Quantum Field Theory Methods in Studies of Ultrasonic Waves Propagation in Random Media

Abstract

Several mathematical methods are used in the studies of ultrasonic wave propagation in random media [1–6]. The length of acoustic waves in comparison to the dimensions of inhomogeneities, as well as the intensity of fluctuations of medium refractive index for acoustic wave, determine the choice of the method actually used. When medium inhomogeneities are large in comparison with the wavelength, the method of optical geometry (or ray theory) can be used [1–3]. In the case of weakly inhomogeneous media the method of small perturbations [1–3] and the so called smooth perturbations method (Rytov’s method) are employed in studies of acoustic wave propagation. If the wavelength is small in comparison with the correlation distance of medium refractive index fluctuations, so that the Fresnel approximation can be used, the method of parabolic equation is preferred [1,3,7]. Recently, progress in the theory of ultrasonic wave propagation in strongly inhomogeneous random media has been achieved by the application of a method elaborated in the quantum field theory [2,4,8].