title: A scaled mapping parabolic equation for sloping range-dependent environments.
abstract: Parabolic equation solutions use various techniques for approximating range-dependent interfaces. One is a mapping approach [M. D. Collins et al., J. Acoust. Soc. Am. 107, 1937-1942 (2000)] where at each range the domain is vertically translated so that sloping bathymetry becomes horizontal, and range dependence is transferred to the upper surface. In this paper, a scaled mapping is suggested where the domain is vertically distorted so that both the bathymetry and upper surface are horizontal. Accuracy is demonstrated for problems involving fluid sediments. Generalizations of the approach should be useful for environments with layer thicknesses that vary with range.
authors.affiliation: Applied Research Laboratories, The University of Texas at Austin, 10000 Burnet Road, Austin, Texas 78758 ametzler@arlut.utexas.edu.
authors.forename: Adam M
authors.initials: AM
authors.lastname: Metzler
authors.affiliation: Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401 daniel.jw.moran@gmail.com, jcollis@mines.edu, pamartin@mines.edu.
authors.forename: Daniel
authors.initials: D
authors.lastname: Moran
authors.affiliation: Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401 daniel.jw.moran@gmail.com, jcollis@mines.edu, pamartin@mines.edu.
authors.forename: Jon M
authors.initials: JM
authors.lastname: Collis
authors.affiliation: Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401 daniel.jw.moran@gmail.com, jcollis@mines.edu, pamartin@mines.edu.
authors.forename: P A
authors.initials: PA
authors.lastname: Martin
authors.affiliation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180 siegmw@rpi.edu.
authors.forename: William L
authors.initials: WL
authors.lastname: Siegmann
mesh_terms: D000162:Acoustics; D019015:Geologic Sediments; D008962:Models, Theoretical; D009038:Motion; D009791:Oceanography / Q000379:methods*; D009792:Oceans and Seas; D011312:Pressure; D012623:Seawater; D012815:Signal Processing, Computer-Assisted; D013016:Sound; D013018:Sound Spectrography; D013997:Time Factors