Uniqueness theorems for 3D inverse problems with incomplete data

AbstractIn Ramm, Phys. Lett. 99A, (1983), 258-260, it is proved that a compactly supported inhomogeneity in the velocity profile is uniquely determined by the values of the acoustic pressure collected for all positions of the source and receiver on the surface of the earth ( on the whole plane P) at low frequencies. Here it is proved that the data collected on ω1 x ω2 suffice for the uniqueness theorem to hold, where ω1 and ω2 are arbitrary open sets on the plane P. This result holds also for the data collected on ω1 × ω2 at a fixed frequency