Propagation of normal mode in the parabolic approximation

The parabolic approximation to the acoustic wave equation is examined within the framework of normal−mode theory. For the case where sOund speed and water de pth are independent of range, three types of errors are found to occur. Discrete modes are shown to propagate with the correct amplitude and mode shape but with errors in phase and group velocities. In addition to these errors, which are inherent in the method, two other sources of error are present. The effect of these other errors may be made negligible in one case by limiting the sound−speed gradients and range considered and, in the other case, by introducing a highly absorptive layer deep in the ocean bottom. Subject Classification: 30.20,30.50;20.40,20.15.