Abstract: Seismic denoising and signal recovery is a key step to improve the quality and accuracy of seismic exploration. By combining the sparsity of the convolution framelet transform and the flexibility of the low dimensional manifold learning, a CFR-LDMM ( Convolutional Framelet Regularization based Low Dimensional Manifold Model) is proposed for seismic signal recovery by using the convolution framelet coefficient energy as the low dimensional constrains. The seismic signals are then jointly represented on the low dimensional manifold in a certain embedded space by the data-driven local and nonlocal basis function, avoiding explicitly defining the manifold coordinate function. Therefore, the significant improvement is made on the denoising ability and signal recovery accuracy. The results of the synthetic and field seismic data tests show that the CFR-LDMM can concentrate the energy of the framelet coefficients for seismic data into a certain block in the coefficient matrix, and the seismic random noise can be removed and the missing traces can be reconstructed well at low signal-to-noise ratio.

Key words: seismic exploration; , signal recovery; , convolution framelet transform; , low dimensional manifold model; , denoising