压缩感知走进地球物理勘探

压缩感知(Compressed Sensing,CS)突破了传统奈奎斯特-香农采样定律的限制,仅用不完备(远低于香农采样率)的测量即可高精度重构未知目标。简要综述了压缩感知的一些基本概念及其在地球物理勘探中的最新应用进展,包括地震数据不规则采集、处理、成像、反演的新理论和新技术。实际应用中可灵活把握CS的三要素:随机采集(包括炮点和检波器点两方面的随机)、目标的稀疏表达和稀疏约束优化重构的快速算法。重构更高维的目标,需要用的采集数据(百分比)可更少。压缩感知结合深度学习技术,可作为未来的一个发展方向。

 Compressive sensing (CS) is based on random sampling and sparsity,which bypasses a limitation of the Nyquist-Shannon sampling theorem.CS enables the reconstruction of signals from incomplete measurements significantly below the Shannon sampling rate.In this paper,we review the theory of CS and its applications in seismic data acquisition,processing,imaging,and inversion.Three key components for the application of CS are random acquisition (including random distribution of shot and detector points),sparse representation of signals,and fast algorithm for optimal reconstruction with sparse constraints.The percentage of data required for reconstructing targets decreases with increasing dimensions involved.The paper also highlights the potential of combining compressed sensing with deep learning.