The undersampled seismic data may suffer from the degraded quality and pose negative impacts on subsequent processing procedures. Seismic data interpolation is a cost-saving technique to obtain regular and high-density data in the modern seismological community. In this study, I present a seismic data interpolation technique that is based on the Shannon entropy and shaping regularization. I consider the seismic data interpolation problem as a process of improving the orderliness of a system. A seismic section with clean and completely sampled signals can be treated as an orderly data system, while the added noise or decimation will destruct such orderliness. Therefore, we can recover the missing signals as the orderliness of the seismic data section is improved. The wave field is predicted by a regularized least-squares matching with the assumption of local plane-wave. The orderliness-improving process is packaged as a shaper and incorporated into the shaping regularization framework to iteratively solve the seismic interpolation problem. Unlike the conventional methods, such as prediction-based, sparsity-promoting-based, or rank-reduction-based methods, which generally assume the observed data are regularly or irregularly undersampled, the presented Shannon entropy shaping-based method has no requirement on the distribution pattern of missing traces and hence can be applied to interpolate both regular and irregular seismic data. I use both synthetic and field seismic data to test the performance of the proposed algorithm on both regular and irregular seismic data interpolation problems. The results demonstrate that the presented approach can achieve superior performance compared with the widely used techniques.

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基于香农熵整形的地震数据插值

欠采样的地震数据可能会受到质量下降的影响，并对后续处理过程造成负面影响。地震数据插值是现代地震学界获取规则和高密度数据的一种节省成本的技术。在这项研究中，我提出了一种基于香农熵和整形正则化的地震数据插值技术。我认为地震数据插值问题是一个提高系统有序性的过程。具有干净和完整采样信号的地震剖面可以被视为有序的数据系统，而添加的噪声或抽取会破坏这种有序性。因此，随着地震数据剖面有序性的提高，我们可以恢复丢失的信号。通过与局部平面波假设匹配的正则化最小二乘法来预测波场。有序性改进过程被打包为整形器，并纳入整形正则化框架，以迭代解决地震插值问题。与基于预测、基于稀疏性或基于秩的方法等传统方法通常假设观察到的数据是定期或不定期欠采样的方法不同，所提出的基于香农熵整形的方法对缺失道的分布模式，因此可用于内插规则和不规则地震数据。我使用合成和现场地震数据来测试所提出的算法在规则和不规则地震数据插值问题上的性能。