Multi-dimensional depth imaging without an adequate velocity model

The problem of imaging through salt or other complicated geology overburdens is a serious issue that impacts the effectiveness of hydrocarbon exploration. One cause for the imaging problem is the unavailability of the adequate velocity information needed for all current seismic imaging algorithms. Currently the velocity field that feeds into the seismic imaging, is obtained by other methods that are collectively termed as velocity analyses (Yilmaz, 2000). But the velocity analysis can fail in situations where there are significant lateral variations in the Earth's properties, which is exactly the same circumstance where the detailed and accurate velocity information is needed. The research in the Mission-Oriented Seismic Research Program (M-OSRP) addresses this issue using the inverse scattering series (ISS). ISS is a comprehensive theory for all seismic processing objectives without the traditional need for the subsurface velocity information. The objective of this dissertation is to extend the ISS depth imaging work of Weglein, Shaw, and Innanen in pre-stack acoustic experiment for medium only with vertical variation. A big step in this dissertation is from the ID into the multi-dimensional subsurface---a step that has a plethora of new issues and challenges to address beyond what is faced in a ID medium. Regardless of added algebraic complexity, many new patterns, and closed-forms are identified. In the presented synthetic examples, I estimate reflector locations associated with increasingly complicated geological models; using, as input, only the data and a homogeneous (and notably inaccurate) reference velocity field. The physical interpretation of the imaging formalism in this dissertation is a cascaded Taylor series in multi-dimension, with the current seismic imaging algorithm as the first term. The current closed-form solution, although very effective for all the existing test models, is far from the full imaging capability in the ISS. Other terms in the ISS which have no 1D analogy are studied, calculated numerically, and are proven to deal with wavefield phenomena associated with rapid lateral variations (for example, diffractions).