Generalization of the rotated parabolic equation to variable slopes

Area of Science:

• Underwater acoustics
• Geophysics
• Computational physics

Background:

• The rotated parabolic equation (RPE) is a standard tool for modeling acoustic propagation in horizontally stratified environments.
• Modeling seismo-acoustics in environments with variable ocean-sediment interfaces presents significant computational challenges.

Purpose of the Study:

• To generalize the RPE for range-dependent seismo-acoustics problems with variable-slope ocean-sediment interfaces.
• To develop a robust numerical method for accurate acoustic field propagation modeling in complex underwater environments.

Main Methods:

• Approximating variable slopes using a series of constant slope regions.
• Applying the original RPE algorithm within each region.
• Using interpolation-extrapolation to generate starting fields for subsequent regions.
• For elastic cases, employing operators to rotate the dependent variable vector and coordinate system.

Main Results:

• The variable rotated parabolic equation (VRPE) provides accurate solutions for fluid cases, confirmed by comparisons with reference solutions.
• For elastic cases, VRPE solutions demonstrate good agreement when compared with energy-conserving and mapping solutions.
• The method effectively handles range-dependent seismo-acoustics problems with varying interface geometries.

Conclusions:

• The generalized VRPE is a powerful tool for accurately simulating acoustic propagation in complex, range-dependent underwater environments.
• This approach extends the applicability of parabolic equation methods to more realistic ocean-sediment interface scenarios.
• The VRPE offers a computationally efficient and accurate solution for both fluid and elastic seismo-acoustics modeling.