Multipath pulse shapes in shallow water: theory and simulation.

In shallow water propagation the steeper ray angles are weakened most by boundary losses. Regarding the sound intensity as a continuous function of angle it can be converted into a function of travel time to reveal the multipath pulse shape received from a remote source (one-way path) or a target (two-way path). The closed-form isovelocity pulse shape is extended here to the case of upward or downward refraction. The envelope of the earliest arrivals is roughly trapezoidal with a delayed peak corresponding to the slowest, near horizontal refracted paths. The tail of the pulse falls off exponentially (linearly in decibels) with a decay constant that depends only on the bottom reflection properties and water depth, irrespective of travel time, a useful property for geoacoustic inversion and for sonar design. The nontrivial analytical problem of inverting explicit functions of angle into explicit functions of time is solved by numerical interpolation. Thus exact solutions can be calculated numerically. Explicit closed-form approximations are given for one-way paths. Two-way paths are calculated by numerical convolution. Using the wave model C-SNAP in several broadband cases of interest it is demonstrated that these solutions correspond roughly to a depth average of multipath arrivals.