Application of the conjugate gradient method to the inverse problem of 3-D acoustic equation

The inverse problem of 3-D acoustic equation 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 conjugate gradient method is employed to solve the optimization problem.By introducing a dual function,the gradient of the objective functional is found with an explicit expression.The inverse problem of 3-D acoustic equation is solved successfully by the conjugate gradient method.The numerical example of reconstructing acoustic parameters is provided.