Seismic reflectivity inversion using spectral compressed sensing

In this paper, we proposed a reflectivity inversion method via spectral compressed sensing (SCS). The reflectivity coefficient plays a key role in stratigraphic description and stratigraphic attribute inversion. However, reflectivity inversion is still a challenge due to the influence of noise and singularity of de-convolution. With the help of SCS, we construct a finer dictionary. The atom in the dictionary is composed of partial Fourier transform spectrum of a pair of odd or even reflection coefficients. The selection of local frequency bands is conducive to enhancing the robustness to noise. And we solve the model by a proper sparse representation method instead of de-convolution which enhances the stability of the inversion. Experiments results on simulated data and field data demonstrate that using the proposed method based on SCS can achieve comparable or better performance with traditional least square method. The continuity and singularity free of the output prove the effectiveness of the proposed method.