Low-rank representation of omnidirectional subsurface extended image volumes

Abstract

Subsurface-offset gathers play an increasingly important role in seismic imaging. These gathers are used during velocity model building and inversion of rock properties from amplitude variations. Although powerful, these gathers come with high computational and storage demands to form and manipulate these high-dimensional objects. This explains why only limited numbers of image gathers are computed over a limited offset range. We avoid these high costs by working with highly compressed low-rank factorizations. These factorizations are obtained via a combination of probings with the double two-way wave equation and randomized singular-value decompositions. In turn, the resulting factorizations give us access to all subsurface offsets without having to form the full extended image volumes (EIVs) that are at best quadratic in image size. As a result, we can easily handle situations in which conventional horizontal offset gathers are no longer focused. More importantly, the factorization also provides a mechanism to use the invariance relation of EIVs for velocity continuation. With this technique, EIVs for one background velocity model can be directly mapped to those of another background velocity model. Our low-rank factorization inherits this invariance property, so that factorization costs arise only once when examining different imaging scenarios. Because all imaging experiments only involve the factors, they are computationally efficient with costs that scale with the rank of the factorization. Examples using 2D synthetics, including a challenging imaging example with salt, validate the methodology. Instead of brute-force explicit crosscorrelations between shifted source and receiver wavefields, our approach relies on the underlying linear-algebra structure that enables us to work with these objects without incurring unfeasible demands on computation and storage.