Expanding Hessian dimensionality

Valenciano et al. (2005b) define the zero subsurface-offset Hessian by using the adjoint of the zero subsurface-offset migration as the modeling operator ${\bf L}$. Then the zero-offset inverse image can be estimated as the solution of a non-stationary least-squares filtering problem, by means of a conjugate gradient algorithm Valenciano et al. (2005a,b). But, from the results reported by Prucha et al. (2000), Kuehl and Sacchi (2001), and Valenciano et al. (2005a), regularization in the reflection angle dimension is necessary to stabilize the wave-equation inversion problem.

 

• Subsurface-offset Hessian
• Angle-domain Hessian
• Explicit vs. implicit Hessian matrix computation