基于区域阈值模型的地震信号凸集投影高效重建方法

POCS high⁃efficient reconstruction method of seismic signals based on regional threshold model

地震信号重建广泛应用的凸集投影(POCS)算法大都采用线性或指数阈值模型,虽然计算效率高,但由于难以完全消除缺失信号泄露引起的噪声,重建效果不佳。为此,提出了一种基于区域阈值模型的POCS地震信号重建方法,将数值阈值转化为区域阈值,将区域滤波窗口作为阈值进行迭代更新。其核心思想是根据时—空域缺失地震信号的频率—波数(F⁃K)谱分布范围,在每次POCS重建迭代时按照一定规律选取固定大小的矩形或扇形区域作为阈值,将区域内和区域外的变换系数分别保留和置零,以尽可能地保留有效信号的变换系数,构建了地震信号POCS重建的矩形与扇形区域阈值模型。数值试验结果表明:相比于F⁃K域指数阈值模型的POCS重建,F⁃K域区域阈值模型对连续缺失信号的重建精度更高;相比于扇形区域阈值模型,矩形区域阈值模型的重建精度和计算效率均略高;与曲波域指数阈值模型的POCS重建相比,F⁃K域区域阈值模型的重建精度相当,但计算效率提高了约90%。

Most of the projection onto convex sets(POCS)algorithms widely used for seismic signal recon⁃struction use linear or exponential threshold models,which have high computational efficiency,but have poor re⁃construction effect due to the difficulty in eliminating the noise caused by the leakage of missing signals.There⁃fore,this paper proposes a POCS seismic signal reconstruction method based on the regional threshold model,which transforms the numerical threshold into a regional threshold,and the regional filtering window is itera⁃tively updated as the threshold.The core idea is to reserve the transform coefficients of effective signal as much as possible by selecting a rectangular or a sectorial region of fixed size as a threshold according to a certain law in each POCS reconstruction iteration based on the frequency⁃wavenumber(F⁃K)spectrum distribution range of missing seismic signal in the spatiotemporal domain,and reserving and zeroing the transform coefficients in⁃side and outside the region respectively.The rectangular and sectorial threshold models for POCS reconstruc⁃tion of seismic signals are thus constructed.The numerical results demonstrated that compared with the POCS reconstruction of the exponential threshold model in the F⁃K domain,the regional threshold model in the F⁃K domain has a higher reconstruction accuracy for continuous missing signals.Compared with the sectorial region threshold model,the reconstruction accuracy and computational efficiency of the rectangular region threshold model are slightly higher.Compared with the exponential threshold model reconstructed by POCS in the curve⁃let domain,the reconstruction accuracy of the regional threshold model in the F⁃K domain is similar,but the com⁃putational efficiency is increased by about 90%.