Integral representation for the field of the wave propagating in a medium with random inhomogeneities of different scales

Some Possibilities of Spatial Signal Processing in an Inhomogeneous Medium Based on DWFT

“…Further development of this approach can be adopted in the following areas of research: Developing a wide‐angle variant of this approach with the use of the Fock proper‐time method on the basis of Tinin (2004, 2016) and Tinin et al (2002) and applying it to describe the effects of random irregularities in vertical, oblique, and backscatter ionospheric sounding. Employing this approach to elaborate methods of sounding thermonuclear plasma, as well as in sounding atmospheres of the Sun and planets. Developing spatial signal processing in communication, navigation, and diagnostic systems. Examining backscatter effects in the vertical sounding as well as in coherent and incoherent sounding systems. …”

Higher Approximations to Study Statistical Characteristics of Waves in Multiscale Inhomogeneous Media

“…+,− ( ) are solutions of ray equations (27) and (22) in the absence of inhomogeneities (̃= 0), and the solutions have the form…”

“…The same approach enabled solving the equation for the product of the desired field and the known solution (termed as "joker wave" in [25]) in extended 3D space for 2D problem [26] and in the extended 5D space for 3D problem [26][27][28][29]. The resulting integral representation in the form of a double weighted Fourier transform (DWFT) describes the wave field, considering for simultaneous effects of inhomogeneities of different scales [26][27][28][29].…”

“…We will use here the DWFT method [26][27][28][29][30], which in the small-angle approximation describes both strong fluctuations associated with the random caustics that form in a large-scale inhomogeneous medium, and the Fresnel type diffraction effects typical for wave propagation in a medium with smallscale inhomogeneities. Unlike the Maslov and interference integral methods, where the Fourier transform is performed in the receiver or transmitter coordinates, respectively, the DWFT method uses the Fourier transform with respect to both receiver and transmitter coordinates.…”

“…In the first DWFT approximation [26][27][28][29][30], the contribution of lowamplitude inhomogeneities to the partial wave phase takes the integral from permittivity perturbation along the unperturbed (direct) ray. For such an effect that inhomogeneities of different scales impose on the wave field we shall call the firstorder effect.…”