Steady‐State Sound Propagation in Continuous, Statistically Isotropic Media

A stochastic Eulerian‐Lagrangian procedure is applied to steady‐state sound propagation from a small, collimated acoustic source to an omnidirectional point receiver imbedded in an infinite, continuous, statistically isotropic medium. An analytic procedure is developed for obtaining the Lagrangian measure function B(x, ξ | s) from its characteristic function φ(k, ξ | s) for stochastic‐Fermat media. The results include a coefficient of intensity variation V that evinces a frequency‐dependent, phase‐dominance region and a frequency‐independent, amplitude‐dominance region. The methods employed in this study are new to the problem of sound propagation through continuous stochastic media and avoid three common difficulties: (1) range limitations due to cumulative phase effects, (2) discrete scattering assumptions, and (3) restriction to an Eulerian path.