Journal of Mathematical Sciences

, Volume 86, Issue 3, pp 2773–2786 | Cite as

Diffraction tomography: Construction and interpretation of tomographic functionals

  • V. N. Troyan
  • G. A. Ryzhikov


On the basis of a linearized model of propagation of seismic wave fields the notion of tomographic functionals is introduced. The physical interpretation of tomographic functionals is that their integral kernels are spatial functions of the influence of variations of the medium parameters in question upon particular measurements of the wave field of the sounding signal. The norm of a tomographic functional is determined by the intensity of the influence function related to the interaction operator. The field is generated by a “source” with the dependence on time determined by the apparatus function of the seismic channel. The analysis of tomographic functionals makes it possible to mathematically design tomographic experiments for monitoring active seismic zones by controlling the parameters of tomographic functionals. The richness in content of a tomographic experiments is determined not only by the norms of tomographic functionals, but also by the region where their supports overlap. Tomographic functionals for the wave and Lamé equations are analyzed. Bibliography:14 titles.


Seismic Wave Physical Interpretation Wave Field Seismic Zone Spatial Function 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. N. Troyan
  • G. A. Ryzhikov

There are no affiliations available

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