Linear time-invariant space-variant filters and the parabolic equation approximation

Wave propagation in a random, inhomogeneous ocean is treated as transmission through a linear, time-invariant, space-variant, random communication channel. Using the parabolic equation approximation of the Helmholtz wave equation, a random transfer function of the ocean volume is derived. The ocean volume is characterized by a three-dimensional random index of refraction which is decomposed into deterministic and random components. Two additional calculations are performed using the transfer function. The first involves the derivation of the equations for the random, output electrical signals at each element in a receive planar array of complex weighted point sources in terms of the frequency spectrum of the transmitted electrical signal, the transmit and receive arrays, and the transfer function of the ocean medium. The second involves the derivation of the coherence function.