Wave-equation angle-domain Hessian

Alejandro A. Valenciano and Biondo Biondi

valencia@sep.stanford.edu, biondo@sep.stanford.edu

ABSTRACT

A regularization in the reflection angle dimension (and, more generally in the reflection and azimuth angles) is necessary to stabilize the wave-equation inversion problem. The angle-domain Hessian can be computed from the subsurface-offset Hessian by an offset-to-angle transformation. This transformation can be done in the image space following the Sava and Fomel (2003) approach. To perform the 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.