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A mapping approach for handling sloping interfaces

Collins¹, Dacol

¹Naval Research Laboratory, Washington, DC 20375, USA.

The Journal of the Acoustical Society of America

|May 2, 2000

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A novel mapping approach simplifies wave equation solutions for sloping interfaces by translating the medium vertically. This method accurately models fluid and elastic sediments with variable topography.

Area of Science:

Computational physics
Acoustic modeling
Numerical methods

Background:

Parabolic equation methods are crucial for wave propagation modeling.
Handling sloping interfaces in these models presents significant challenges.
Existing methods may struggle with complex topographical variations.

Purpose of the Study:

To develop and validate a new mapping approach for parabolic equation solutions.
To effectively manage sloping interfaces in wave propagation models.
To enhance the accuracy of modeling acoustic phenomena in complex environments.

Main Methods:

A vertical translation mapping is applied to horizontalize sloping interfaces at each range.
Small slope approximations are used, neglecting higher-order terms from the wave equation.

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A leading-order phase correction is introduced to account for neglected terms.

The method is tested with pressure-release boundary conditions and fluid sediments.

Main Results:

The mapping approach successfully handles sloping interfaces by transforming them into horizontal ones.
Neglected terms are approximately corrected using a leading-order phase correction.
The method demonstrates accuracy for problems involving fluid sediments.
The approach is expected to be accurate for elastic sediments and 3D variable topography.

Conclusions:

The developed mapping approach offers an effective way to handle sloping interfaces in parabolic equation solutions.
This method provides a robust framework for acoustic modeling in geologically complex media.
The approach is versatile and applicable to fluid and elastic sediments, including 3D scenarios.