Modeling three-dimensional acoustic waves in the ocean

Conventional three-dimensional ocean acoustic modeling ignores Earth flattening, while this effect, as has been shown by Munk et. al. (J. Phys. Oceanogr, 18, 1988, 1876-1898), can not be ignored for long-range transmissions. To take into account the Earth flattening, a new three-dimensional wave equation is derived, in the paper, in terms of a new coordinate system: the ellipsoidal coordinates (geographic latitude, longitude, and depth). From the wave equation, a set of three-dimensional ray equations is then obtained. Both the wave equation and the ray equations account for Earth flattening and Earth curvature, so that they are very useful for solving long-range problems in ocean acoustics and in seismology. The derivations of these new equations are presented in the paper.>