Fast and Memory-Efficient Frequency-Domain Least-Squares Reverse-Time Migration Using Singular Value Decomposition (SVD)

Least-squares reverse-time migration (LSRTM) is linearized inversion based on the Born approximation, which commonly seeks to high-quality migration result by the least-squares sense. Contrary to time-domain LSRTM which performs the wavefield simulation as much as several times of the number of shots, frequency-domain LSRTM (F-LSRTM) has the advantage to efficiently deal with multiple shot records. Furthermore, if Green's function can be saved on memory storage, the full wavefield simulation is implemented only once at the first iteration during entire LSRTM iterations. However, huge memory storage may be required to save the Green's function for large dataset and model size. To alleviate this computational issue, we propose an efficient F-LSRTM scheme using singular value decomposition (SVD). In our scheme, Green's function can be saved efficiently as two unitary matrices and one singular value vector with a few number of dominant singular values. Because the number of dominant singular values, called the optimal rank, is much smaller than the minimum value in each dimension size of Green's function, the proposed method can make it possible to save the Green's function into the computing memory with keeping the accuracy. After demonstrating the feasibility of reducing the rank of Green's function, we examine our proposed F-LSRTM scheme and comparative F-LSRTM schemes (F-LSRTM using an adjoint-state method and saved full Green's function, respectively) using the simple layered and modified marmousi-2 model. Numerical tests indicate that our proposed F-LSRTM scheme can generate migration results as accurate as comparative F-LSRTM schemes with less memory usage and computational cost.