### You can't get there from here: Shallow water sound propagation and whale localization

#### Abstract

Sound propagation in summer conditions in the Bay of Fundy is modelled here for the case of a shallow source (a whale at 10 m depth) communicating with a bottomed receiver (an ocean bottom hydrophone at 163.1 m depth). It is shown that the signal strength along the direct path at long ranges (5-8 km) is extremely weak, for three reasons: (1) destructive interference of the shallow source and its image in the sea surface, (2) destructive interference between paths arriving at the bottom and their bottom-reflected counterparts, and (3) upward refraction by the positive sound speed gradient at the seabed. The first significant signals arriving at long ranges are paths that reflect from the surface and the bottom several times, the number of times increasing with range. Consequently, localization algorithms based on the assumption of direct straight-line paths are prone to bias and error. It is suggested that a simple straight-line, average-speed model could be made to work if the algorithm were to admit the hypothesis that the paths could be reflected paths, which could be accommodated simply by using the method of images.

#### Keywords

Acoustic waves; Algorithms; Error analysis; Image analysis; Oceanography; Signal theory; Destructive interference; Shallow water; Sound propagation; Whale localization

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