Self-consistent equations for variable velocity three-dimensional inverse scattering

This paper considers the three-dimensional inverse scattering problem for the wave equation with variable velocity. A possible solution is presented in terms of equations whose self-consistent solution determines the velocity from scattering data. These self-consistent equations are (1) the wave equation in integral form, (2) a linear integral equation which relates the wave field and scattering data, and (3) a novel formula for the velocity in terms of the wave field.