Diffraction tomography: construction and interpretation of tomographic functionals

On the basis of a linearized model of the seismic wave fields propagation the notion of tomographic functionals is introduced. The physical interpretation of tomographic functionals lies in the fact that its integral kernels are the spatiel functions of the influence of the variations of the medium parameters sought for on the particular measurement of the sounding signal wave field. The tomographic functional norm is determined by the intensity of the influence function connected with the interaction operator. The field is generated by the “source” with the temporal dependence determined by the apparatus function of the seismic channel. The analysis of the tomographic functionals makes it possible to carry out the mathematical design of the tomographic experiment for the monitoring of the seismic active zones controlling the tomographic functionals parametres. The richness of the content of a tomographic experiment is determined not only by the norm of the tomographic functionals, but the region of the overlapping of the tomographic functionals. It is carried out the analysis of the tomographic functionals for the wave equation and Lame equation. Bibliography: 14 titles.