Missing traces in seismic surveys create gaps in the data and cause problems in later stages of the seismic processing workflow through aliasing or incoherent noise. Compressive sensing (CS) is a framework that encompasses data reconstruction algorithms and acquisition processes. However, CS algorithms are mainly ad hoc by focusing on data reconstruction without any uncertainty quantification or feature learning. To avoid ad hoc algorithms, a probabilistic data-driven model is used, the relevance vector machine (RVM), to reconstruct seismic data and simultaneously quantify uncertainty. Modeling of sparsity is achieved using dictionaries of basis functions, and the model remains flexible by adding or removing them iteratively. Random irregular sampling with time-slice processing is used to reconstruct data without aliasing. Experiments on synthetic and field data sets illustrate its effectiveness with state-of-the-art reconstruction accuracy. In addition, a hybrid approach is used in which the domain of operation is smaller while, simultaneously, learned dictionaries of basis functions from seismic data are used. Furthermore, the uncertainty in predictions is quantified using the predictive variance of the RVM, obtaining high uncertainty when the reconstruction accuracy is low and vice versa. This could be used for the evaluation of source/receiver configurations guiding seismic survey design.

中文翻译：

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地震贝叶斯压缩感知的相关矢量机

地震勘测中丢失的迹线会在数据中造成间隙，并在地震处理工作流程的后期阶段会因混叠或非相干噪声而引起问题。压缩感测（CS）是一个包含数据重建算法和采集过程的框架。但是，CS算法主要是临时性的，着眼于数据重建而没有任何不确定性量化或特征学习。为了避免临时算法，使用概率数据驱动模型（相关矢量机（RVM））来重建地震数据并同时量化不确定性。稀疏性的建模是通过使用基函数的字典来实现的，并且该模型通过迭代地添加或删除它们而保持了灵活性。带有时间切片处理的随机不规则采样用于重建数据而不会出现混叠。综合和现场数据集上的实验证明了其有效性以及最新的重建精度。另外，使用了一种混合方法，其中操作范围较小，同时，还使用了从地震数据中学习到的基函数字典。此外，使用RVM的预测方差对预测中的不确定性进行量化，当重构精度较低时则获得较高的不确定性，反之亦然。这可用于评估指导地震勘测设计的源/接收器配置。此外，使用RVM的预测方差对预测中的不确定性进行量化，当重构精度较低时则获得较高的不确定性，反之亦然。这可用于评估指导地震勘测设计的源/接收器配置。此外，使用RVM的预测方差对预测中的不确定性进行量化，当重构精度较低时则获得较高的不确定性，反之亦然。这可用于评估指导地震勘测设计的源/接收器配置。