### Abstract

We present a numerical implementation of the Biot equations for two-dimensional problems based upon the spectral-element method (SEM) in the time domain. The SEM is a high-order variational method, which has the advantage of accommodating complex geometries like a finite-element method, while keeping the exponential convergence rate of (pseudo)spectral methods. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well-suited to simulations on parallel computers. We also derive finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present an example of finite-frequency kernels for seismic phases in porous media.

Original language | English (US) |
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Title of host publication | Poromechanics IV - 4th Biot Conference on Poromechanics |

Publisher | DEStech Publications |

Pages | 649-654 |

Number of pages | 6 |

ISBN (Electronic) | 9781605950068 |

State | Published - Jan 1 2009 |

Event | 4th Biot Conference on Poromechanics - New York, United States Duration: Jun 8 2009 → Jun 10 2009 |

### Other

Other | 4th Biot Conference on Poromechanics |
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Country | United States |

City | New York |

Period | 6/8/09 → 6/10/09 |

### All Science Journal Classification (ASJC) codes

- Acoustics and Ultrasonics
- Condensed Matter Physics
- Mechanics of Materials

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## Cite this

*Poromechanics IV - 4th Biot Conference on Poromechanics*(pp. 649-654). DEStech Publications.