基于压缩感知的稀疏脉冲反射系数谱反演方法研究

A spectral inversion method of sparse-spike reflection coefficients based on compressed sensing

基于压缩感知稀疏信号采样和重构理论提出了一种稀疏脉冲反射系数谱反演方法。在稀疏地层假设下,利用地震资料的部分谱信息,采用基追踪算法,反演地下地层在L1范数意义下的宽带稀疏脉冲反射系数。利用褶积宽频带的四参数Morlet子波,生成高分辨率地震剖面,提高地震资料对薄层的识别能力。一维理论模型试验结果证实了利用地震资料的部分谱信息可以准确地反演出稀疏脉冲反射系数序列。二维理论模型试验结果表明,得到的反演结果不仅能识别薄(互)层界面、透镜体边界和地层尖灭位置等薄层结构,还能保持原始地层模型的横向连续性特征,并且具有一定的抗噪性。最后,实际资料的应用结果显示,反演得到的高分辨率剖面不仅在整体地层格架上忠实于原始地震资料,而且能够分辨出原始地震记录中无法识别的薄层结构,使得地下地层的接触关系更加清晰,为地震地层学精细解释提供依据。

Based on the theory of sparse sampling and signal reconstruction of compressed sensing,a spectral inversion method of sparse-spike reflection coefficients is proposed.Under the sparse-layer assumption,the sparse-spike broadband reflection coefficients can be inverted by the basis pursuit algorithm corresponding to the L1-norm constraint using the partial spectrums of seismic data.Through the convolution with a broadband four-parameter Morlet wavelet,the obtained sparse-spike reflection coefficients can be converted into high-resolution seismic data that can be applied to enhance the capacity of detecting thin beds.The inversion results on 1Dsynthetic data confirm the feasibility of reconstructing the sparse-spike reflectivity series accurately from the partial spectrums of seismic data.Furthermore,the testing on 2Dsparse-layer synthetic data demonstrates that the inversion results can identify such thin-layer structures as the interfaces of thin interbed,the boundaries of lenticular sand body and the positions of stratigraphic pitchout,and preserve a good lateral continuity of the original sparselayer model with a certain anti-noise capability.Finally,the actual application results shows that the obtained high-resolution seismic profile keeps the whole stratigraphic framework consistent with the original seismic data,distinguishes some thin-layer structures that cannot be identified by the original seismic data,and makes the subsurface stratigraphic contact relationship clearer,which can support the fine interpretation of seismic stratigraphy.