Low-rank representation of omnidirectional subsurface extended image volumes

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. While 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. We arrive at these factorizations 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. The latter is computationally prohibitive because extended image volumes are quadratic in image size. As a result, we can easily handle situations where conventional horizontal offset gathers are no longer focused. More importantly, the factorization also provides a mechanism to use the invariance relation of extended image volumes for velocity continuation. With this technique, extended image volumes for one background velocity model can directly be mapped to those of another background velocity model. Our low-rank factorization inherits this invariance property so we incur factorization costs only once when examining different imaging scenarios. Because all imaging experiments only involve the factors, they are computationally cheap with costs that scale with the rank of the factorization. We validate our methodology on 2D synthetics including a challenging imaging example with salt. Our experiments show that our low-rank factorization parameterizes extended image volumes naturally. Instead of brute force explicit cross-correlations 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.