Systematic Splitting of Wavefields into Unidirectional Modes: Long-RangeAsymptotic Methods for Weakly Uniform Media

摘要

A series of pseudo-unitary transforms is devised and applied to the Helmholtzequation 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 d'Alembert 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.