Abstract：Many edge detection methods can achieve good application results. However, these methods have their shortcomings and limited edge detection ability, especially the unsatisfying effects of edge detection for noise interference, multi-edge interference, and weak small targets. Therefore, the spatial distribution characteristics of fault, fracture, and cave edges are analyzed. According to the seismic response characteristics of those edges, the low-rank sparse analysis theory is introduced into edge detection to study the low-rank sparse decomposition and reconstruction of edge information, background information, and noise information. For the improvement of the edge detection ability and resolution, the in-depth sparse representation of seismic data is carried out on the basis of the compressed sensing sparse representation. Given the vector sparse representation and matrix sparse representation, a new edge detection method, i.e., an edge detection method for low-rank sparse reconstruction analysis, is formed through the low-rank sparse analysis theory. The specific steps are as follows:First, the seismic data is decomposed into stationary wavelets. Second, multi-scale wavelet coefficients are optimized. Then, the tensor matrix is established and modeled according to the multi-scale optimized wavelet coefficients. Fourth, the singular values of the tensor matrix are decomposed. Fifth, low-rank optimization of those singular values is conducted. Finally, the multi-scale double sparse and double optimization results are fused and reconstructed. The model analysis and the analysis of practical data application effect show that the proposed method has strong noise resistance and applicability and is capable of effectively depicting the edges of faults, fractures, and caves.
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