Abstract
The stochastic Helmholtz equation is expressed by an outer expansion of its rms refractive variation. The two-term outer expansion is shown to be the conventional Born or single-scattering approximation. This Eulerian sound propagation relation is systematically analyzed from a physical point of view to provide a basis for comparison with the stochastic ray theory result. Single scattering is then imposed on the comparable ray theory result, which reduces its Lagrangian form to the Eulerian form of the other result. Since the free-space Green's function then appears, the volume integral gives the (Eulerian) Born approximation as the single-scattering limit of the stochastic ray theory pressure relation.
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