A B S T R A C TIn the last decade the seismic imaging industry has begun collecting data volumes with a substantial amount of data redundancy through new acquisition geometries including: wide-azimuth, rich-azimuth and full-azimuth geometries. The increased redundancy significantly improves image quality in areas with complex geology, but requires considerably greater computational power to construct an image because of the additional data and the need to use advanced imaging algorithms. One way to reduce the computational cost of processing such datasets is to blend shot-records, using shot-encoding, together prior to imaging which reduces the number of migrations necessary for imaging. The downside to doing so is that blending introduces strong, non-physical, cross-talk noise into the final image. By carefully choosing the shot-encoding scheme, we can reduce the additional noise inserted into the image and maximally reduce the number of migrations necessary. We describe a theory of blended imaging that explains all shot-encoding schemes, and use the theory to design a new class of encodings that use amplitude weights instead of phase-shifts or time-delays. We are able to use amplitude encoding to produce blended images of the same quality as previous encoding schemes at a similiar computational cost. Furthermore, we compare the results of amplitude encoding with the results from well-known shot-encoding schemes from previous work including: plane-wave migration, random-time delay, modulated-shot migration, and decimated shot-record migration. In our comparison, we find that plane-wave migration is in many ways an optimal shot-encoding scheme. However, we find that plane-wave migration produces results that are comparable to decimated shot-record migration when the total cost of imaging is taken into account, thereby calling into question the utility of shotencoding in general. Overall, this work questions the potential for shot-encoding in standard (shot-record) seismic imaging because blended imaging does not appear to sufficiently reduce the cost of imaging given the quality of the blended image compared to decimated shot-record migration..

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.

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