Double Plane Wave Least Squares Reverse Time Migration with Sparse Fequency and Pane Wave Sampling

Abstract

Summary Least squares reverse time migration (LSRTM) is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot profile LSRTM is computationally expensive because computing the gradient involves solving the two-way wave equation several times in every iteration. To reduce the computational effort of LSRTM, we propose to implement frequency domain LSRTM using double plane wave (DPW) data with sparse frequency sampling and sparse plane wave sampling. Theoretically, frequency sampling and plane wave sampling used in migration should obey the Nyqusit theorem. Otherwise, the well-known wrap-around artifacts and linear artifacts might contaminate images. In this research, we demonstrate that images with correct reflector amplitudes and reasonable resolution can be achieved even if frequency sampling and plane wave sampling are larger than that determined by the Nyquist theorem. The artifacts generated due to undersampling in frequency and plane wave can be effectively suppressed during iterations. Using sparse frequency and plane wave sampling for DPW LSRTM greatly reduces the number of wavefield computations. We show that the computational efficiency can be improved by an order of magnitude.