Effects of phase errors on pulse synthesis Free

One way of modeling pulse propagation in the ocean is to decompose the pulse into a weighted sum of functions e^iωt, summed over various values of ω. One then solves the Helmholtz equation numerically for each required value of ω. The weighted sum of these fields then gives the desired response to the pulse in question. An alternate approach solves the parabolic equation for each required value of ω, rather than the Helmholtz equation, thereby introducing phase errors. These two results can be related by an integral transform, or transmutation, that converts the approximate solution obtained from the parabolic equation into the true solution obtained from the Helmholtz equation. As a result, corrections can be made and/or errors can be estimated or bounded.