In this paper, we propose a new method of seismic spectral sparse reflectivity inversion that, for the first time, introduces Expectation-Maximization-based sparse Bayesian learning (SBL-EM) to enhance the accuracy of stratal reflectivity estimation based on the frequency spectrum of seismic reflection data. Compared with the widely applied sequential algorithm-based sparse Bayesian learning (SBL-SA), SBL-EM is more robust to data noise and, generally, can not only find a sparse solution with higher precision, but also yield a better lateral continuity along the final profile. To investigate the potential of SBL-EM in a seismic spectral sparse reflectivity inversion, we evaluate the inversion results by comparing them with those of a SBL-SA-based approach in multiple aspects, including the sensitivity to different frequency bands, the robustness to data noise, the lateral continuity of the final profiles and so on. Furthermore, we apply the mean square error (MSE), residual variance (RV) of seismograms and residual energy (RE) between the frequency spectra of the true and inverted reflectivity model to highlight the advantages of the proposed method over the SBL-SA-based approach in terms of spectral sparse reflectivity inversion within a sparse Bayesian learning framework. Multiple examples, including both numerical and field experiments, are carried out to validate the proposed method.
In this paper, we propose a novel approach of deep-learning-based seismic horizon auto-picking that introduces a modified vector quantized variational autoencoder (VQ-VAE) framework to improve the accuracy of seismic horizon interpretation and, for the first time, quantitatively evaluate the uncertainty of the auto-picked horizon by exploiting the concept of entropy. Compared with the conventional VQ-VAE approach, the proposed method not only modifies the VQ-VAE model with more deep-learning channels at each layer of the network to enhance the performance of horizon auto-picking within the VQ-VAE framework, but also extends the 1D seismic labels with more continuous samplings within a single trace to boost the stability of auto-picked horizon in geologically complex settings and also significantly suppress the resulting uncertainty. To further improve the resulting accuracy in geologically complex settings, we introduce the directional structure tensor to extract a more reliable initial horizon and, moreover, a dilated horizon searching strategy to extend the capacity of the proposed method in dealing with the large fault displacement and reducing the computational cost simultaneously. Additionally, the resulting uncertainty quantitatively measured by entropy can also serve as an effective indicator to enable a further refinement of the auto-picked result accordingly. Both 2D example and 3D field applications are carried out to validate the effectiveness of the proposed method.
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