Until recently, conventional seismic exploration techniques successfully escaped the problem of data regularization. Two-dimensional seismic exploration (seismic profiling) conveniently positions seismic sources and receivers at regular locations. Although the problem of missing data does occur occasionally (missing near offsets in marine surveys, dead or severely contaminated traces, etc.), it has only minor importance in 2-D data processing.
The rapid development of three-dimensional seismic methods in recent years has brought another spatial dimension to the acquisition patterns. In fact, the data dimensionality has increases by two, because both the source and receiver locations become two-dimensional variables in a 3-D seismic setting. The difficulty of acquiring regularly positioned data has become apparent. An ideal situation, where both sources and receivers are uniformly distributed on the surface, almost never occurs in the practice of 3-D exploration. In typical marine observations, receiver streamers are towed behind a vessel. This setting leads to an irregular offset-azimuth distribution. Furthermore, the regularity of midpoint distribution at large offsets is often affected by cable feathering. On land, there is more variety in observation systems, but uniform 3-D coverage is rarely achieved because of practical and economic constraints Stone (1994).
Figure shows the common-midpoint (CMP) distribution for a selected range of offsets in a 3-D marine dataset, acquired in the North Sea. The CMP distribution looks fairly uniform, but the data irregularity becomes apparent if we consider an analogous plot for a selected bin in in-line and cross-line offsets (Figure ). Such irregularities are fairly common in marine acquisition Biondi (1999). I use this North Sea dataset for testing data regularization techniques presented in this dissertation.
Figure 1 Midpoint distribution for a wide range of offsets in the North Sea dataset.
Figure 2 Midpoint distribution for a 50 by 50 m offset bin in the North Sea dataset.
The problem of data irregularity in 3-D seismic exploration manifests itself in different situations. Some of them are
In this dissertation, I focus on a general approach to three-dimensional seismic data regularization. I address the following problem: given irregularly spaced data as input, produce a regularly spaced output that will preserve the essential features of the input. Although this is a well-known problem in some other Earth sciences (atmospheric sciences, potential fields, mining and petroleum engineering), two particular properties of seismic exploration data require special treatment. First, the extremely large exploration datasets prohibit computationally expensive methods and require algorithmic efficiency. Second, multiple coverage makes seismic data predictable in the offset direction, which can be additionally explored for optimal results.
The goal of this work is to develop a collection of efficient, practically affordable numerical methods for data regularization. The most optimal methods need to be specifically tailored for seismic reflection data to take advantage of the additional degrees of predictability that such data possess.