Multi-azimuth velocity estimation

It is well known that the inverse problem of estimating interval velocities from reflection data is poorly constrained in 2-D. We show that the interval velocity estimation problem in 3-D is much better constrained when the velocity function is estimated by jointly inverting the data collected along multiple offset-azimuth, even when the azimuth range is fairly limited. We extend to 3-D the linear operator presented by (Toldi, 1985) for relating stacking velocities with interval velocities. We then apply a Singular Value Decomposition (SVD) analysis to the derived operator. This analysis suggests that methods that take advantage of the azimuth range in the data should yield better velocity functions than currently used velocity estimation methods that neglect the additional information provided by multi-azimuth coverage.