The computational cost of conventional imaging is large for today’s wide-azimuth seismic surveys. One strategy to reduce the overall cost of seismic imaging is to migrate with multiple shot-gathers at once, a technique which is known as blended source imaging. Blended source imaging trades the reduced cost of imaging with the presence of artifacts (cross-talk) in the image. We show that a theoretical framework using a matrix representation of the imaging process adequately describes conventional, and blended source imaging. Furthermore, the matrix representation predicts both the quantity and strength of cross-talk artifacts prior to imaging, thus allowing us to decide a priori the trade off between cross-talk and speed. By exploiting our theoretical framework, we are able to design an amplitude encoding scheme, referred to as Truncated Singular Vector (TSV), that trades a significantly reduced cost of imaging with spatial resolution and cross-talk noise. The TSV encoding allows us to reduce the cost of imaging by at least an order of magnitude relative to conventional shot-record migration. Overall, we provide a framework for finding blended source encoding schemes, that produce good quality images at lower computational cost.


Today’s seismic imaging challenges include imaging areas with increasingly complex geology, such as salt domes and overthrust regions. The major issues for imaging these areas are poor data quality and lack of seismic illumination, as the complex geology severely deforms seismic wavefields. One approach to resolving these issues is to obtain large amounts of redundant information from various acquisition directions via wide-azimuth or fullazimuth seismic surveys (Michell et al., 2006; Kapoor et al., 2007; Ting and Zhao, 2009). Subsequently, wideazimuth surveys require significantly more time to acquire and even greater amounts of time to process and image the data. However, recent technological advances may reduce the cost of imaging for large seismic surveys. One of these technologies is blended imaging, where multiple shotgathers are combined together by applying an amplitude or phase-encoding prior to migration (Romero et al., 2000). This process reduces the number of migrations that are needed to produce a final image (Liu, 1999; Morton, 1999; Romero et al., 2000; Soubaras, 2006; Zhang et al., 2007; Berkhout et al., 2009; Perrone and Sava, 2009). The encoding process introduces additional noise into the image, called cross-talk (Romero et al., 2000). Previous work has shown that the cross-talk is related to the encoding scheme used, so many encodings have been developed including: planar (Liu, 1999), random (Romero et al., 2000), modulated (Soubaras, 2006), harmonic (Zhang et al., 2007), and planar with dithering (Perrone and Sava, 2009). The standard method to attenuate cross-talk in blended images is conventional stacking. A special case of blended source imaging is simultaneous source imaging, i.e. linearly combining shot-gathers with zero phase- and time-delay. The major advantage of simultaneous source imaging compared to blended imaging is that simultaneous source data can be acquired using the same recording time length, whereas blended source acquisition requires long recording times due to time-delays between sources.

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