Modeling the long-range wave propagation by a split-step wavelet method

Abstract

A split-step wavelet method for simulating the long-range wave propagation is introduced. It is based on the fast wavelet transform. Compared to the split-step Fourier method, this method improves the computation efficiency while keeping a good accuracy. The propagation is performed iteratively by means of a pre-computed matrix containing the individual propagations of the wavelets. A fast computation method of this matrix is also presented. For the radiowave propagation in the low troposphere, a local image method is proposed to account for an impedance ground. Inhomogeneous atmospheres and irregular grounds are also considered. Finally, numerical tests of long-range propagations are performed to show the accuracy and time efficiency of this method.

Split-step wavelet propagation modelling using local operators

“…In this section the SSW method [3,4] is summarized. SSW is an iterative method to compute the propagation going back and forth from a spatial to a wavelet representation of the wave.…”

“…The properties of translation and dilation of wavelets are taken into account for filling P efficiently. The detailed method is given by Zhou et al [3,4] and summarised below.…”

“…To do that, we compare the results of these 2 methods with DSSF. The signal and propagator thresholds are V s = 10 −3 and V m = 6 × 10 −5 respectively, so as to obtain an error of −30 dB at the last iteration using the formula given by Zhou et al [4,3]. The image layer for the ground condition is of size 0.1z max .…”

“…Recently an alternative method based on the wavelet transform has been proposed [3,4]. The main difference is that instead of going in the spectral domain for the free-space propagation, the field is decomposed in the wavelet domain with the fast wavelet transform (FWT) [6], and propagated with a wavelet-to-wavelet propagation matrix.…”

On the Use of Adjoint Methods for Refractivity Estimation in the Troposphere

“…In accordance with the forward model, the adjoint model can be derived directly from the one-way wave equation and can be approximated in a second time (e.g., to wide-angle PE (WAPE)). Rapidity of inversion can be further improved by adopting the numerical solution of WAPE for both forward and adjoint models from split-step wavelet (SSW) [7] which outperforms SSF in terms of computational time. Consequent RFC system computes the gradient at the cost of two inexpensive SSW runs only, regardless of the number of parameters to invert.…”