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Least‐squares reverse time migration, a linearized inversion problem, can provide high‐quality migration image by minimizing the misfit function, which is defined by predicted and observed data. According to the theory of data‐domain least‐squares reverse time migration, a forward source wavefield that is simulated with a fixed background velocity does not change during iterations. However, storing the forward source wavefield directly into computer memory involves substantial memory consumption. Although a source wavefield reconstruction technique can be applied during least‐squares reverse time migration iterations, this approach can increase the computational cost because of the need for additional wavefield simulations. To alleviate this computational issue in storing the forward source wavefield, we propose an efficient least‐squares reverse time migration scheme based on an excitation amplitude method. Unlike conventional excitation amplitude imaging conditions, the proposed least‐squares reverse time migration scheme enables one to reconstruct the forward source wavefield by convolving a source wavelet with the excitation amplitude of Green's function at the excitation time. With this excitation amplitude method, the forward source wavefield can be efficiently stored in the computer memory because the sizes of the excitation amplitude and excitation time maps are equal to the size of one snapshot. To validate the feasibility of our least‐squares reverse time migration scheme, we perform dot‐product tests and compare forward source wavefields, demigrated data and gradient vectors obtained by conventional least‐squares reverse time migration and our proposed least‐squares reverse time migration. Using numerical tests on synthetic data, we confirm that our least‐squares reverse time migration can produce high‐quality migration results with a significant improvement in computational efficiency with respect to performance time and memory consumption. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]