基于压缩感知和稀疏反演的地震数据低频补偿

摘要

Full waveform inversion (FWI) is a hot topic in the subsurface velocity imaging.However,the lack of effective low frequency energy in seismic data restricts the performance of FWI.A method about low frequency information compensation of seismic based on compressed sensing theory and sparse inversion technique is proposed in this paper.A L1 norm constrained sparse inversion problem is first constructed according to the sparsity of reflectivity and the theory of compressed sensing.This inversion equation can be effectively solved by Fast Iterative Thresholding Algorithm (FISTA) and the full frequency components are then reconstructed in the Fourier domain with band-limited seismic dada.The low frequency components form the reconstructed data and high frequency components of the original data are reasonably combined to obtain the final low frequency compensated data.Synthetic and real data examples are tested to demonstrate the performance of the proposed method.%目前波形反演是地下速度成像技术研究的热点,但地震采集数据低频能量的缺失制约着波形反演的效果.笔者基于压缩感知理论和稀疏约束反演技术,提出了一种地震数据低频补偿方法.第一步,利用反射系数的稀疏性,根据压缩感知概念,构造L1范数约束的稀疏反演问题,在Fourier域通过有限带宽重构全带宽频谱,实现对地震数据全带宽拓频.这个过程借助快速迭代阈值法求解反问题.第二步,截取拓频后数据的低频能量和原数据的高频能量构成最终的低频补偿地震数据.模拟数据例子和实际数据例子证明了该方法能够有效地对10 Hz以下的频率进行补偿.