Research note: Derivations of gradients in angle-independent joint migration inversion

Although joint migration inversion has been proposed for several years, a thorough derivation and description of the involved gradients was not published. In this paper, we derive the gradient of both the angle-independent reflectivity and the velocity in a framework of acoustic angle-independent joint migration inversion. With some further approximations taken, the conclusions shown in previous publications can also be reached from our new derivation.