A scaled mapping parabolic equation for sloping range-dependent environments.

Area of Science:

• Ocean Acoustics
• Computational Physics
• Numerical Methods

Background:

• Parabolic equation methods are crucial for modeling underwater sound propagation.
• Approximating range-dependent interfaces, like bathymetry, presents significant computational challenges.
• Existing mapping techniques involve vertical translation, transferring range dependence to the upper surface.

Purpose of the Study:

• To introduce a scaled mapping approach for enhanced accuracy in parabolic equation solutions.
• To address limitations of previous mapping techniques in handling complex underwater environments.
• To provide a method applicable to environments with range-varying layer thicknesses.

Main Methods:

• A scaled mapping technique is proposed, involving vertical distortion of the computational domain.
• This distortion aims to render both the bathymetry and upper surface horizontal.
• The accuracy of the scaled mapping is validated using problems with fluid sediments.

Main Results:

• The scaled mapping approach demonstrates accuracy for problems involving fluid sediments.
• The method effectively handles range-dependent interfaces by simplifying the domain geometry.
• The approach offers a more robust solution compared to simple vertical translation methods.

Conclusions:

• The scaled mapping technique offers an accurate and efficient method for parabolic equation solutions.
• This approach is particularly beneficial for underwater acoustic modeling in complex, range-dependent environments.
• Generalizations of this method hold promise for future applications involving variable layer thicknesses.