Extinction theorem for object scattering in a stratified medium

A simple relation for the rate at which energy is extinguished from the incident wave of a far field point source by an obstacle of arbitrary size and shape in a stratified medium is derived from wave theory. This relation generalizes the classical extinction theorem, or optical theorem, that was originally derived for plane wave scattering in free space and greatly facilitates extinction calculations by eliminating the need to integrate energy flux about the obstacle. The total extinction is shown to be a linear sum of the extinction of each wave guide mode. Each modal extinction involves a sum over all incident modes that are scattered into the extinguished mode and is expressed in terms of the object’s plane wave scatter function in the forward azimuth and equivalent plane wave amplitudes of the modes. The only assumptions are that multiple scattering between the object and wave guide boundaries is negligible, and the object lies within a constant sound speed layer. Modal extinction cross sections of an object for the extinction of the individual modes of a wave guide are then defined. Calculations for a shallow water wave guide show that, after correcting for absorption loss in the medium, the modal cross section of an object for mode 1 in a typical ocean wave guide is very nearly equal to its free space cross section. This new extinction theorem may be applied to estimate the cross section of an object submerged in a wave guide from a measurement of its forward scattered field.