Three factors influence the accuracy with which subsurface parameters can be obtained—measurement accuracy, aptness of the model, and completeness of the theory. In exploration seismology, as in all other geophysical methods concerned with solving inverse problems, there exists a dualism between observation and theory which is fundamental. This dualism is embodied, in particular, in the notion of subsurface models. If the agreement between model and reality is poor, the model must be altered. Ambiguities are resolved by bringing in new information and altering the model. New ideas then take the form of new models. The complexity of the model depends on the amount and types of parameters one wants to extract. Though one has to acknowledge the likely existence of a complex geology in a seismic survey region or prospect area, one must at the same time allow for certain simplifying assumptions regarding lithology and structure, at least within the spread length of seismic receivers (which can be up to 5 km).
For our algorithms to work successfully without too many complications, we permit only smoothly curved first-order interfaces separating layers assumed to be continuous within a local model. In fact, we shall usually assume layers to be of constant velocity. A local model may be part of a larger regional model that need not be subjected to these restrictions. We also assume, in most of the work, that the radii of curvature of reflecting interfaces are much larger than the wavelengths of waves impinging upon them because, with this
Figures & Tables
“Over the years, ray theory has furnished the exploration geophysicist with most of the working tools for understanding and interpreting events observed on reflection seismic sections. Even today, notwithstanding the pace at which the more powerful acoustic wave theory is introducing its new tools, ray theory, in the hands of the authors, retains its preeminence for providing insights into fundamental problems in reflection seismology. Professor Krey's earlier contributions are part of ray theory's rich heritage. Alongside C. Hewitt Dix and Hans Durbaum, he elucidated relationships between interval velocity and observed reflection moveout.”