### Abstract

Summary: The fact that the computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem-where simulated data is recovered from a relatively small number of independent simultaneous sources-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield's sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.

Original language | English |
---|---|

Pages (from-to) | 2577-2581 |

Number of pages | 5 |

Journal | SEG Technical Program Expanded Abstracts |

Volume | 28 |

Issue number | 1 |

Publication status | Published - 2009 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Geophysics
- Geotechnical Engineering and Engineering Geology

### Cite this

*SEG Technical Program Expanded Abstracts*,

*28*(1), 2577-2581.

**Compressive simultaneous full-waveform simulation.** / Lin, Tim T Y; Herrmann, Felix J.; Erlangga, Yogi A.

Research output: Contribution to journal › Article

*SEG Technical Program Expanded Abstracts*, vol. 28, no. 1, pp. 2577-2581.

}

TY - JOUR

T1 - Compressive simultaneous full-waveform simulation

AU - Lin, Tim T Y

AU - Herrmann, Felix J.

AU - Erlangga, Yogi A.

PY - 2009

Y1 - 2009

N2 - Summary: The fact that the computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem-where simulated data is recovered from a relatively small number of independent simultaneous sources-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield's sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.

AB - Summary: The fact that the computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem-where simulated data is recovered from a relatively small number of independent simultaneous sources-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield's sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.

UR - http://www.scopus.com/inward/record.url?scp=84857240426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857240426&partnerID=8YFLogxK

M3 - Article

VL - 28

SP - 2577

EP - 2581

JO - SEG Technical Program Expanded Abstracts

JF - SEG Technical Program Expanded Abstracts

SN - 1052-3812

IS - 1

ER -