Systematic Splitting of Wavefields into Unidirectional Modes: Long-Range Asymptotic Methods for Weakly Uniform Media,
NAVAL RESEARCH LAB WASHINGTON DC ANALYTICAL ACOUSTICS SECTION
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A series of pseudo-unitary transforms is devised and applied to the Helmholtz equation for a weakly nonuniform one-dimensional medium, decoupling the wave field in a consistent order-by-order way into counter-propagating modes. The result is a generalized form of dAlembert decomposition, providing an asymptotic solution without backscatter at arbitrary order. Low-order contributions correspond to the standard WKB approximation. Higher orders provide additional terms of potential importance in applications involving propagation over long ranges, e.g., long time-of-flight measurement and very-long-baseline interferometry. Evidence is presented that this decoupling scheme is equivalent to high-order Born approximations.
- Numerical Mathematics
- Radiofrequency Wave Propagation