Double Plane Wave Research Articles

Reciprocity and double plane-wave migration

In plane-wave migration techniques, plane-wave data sets with seismic energy in both positive and negative ray-parameter sections are more desirable than those with seismic energy only in either positive or negative ray-parameter sections. Such plane-wave data sets are often referred to as optimal plane-wave data sets because they can be used to illuminate the subsurface from both sides of the targets and, therefore, can produce sharp images. Traditionally, to obtain optimal plane-wave data sets from one-sided gathers generated by marine seismic acquisition geometry, one needs to invoke the reciprocity principle to sort split-spread gathers prior to implementing plane-wave decomposition. We have investigated the applicability of the reciprocity principle in the double plane-wave (DPW) domain. We have developed an easy and efficient merging method that generates optimal plane-wave data sets in the DPW domain using one-sided shot gathers. We call this resultant plane-wave data set the “optimal DPW data set.” We find that an optimal DPW data set transformed from one-sided gathers is a good approximation to a DPW data set transformed from split-spread gathers with the same maximum offset as that of the one-sided gathers. We find that ray-parameter common-image gathers with continuous events in both positive and negative ray-parameter sections can be generated by migrating optimal DPW data sets. This helps migration velocity analysis and improves the subsurface illumination. In addition, we show that the computational cost of DPW migration methods could be reduced with the help of the reciprocity principle. We test our proposed method using a synthetic model to demonstrate its effectiveness.

Double-plane-wave reverse time migration in the frequency domain

We have developed an efficient, accurate, and flexible plane-wave migration algorithm in the frequency domain by using a compressed and coupled-plane-wave data set, known as the double-plane-wave (DPW) data set. The DPW data set obtained by slant stacking of seismic shot profiles over source and receiver/offset represents seismic data in a fully decomposed plane-wave domain, which is called the DPW domain. A new DPW migration algorithm is derived under the Born approximation in the frequency domain, and it is referred to as the frequency-domain DPW reverse time migration (RTM). Frequency plane-wave Green’s functions need to be constructed and used during the migration. Time dips in shot profiles help to estimate the range of plane-wave decomposition. Therefore, the number of frequency plane-wave Green’s functions required for migration is limited. Furthermore, frequency plane-wave Green’s functions can be used for imaging each set of plane waves — either source or receiver/offset plane waves. As a result, the computational burden of computing Green’s function is substantially reduced; this results in increasing the migration efficiency. A selected range of plane-wave components can be migrated independently to image specific targets. Ray-parameter common-image gathers can be generated after migration without extra effort. The algorithm was tested on several synthetic data sets to show its feasibility and usefulness. The frequency-domain DPW RTM can also include anisotropy by constructing plane-wave Green’s function in anisotropic media.