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
A transformation of the environment eliminates parabolic equation phase errors. / Rypina, Irina I.; Udovydchenkov, Ilya A.; Brown, Michael G.
In: Journal of the Acoustical Society of America, Vol. 120, No. 3, 2006, p. 1295-1304.Research output: Contribution to journal › Article
}
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 -