Robust boundary-preserving multi-source least-squares reverse-time migration with combined sparse constraints

Abstract

Least-squares reverse time migration (LSRTM) can generate a higher-resolution image than other algorithms but with a higher computation cost. Although the conventional source-encoding algorithm can improve the efficiency, it faces the problems of multi-source crosstalk noise and observed-synthetic data mismatching caused by the unpractical assumption of the fixed acquisition setup. In this paper, we propose a hybrid sparsity-constrained multi-source encoding algorithm to overcome the above bottleneck problems. Harmonic wavelets are used as an encoding operator so that the blended multi-source wavefields can be decomposed as each original single-source wavefield based on the orthogonality of trigonometric functions. Due to that the harmonic frequency selection might lead to an insufficient stack of single-frequency components, there would generate background noise on the image, reducing the image quality and convergence rate. Therefore, we apply a combined-sparsity constraint to improve the robustness and convergence rate of this algorithm. Besides, we use the convolution-norm misfit function to eliminate the influence of incorrect source wavelet. Synthetic data examples show the rationality and feasibility of our algorithm.