The wave-equation angle-domain Hessian can be computed from the subsurface offset wave-equation Hessian via an angle-to-offset transformation following the approach presented by Sava and Fomel (2003). This result allow us to implement an angle-domain regularization that stabilizes the the wave equation inversion problem.
In order to perform the wave-equation angle-domain inversion, the angle-domain Hessian matrix can be used explicitly or, implicitly as a chain of the offset-to-angle operator and the subsurface offset Hessian matrix. Since each approach has its advantages and disadvantages the specific application will dictate which path to follow.