Limited‐Angle inverse scattering problems and their applications for geophysical explorations

The effect of the limited‐angle measurements on the nonlinear inverse scattering problem is investigated. Because of incomplete information obtained in the limited‐angle inverse problem, the linearized system matrix in the inversion procedure becomes more ill‐conditioned compared to that of the conventional inverse scattering problem where the receivers are placed in a circle that completely surrounds the object. Consequently, the quality of the reconstruction is considerably reduced, and sometimes it is almost impossible to reconstruct the profile because of the sparsity of the measurement data. To overcome the above difficulty, a boosting procedure, which will help us to obtain the maximum amount of information for an arbitrary predefined experimental setup, has been proposed based on a physical viewpoint. The results of the computer simulations for well‐to‐well tomography demonstrate that by applying the boosting procedure the quality of the reconstruction and the speed of the convergence are improved significantly. Furthermore, for subsurface detection where both the transmitters and receivers are confined to the ground, the reconstruction becomes possible after applying the boosting procedure.