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

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 1D synthetic data confirm the feasibility of reconstructing the sparse-spike reflectivity series accurately from the partial spectrums of seismic data. Furthermore, the testing on 2D sparse-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 sparse-layer 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. ©, 2015, Science Press. All right reserved.