### Abstract

It is shown that phase errors associated with the standard parabolic wave equation can be eliminated in a range-independent environment by appropriately transforming the environment. Solutions to the standard parabolic equation (PE) in the transformed environment are close to solutions to the Helmholtz equation in the original environment in the sense that ray and asymptotic mode contributions to the PE wave fields have no phase errors relative to their Helmholtz equation counterparts. Although phase errors are eliminated in the PE wave fields, complete asymptotic equivalence to the Helmholtz equation wave fields is not attained. Ray- and mode-based wave-field expansions are used to illustrate similarities and differences between PE and Helmholtz equation wave fields. Numerical simulations show excellent agreement between PE wave fields in the transformed environment and mode-based solutions to the Helmholtz equation in the true environment.

Original language | English (US) |
---|---|

Pages (from-to) | 1295-1304 |

Number of pages | 10 |

Journal | Journal of the Acoustical Society of America |

Volume | 120 |

Issue number | 3 |

DOIs | |

State | Published - 2006 |

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### ASJC Scopus subject areas

- Acoustics and Ultrasonics

### Cite this

*Journal of the Acoustical Society of America*,

*120*(3), 1295-1304. https://doi.org/10.1121/1.2227373

**A transformation of the environment eliminates parabolic equation phase errors.** / Rypina, Irina I.; Udovydchenkov, Ilya A.; Brown, Michael G.

Research output: Contribution to journal › Article

*Journal of the Acoustical Society of America*, vol. 120, no. 3, pp. 1295-1304. https://doi.org/10.1121/1.2227373

}

TY - JOUR

T1 - A transformation of the environment eliminates parabolic equation phase errors

AU - Rypina, Irina I.

AU - Udovydchenkov, Ilya A.

AU - Brown, Michael G

PY - 2006

Y1 - 2006

N2 - It is shown that phase errors associated with the standard parabolic wave equation can be eliminated in a range-independent environment by appropriately transforming the environment. Solutions to the standard parabolic equation (PE) in the transformed environment are close to solutions to the Helmholtz equation in the original environment in the sense that ray and asymptotic mode contributions to the PE wave fields have no phase errors relative to their Helmholtz equation counterparts. Although phase errors are eliminated in the PE wave fields, complete asymptotic equivalence to the Helmholtz equation wave fields is not attained. Ray- and mode-based wave-field expansions are used to illustrate similarities and differences between PE and Helmholtz equation wave fields. Numerical simulations show excellent agreement between PE wave fields in the transformed environment and mode-based solutions to the Helmholtz equation in the true environment.

AB - It is shown that phase errors associated with the standard parabolic wave equation can be eliminated in a range-independent environment by appropriately transforming the environment. Solutions to the standard parabolic equation (PE) in the transformed environment are close to solutions to the Helmholtz equation in the original environment in the sense that ray and asymptotic mode contributions to the PE wave fields have no phase errors relative to their Helmholtz equation counterparts. Although phase errors are eliminated in the PE wave fields, complete asymptotic equivalence to the Helmholtz equation wave fields is not attained. Ray- and mode-based wave-field expansions are used to illustrate similarities and differences between PE and Helmholtz equation wave fields. Numerical simulations show excellent agreement between PE wave fields in the transformed environment and mode-based solutions to the Helmholtz equation in the true environment.

UR - http://www.scopus.com/inward/record.url?scp=33748524186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748524186&partnerID=8YFLogxK

U2 - 10.1121/1.2227373

DO - 10.1121/1.2227373

M3 - Article

AN - SCOPUS:33748524186

VL - 120

SP - 1295

EP - 1304

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 3

ER -