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The spatial and temporal structures of time-dependent signals can be appreciably affected by random changes of the parameters of the medium characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. When there is also spatial variation of the background refractive index, the observer can be accessed by a number of background rays. In order to compute the pulse characteristics along each separate ray, there is a need to know the behaviour of the two-frequency mutual coherence function. In this work, we formulate the equation of the two-frequency mutual coherence function along a curved background ray trajectory. To solve this equation, a recently developed reference-wave method is applied. This method is based on embedding the problem into a higher dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize 'fast' and 'slow' varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameters defined as ratios of the characteristic scales and allows us to present the proper ordering of terms in the desired equation. The performance of the main order solution is demonstrated for the homogeneous background case when the transverse structure function of the medium can be approximated by a quadratic term.

Modelling of wave propagation for modern high-frequency radio links must take into account the fluctuation phenomena caused by random changes of the medium's parameters. There are two factors that cause signals from transmitter to receiver to arrive via multiple random paths. The first is a result of scattering by boundaries and various obstacles, while the second is related to random changes in the refractive index of the medium. Similar phenomena are observed in underwater acoustic propagation. In this work the influence of both factors is demonstrated in a simple example when the propagation takes place above a perfectly reflecting surface in the presence of a randomly fluctuating medium.

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.

In wave-based remote sensing or radio-location of distant objects in a random medium, a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field. The statistical dependence of the forward-backward travelling events results in an anomaly in the backscattered intensity pattern that carries information about the scattering object. The quality of this information depends on the ability to resolve the fine-structure elements. In this work we investigate the resolving properties of periodic spatial objects by using the random propagators of the stochastic geometrical theory of diffraction.

For construction of statistical measures of the high-frequency field propagating in a random medium it is convenient to deal with a field solution in which the information about the random variation of the medium parameters along the propagation path is preserved. The existing solution in the form of the extended Huygens-Kirchoff method gives only a qualitative description of the intensity fluctuation phenomena. In this work, We present an alternative solution in the form of a paired field measure defined in the text as the two-point random function. Except for the fact that this solution contains the information about the random refractive index variation in explicit functional form, it allows us also to formulate the initial source conditions both in configurational and spectral domains. In the first part, the above solution is adopted for construction of spectral correlation characteristics of the two-frequency spherical wave. Numerical results are presented for a medium with a Gaussian correlation function of the refractive index fluctuations. The second problem considered in this work is related to the finite aperture effects on the spatial intensity correlation characteristics. Here, the presentation of a directional point source in the mixed configurational-spectral domain allowed to present a computable algorithm for the intensity correlation function of a Gaussian beam. The numerical evaluation of the algorithm shows a different behaviour of intensity correlation characteristics comparing with those of plane and spherical waves.