Statistical estimation of the spatial spectrum of secondary sources

A statistical problem of estimating the shape and maximum possible width of the spatial energy spectrum of secondary sources is formulated and solved. The secondary sources under consideration are characteristic of the class of scatterers with preset statistical mean parameters. This estimation is important for analyzing the possibility of solving inverse scattering problems, including the question of the uniqueness and stability of the solution and also the correct organization of a tomographic experiment. Results of a computer simulation are presented, and the expected statistical mean spectrum is compared with a particular realization of the spectrum. In the case of a strongly pronounced rescattering, the statistical mean width of the spectrum is mainly determined by the effective velocity contrast in the ensemble of scatterers and depends only weakly on the scale of spatial fluctuations of the scatterers’ characteristics.