simulations with multiple sources, material dispersion and attenuation. Herein, we systematically develop a+ SEM in the frequency domain to simulate coupled poroelastic, elastic, and acoustic waves in anisotropic (i.e., porosity, permeability, and elastic coefficients with anisotropy), heterogeneous, and lossy media. Furthermore, we completely remove the dimension inconsistency between the displacement field and the pressure in porous media to reduce the condition number of the system matrix by around 16 orders of magnitude while maintaining the symmetry of the system matrix. To solve the multiphysics coupling problems, we apply different coupling conditions to different interface types, and use basis functions to discretize the corresponding governing equations. Numerical examples show that the proposed SEM can obtain higher accuracy with much fewer unknowns compared with the FEM and has the capacity to solve the large-scale real coupling problems.Keywords
Funding Information
- National Natural Science Foundation of China
- National key research and development program
This publication has 33 references indexed in Scilit:
- Large-scale Sparse Inverse Covariance Matrix EstimationSIAM Journal on Scientific Computing, 2019
- Performance of convolutional perfectly matched layers for pseudospectral time domain poroviscoelastic schemesComputers & Geosciences, 2012
- Computational poroelasticity — A reviewGeophysics, 2010
- A NON-SPURIOUS VECTOR SPECTRAL ELEMENT METHOD FOR MAXWELL'S EQUATIONSProgress In Electromagnetics Research, 2009
- Finite element solution of new displacement/pressure poroelastic models in acousticsComputer Methods in Applied Mechanics and Engineering, 2006
- A mixed displacement-pressure formulation for poroelastic materialsThe Journal of the Acoustical Society of America, 1998
- The effects of multilayer sound-absorbing treatments on the noise field inside a plate backed cavityNoise Control Engineering Journal, 1996
- A simple method to calculate Green's functions for elastic layered mediaBulletin of the Seismological Society of America, 1981
- Generalized Theory of Acoustic Propagation in Porous Dissipative MediaThe Journal of the Acoustical Society of America, 1962
- Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency RangeThe Journal of the Acoustical Society of America, 1956