Frequency-broadening method of seismic data based on sparse reconstruction inversion strategy

To broaden the effective frequency bandwidth of seismic data and enhance its resolution, we investigate the high-resolution reconstruction method grounded in compressed sensing sparse theory, utilizing the characteristics of sparse decomposition of seismic signals. First, we examine the construction of an over-complete dictionary, which is then employed to sparsely represent the seismic data and derive the reflection coefficient, combined with noise, forms a mixed sparse component. By removing the noise sparse component from this mixture, we isolate a clean reflection coefficient. In the iterative reconstruction process of compressed sensing sparse decomposition, weak signal can easily be overwhelmed by the application of the maximum energy principle. To address this issue, we propose a useful signal control retention method incorporating lateral adjacent low-rank constraints. This approach increases the probability of optimizing weak signal dictionary atoms, mitigates the unbalanced reconstruction of strong and weak signals, and facilitates the comprehensive reconstruction of both signal types. Ensuring reconstruction accuracy is crucial, as the conditions for reconstruction significantly affect reliability. Therefore, we employ a signal-to-noise ratio estimation method to establish an adaptive iteration stop condition based on a residual threshold. During each iteration, the signal-to-noise ratio is recalculated, and the signal-to-noise ratio is multiplied by the residual to produce a weight residual. Finally, this new residual is used in the inner product calculations, allowing for the preferential selection of dictionary atoms. Both theoretical models and actual data validate the rationality and effectiveness of the proposed method. Analysis of real data demonstrates that our approach significantly enhances the seismic frequency band width and markedly improves the resolution of seismic data.