Simultaneous reconstruction of the acoustic equation via a direct optimization approach

The acoustic inverse problem on a stratified half-space is considered in the time domain.By constructing the objective functional,the inverse problem is thereby reduced to an optimization problem where the profiles of the velocity and the density minimizing the functional are to be found.A direct optimization algorithm is employed to solve the optimization problem and reconstruct the profiles of the velocity and the density simultaneously.The stability theorem and numerical examples are given.The results of reconstruction excellently agree with the true profiles