### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 1388-1406 |

Number of pages | 19 |

Journal | SIAM journal on applied mathematics |

Volume | 65 |

Issue number | 4 |

DOIs | |

Publication status | Published - 26 Apr 2005 |

### Keywords

- Seismic modeling microlocal analysis double-square-root equation
- EWI-13982
- double-square-root equation
- seismic modeling
- IR-53450
- microlocal analysis
- MSC-35R30
- METIS-226232
- MSC-86A15

### Cite this

*SIAM journal on applied mathematics*,

*65*(4), 1388-1406. https://doi.org/10.1137/S0036139904439545

}

*SIAM journal on applied mathematics*, vol. 65, no. 4, pp. 1388-1406. https://doi.org/10.1137/S0036139904439545

**Modeling of seismic data in the downward continuation approach.** / Stolk, C.C.; de Hoop, Maarten V.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Modeling of seismic data in the downward continuation approach

AU - Stolk, C.C.

AU - de Hoop, Maarten V.

PY - 2005/4/26

Y1 - 2005/4/26

N2 - Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.

AB - Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.

KW - Seismic modeling microlocal analysis double-square-root equation

KW - EWI-13982

KW - double-square-root equation

KW - seismic modeling

KW - IR-53450

KW - microlocal analysis

KW - MSC-35R30

KW - METIS-226232

KW - MSC-86A15

U2 - 10.1137/S0036139904439545

DO - 10.1137/S0036139904439545

M3 - Article

VL - 65

SP - 1388

EP - 1406

JO - SIAM journal on applied mathematics

JF - SIAM journal on applied mathematics

SN - 0036-1399

IS - 4

ER -