Discussion

While the methodologies described in this paper are valid for general linear operators, they have several fundamental limitations. Most importantly, they require an accurate forward modeling operator: both the physics of wave propagation and the true earth velocity must be accurately modeled. While the physics of wave-propagation is broadly understood, earth velocity models are never completely true-to-life.

Another important caveat is that the ``wave-equation methods'' outlined here require the data and models to be represented on a regular grid. While we can choose our model-space, prestack seismic data is never recorded on a perfectly regular grid. Before we can apply any wave-equation technique (such as those described here), we need to regularize the data. Chemingui (1999) and Fomel (2000) provide two different approaches to solving this problem.