Reflectivity Inversion Based on Sparse Bayesian Learning

A spectral reflectivity inversion method based on sparse Bayesian learning, called as SSBLRI, is presented in this paper. For this method, probability rules are deduced to invert sparse reflectivity in frequency domain. During the inversion, the effect of noise is taken into account, and the phase error for wavelet estimation is tolerated. In addition, geological assumptions about reflectivity are automatically controlled according to a series of hyper-parameters, rather than predetermined by parameters. A 3D synthetic seismic data example which contains a wedge volume, and a 2D section extracted from seismic response of a 3D physical model are exploited to test the feasibility and effect of the method. As the inversion results of synthetic data example show, when the number of stratigraphic layers is entirely unknown, though the periodicity of amplitude spectrum corresponding to medium frequency band is deteriorated by noise, the thin bed below tuning thickness still can be identified using SSBLRI method, without any obvious false detail. The physical model data example demonstrates that this method can not only identify about 8-m thick bed, but also characterize stratigraphic boundary with remarkable detail.