FK和Shearlet域联合压缩感知数据重构技术

由于稀疏炮检点采集或野外采集因素造成地震数据的不规则，影响地震资料成像质量。基于压缩感知理论的重构方法，能够在有限采样的情况下有效重构地震数据。由于地震道的空间随机缺失在波数域表现为空间假频，文中将时空域的地震道重构转化为频率波数（FK）域的随机噪声压制问题。对FK域数据做多尺度、多方向性的剪切（Shearlet）变换，通过反演迭代消除FK域的空间假频，从而实现地震道的空间重构。该方法是在FK变换后进行Shearlet变换，可以看作一种新的稀疏基变换。由于全局随机采样因子频谱呈白噪特征，分段随机采样因子频谱呈蓝谱特征，因此分段采样数据有效信号与假频的混叠相对减少，更有利于数据重构。实验结果表明，分段随机采样FK+Shearlet域重构精度高于全局随机采样Shearlet域重构、分段随机采样Shearlet域重构和全局随机采样FK+Shearlet域重构。

Compressed sensing data reconstruction technology in joint FK and Shearlet domain

The irregularity of seismic data caused by sparse source-receiver acquisition or field acquisition affects the imaging quality of seismic data. The reconstruction method based on compressed sensing theory can effectively reconstruct seismic data under the condition of limited sampling. Since the spatial random absence of seismic traces is shown as spatial aliasing in the wavenumber domain, we transform the reconstruction of seismic traces in the spatiotemporal domain into random noise suppression in the frequency-wavenumber (FK) domain. Specifically, the multi-scale and multi-directional Shearlet transform is performed on FK-domain data, and by iterative inversion to eliminate spatial aliasing in the FK domain, the spatial reconstruction of seismic traces is realized. The method in this paper performs the Shearlet transform after the FK transform, which can be viewed as a new sparse basis transform. Since the spectrum of the global random sampling factor is characterized by white noise, and the spectrum of the piecewise random sampling factor is characte-rized by blue spectra, the interference of the effective signal and aliasing of the piecewise sampling data is relatively reduced, which is more conducive to data reconstruction. The reconstruction experiment indicates that the reconstruction accuracy in the FK + Shearlet domain for piecewise random sampling is higher than that in the Shearlet domain for global or piecewise random sampling as well as that in the FK + Shearlet domain for global random sampling.