| Abstract: | 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.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 218, 1994, pp. 176–196.
This work was supported by the Russian Foundation of Fundamental Research (Grant 93059961) and by the ISF.
Translated by V. N. Troyan. |
