Comparison of one-way and full-wave linear propagation models in inhomogeneous medium

Abstract

One-way wave propagation models based on the parabolic approximation or its wide-angle extensions are often used for describing bounded acoustic beams. Such models are highly demanded when solving nonlinear problems that are computationally intensive and thus technically difficult to solve using full-wave approaches. When describing the propagation of a wave beam in a homogeneous medium, the one-way assumption is fulfilled exactly, and therefore, the inaccuracy is caused only by the limitations of the parabolic approximation. Such an error is significantly reduced within the wide-angle approach and completely disappears when using the exact propagator in the framework of the angular spectrum method. The situation is less obvious in the case of a heterogeneous environment, when a part of the wave energy is inevitably reflected becoming a counter-propagating wave and thus is not taken into account in the one-way approximation. The degree this phenomenon affects the accuracy of the one-way approach is still under discussion. In the current paper, a one-way propagator based on the pseudo-differential wide-angle equation is proposed. The propagator is tested for the homogeneous medium and for several configurations of media with regular and random inhomogeneities. The corresponding solutions are compared with those obtained using the k-Wave toolbox. Results of comparison show how the one-way propagator accuracy depends on the contrast and smoothness of the inhomogeneities. [Work supported by RSF No. 18-72-00196.]