A scheme for missing-trace interpolation of a common midpoint (CMP) gather is proposed. Spatial aliasing in a CMP gather can be overcome by normal-moveout (NMO) correction. After NMO correction, we fill in missing traces so as to minimize the output of high-pass, recursive dip filtering. For optimization using a conjugate gradient, we derive the conjugate operator of the recursive dip filter. The proposed scheme is applied to three kinds of missing data problems - interlaced missing traces, truncation at the end of survey and randomly positioned missing traces.
Trace interpolation procedures are becoming an integral part of processing coarsely or irregularly sampled field data. Generally speaking, trace interpolation is used to improve the quality of multitrace processing, especially that of migration. All standard methods of migration yield poor results when sampling is too coarse, although each method causes different types of errors. In this paper, we will consider CMP gathers that are regularly sampled in space, but have some number of missing traces. The missing traces can occur at the end of the CMP gather, they can be the result of spatial aliasing (interlaced missing traces), or they can be missing traces located randomly throughout the gather.
First we will review the recursive dip filter, including its
character, implementation and conjugate operator.
We will then discuss the dealiasing effect of NMO correction and
the spectral characteristics of various missing-trace patterns.
The final section will demonstrate the validity of the method given
in this paper using a synthetic CMP gather and real data.