Expansions applicable to a nonstationary scattering medium


  • P. v. d. Woude,

  • H. Bremmer


This paper concerns the wave equation for an irregular time-dependent nondispersive medium contained in a slab, while a plane monochromatic primary wave passes through the latter in a perpendicular direction. The equation is reduced to an equivalent integral relation in which the influence of the medium in directions perpendicular to that of the incident wave is accounted for by an operational expression. The application of a corresponding forward-scattering approximation, the reliability of which is discussed, enables the derivation of two alternative versions for the integral equation that refers to a mainly forward-scattering medium. The second version contains as a factor the geometric optical approximation that is associated with a rectilinear propagation of the incident wave toward the point of observation. It is shown that the Neumann-Liouville series for the solution of the two mentioned versions correspond, respectively, to the well-known Born series (but including the time dependence of the slab medium) and to a series containing corrections to the above-mentioned geometric optical factor.