Memory-Efficient Frequency-Domain Least-Squares RTM Using Low-Rank Green's Functions via Stochastic SVD Algorithms

Frequency-domain least-squares reverse time migration (FLSRTM) is capable of producing a high-resolution reflectivity model, provided that Green's functions can be stored in memory. Green's functions employed to compute the gradient and Born-modeled data must be calculated once and then stored; however, their size can be large, making this storage infeasible depending on the available hardware. FLSRTM using low-rank Green's functions decomposed via singular value decomposition (SVD) can be used to alleviate this constraint. However, the SVD decomposition could result in a significant increase in computational time when dealing with large datasets and models of considerable size. To overcome this issue, we propose the FLSRTM scheme with a low-rank Green's function by exploiting randomized (rSVD) and compressed SVD (cSVD) algorithms. Green's functions can then be saved efficiently as two unitary matrices with a few dominant singular values, thus requiring little memory. Following the demonstration of the feasibility of rank reduction in Green's functions, we evaluate the proposed rSVD and cSVD FLSRTM schemes versus the reference fully stored Green's functions FLSRTM and conventional low-rank SVD FLSRTM. These evaluations are conducted using both a layered model and the modified Marmousi-2 model. Our proposed FLSRTM scheme can generate image results identical to the comparative methods while also requiring less memory than FLSRTM, which saves the complete Green's functions, and less computational time compared to the FLSRTM scheme with low-rank Green's functions via conventional SVD.