Wide-angle formulation of the Beilis-Tappert method.

Area of Science:

• Computational physics
• Wave propagation modeling
• Geophysics

Background:

• The Beilis-Tappert method is used for modeling wave propagation.
• Previous formulations did not account for the non-physical nature of the vertical wave number k.
• Accurate modeling over irregular terrain requires addressing these limitations.

Purpose of the Study:

• To introduce and validate a wide-angle formulation of the Beilis-Tappert method.
• To identify and incorporate a crucial, previously unrecognized element: a vertical wave number filter (k-control).
• To assess the impact of k-control and wide-angle extensions on wave propagation accuracy over varied terrain.

Main Methods:

• Development of a wide-angle Beilis-Tappert method formulation.
• Introduction of a slope-dependent k-space vertical wave number filter (k-control).
• Theoretical analysis and numerical simulations of wave propagation over steep and shallow hills.

Main Results:

• The vertical wave number k in the Beilis-Tappert method requires a slope-dependent filter (k-control) to select physical wave numbers.
• k-control is critical for accurate wave propagation modeling over steep hills, comparable in importance to wide-angle extensions.
• For shallow hills, k-control and wide-angle extensions have less impact, with the narrow-angle formulation sometimes providing sufficient accuracy.

Conclusions:

• The Beilis-Tappert method necessitates a k-control filter for accurate wave propagation over irregular terrain.
• The significance of k-control and wide-angle extensions varies with terrain complexity.
• The findings provide guidance on selecting appropriate formulations for specific wave propagation applications.