Time domain analysis of normal mode, parabolic, and ray solutions of the wave equation

Abstract

Estimation of sound speed and temperature fields from tomographic data requires knowledge of the accuracy of the forward model. For this reason, time domain results using three models derived from the acoustic wave equation are compared here. The models chosen for the analysis are normal modes (NM) and the parabolic equation (PE) and ray approximations. (The NM and PE time series are obtained via Fourier synthesis). The analysis is done using a depth-dependent sound-speed profile where only refracted and surface-reflected/refracted energy is allowed to propagate. Because the NM representation is theoretically exact in this environment, it is used as the comparative base. Travel-time sequences generated using the PE and ray approximations are compared to those generated using NM. For the angular aperature analyzed (±9 to ±16.5 deg), phase errors in the PE models investigated limit reliable predictions of travel time to distances of about 1000 km. However, the ray approximation is found to be adequate for estimating arrival times at ranges out to 4000 km for frequencies of 100 Hz and above.