ASYMPTOTIC APPROXIMATION OF OCEAN-ACOUSTIC PULSE PROPAGATION IN THE TIME DOMAIN
Abstract
Broadband and narrowband time-domain asymptotics are proposed for pulse propagation in range-independent ocean environments. The broadband approximation results by applying the stationary-phase method to the Fourier transform of the Green's function, expressed in terms of normal modes. The narrowband approximation is obtained by incorporating the shape function of the emitted signal — assumed Gaussian — into the phase term and applying the steepest-descent method. The roots of the frequency-derivative of the phase are located in the complex plane by using a second-order expansion of the eigenvalues. The performance of the two approximations is studied numerically. While the broadband approximation improves with increasing bandwidth, the narrowband approximation improves when the bandwidth decreases. Both approximations improve with increasing range, and they can be used for delivering time-domain results more efficiently than with standard Fourier synthesis.
