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| Abstract: |
| Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix, the rank-reduced methods have been applied successfully for seismic interpolation and denoising. These rank-reduced methods mainly include Cadzow reconstruction that uses eigen decomposition of the Hankel matrix in the f-x (frequency-spatial) domain， and nuclear-norm minimization (NNM) based on rigorous optimization theory on matrix completion (MC). In this paper, a low patch-rank MC is proposed with a random-overlapped texture-patch mapping for interpolation of regularly missing traces in a three-dimensional (3D) seismic volume. The random overlap plays a simple but important role to make the low-rank method effective for aliased data. It shifts the regular column missing of data matrix to random point missing in the mapped matrix, where the missing data increase the rank thus the classic low-rank MC theory works. Unlike the Hankel matrix based rank-reduced method, the proposed method does not assume a superposition of linear events, but assumes the data have repeated texture patterns. Such data lead to a low-rank matrix after the proposed texture-patch mapping. Thus the methods can interpolate the waveforms with varying dips in space. A fast low-rank factorization method and an orthogonal rank-one matrix pursuit method are applied to solve the presented interpolation model. The former avoids the singular value decomposition (SVD) computation and the latter only needs to compute the large singular values during iterations. The two fast algorithms are suitable for large-scale data. Simple averaging realizations of several results from different random-overlapped texture-patch mappings can further increase the reconstructed signal-to-noise ratio (SNR). Examples on synthetic data and field data are provided to show successful performance of the presented method. |
| Key words: seismic data interpolation low-rank method random patch geophysics |
| DOI：10.11916/j.issn.1005-9113.20017 |
| Clc Number:P315, Q29, Q242.1[KG*2] |
| Fund: |
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| Descriptions in Chinese: |
| 基于随机块低秩方法的地震数据规则重建 马坚伟 （哈尔滨工业大学 数学学院，地球物理中心，哈尔滨 150001） 创新点说明：提出了可用于规则数据插值重建的随机块投影低秩矩阵优化方法，扩展了之前低秩方法的使用范围，提供一种有效的三维地震勘探数据道加密技术。 研究目的： 解决块投影降秩方法无法用于规则地震道缺失的重建问题。 研究方法： 通过研究相邻数据块随机重叠的矩阵投影，使得降秩重构的数学理论与地震数据规则重建问题相匹配，从而把低秩优化算法的良好性能推广应用到了解决油气资源勘探的工程实际问题。 结果和结论： 通过对模拟数据和实际数据的测试比较分析，验证了所提方法具有较好的重构效果。未来可进一步推广到五维地震数据的重建， 关键词：低秩矩阵优化，随机块投影，地震数据重建，插值，油气勘探 |
