Comparative analysis of boundary control and Gel'fand-Levitan methods of solving inverse acoustic problem

Abstract

This chapter explains the inverse problem for the acoustic equation. The Gel’fand-Levitan method (G-L method) and the boundary control method (BC method) are investigated and compared. The BC-method and G-L method are similar to each other— namely, they coincide in one dimensional case. The BC-method and G-L method determine the solution of inverse problem in particular point x0 in depth without any special calculations of unknown coefficients on the interval (0, x0). BC method allows to find the velocity of wave propagation c(x,y) if the density p (x, y) is known.