Effect of pulse propagation on refraction corrections for multibeam soundings

Pulse propagation in a stochastic medium is displayed for an incident unit plane wave impulse obliquely incident on a half space with random sound speed fluctuations. Results are expressed in terms of launch angle and dimensionless time and depth variables formed from the relevant parameters of the problem, viz., strength and correlation length of fluctuations, background sound speed, and depth reached by the pulse. Three stages of pulse evolution are distinguished. They are characterized as initial pulse break-up, transition, and fully developed diffusion. In the final stage the pulse diffuses about its centroid, which moves with a speed slightly less than the characteristic sound speed of the medium. Pulse width is calculated as a function of depth and launch angle. The bias error associated with centroid time delay is expressed in terms of a dimensionless function scaled by the strength of fluctuations. Errors are found to accelerate as launch angle increases.