Uniqueness theorem of solution the integral geometry problem for family curves in multidimensional space

Abstract

In this article the following class of integral geometry problems is considered: about the function
reconstruction, shared by the integrals on some set of curves. These problems are correlated with
several applications. In order to study internal earth structure multiple explosions are held on Earth
surface. Then, fluctuations regimes of earth surface are measured on equipment for each explosion.
The purpose of research is to determine distribution of physical parameters inside the Earth
according to equipment measurements correlated with laws on dissemination of seismic waves.
The most clear functional of such equipment is arrival time of seismic wave, which exactly serves
as a base for interpretation practice. It is known that linearized problem of seismic-exploration
data interpretation is actually the problem of integral geometry. Integral geometry also includes
problems related to radiography, particularly interpretation problem of X-ray images. For instance,
an X-ray film darkening is functionally correlated with absorption coefficient is also actually an
integral geometry problem. In this case, it is required to determine the function if the integrals
of this function on set of rays were set. An integral geometry problem in multidimensional space
is studied in this work. The theorem of solution uniqueness is proven for the considered integral
geometry problem.