### Abstract

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

Pages (from-to) | 111-121 |

Number of pages | 11 |

Journal | Wave motion |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- Acoustic equation
- One-way wave equation
- Pseudodifferential calculus
- MSC-35L05
- MSC-35S10

### Cite this

*Wave motion*,

*40*(2), 111-121. https://doi.org/10.1016/j.wavemoti.2003.12.016

}

*Wave motion*, vol. 40, no. 2, pp. 111-121. https://doi.org/10.1016/j.wavemoti.2003.12.016

**A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media.** / Stolk, C.C.

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

TY - JOUR

T1 - A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media

AU - Stolk, C.C.

PY - 2004

Y1 - 2004

N2 - A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.

AB - A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.

KW - Acoustic equation

KW - One-way wave equation

KW - Pseudodifferential calculus

KW - MSC-35L05

KW - MSC-35S10

U2 - 10.1016/j.wavemoti.2003.12.016

DO - 10.1016/j.wavemoti.2003.12.016

M3 - Article

VL - 40

SP - 111

EP - 121

JO - Wave motion

JF - Wave motion

SN - 0165-2125

IS - 2

ER -