A field expansions method for scattering by periodic multilayered media.

Area of Science:

• Geophysics
• Computational Seismology
• Wave Propagation

Background:

• Acoustic and electromagnetic wave interactions with periodic structures are crucial in science and technology.
• Simulating wave scattering from complex geological formations, like layered sediments, presents significant computational challenges.

Purpose of the Study:

• To develop a robust and high-order numerical method for simulating acoustic wave scattering from irregularly shaped, periodic layered media.
• To improve the efficiency and accuracy of numerical simulations for geophysical problems involving subsurface wave propagation.

Main Methods:

• A boundary perturbation method is presented, generalizing Bruno and Reitich's 'Method of Field Expansions' to multiple layers.
• The method discretizes only layer interfaces, drastically reducing the number of unknowns compared to finite difference/element methods.
• It avoids specialized quadrature rules and the dense linear systems typical of boundary integral methods.

Main Results:

• The developed method achieves robust and high-order numerical simulations of pressure wave interactions with layered sediments.
• The simulation time is proportional to the number of interfaces, offering significant speed advantages.
• The approach demonstrates spectral accuracy, comparable to the original field expansions method.

Conclusions:

• This generalized boundary perturbation method provides an efficient and accurate tool for simulating acoustic wave scattering in layered media.
• The technique offers a computationally advantageous alternative to existing numerical methods for geophysical exploration and subsurface modeling.
• The spectral accuracy and reduced complexity make it suitable for complex geological structures.