An Application of Elastic-Net Regularized Linear Inverse Problem in Seismic Data Inversion

Abstract

In exploration geophysics, seismic impedance is a physical characteristic parameter of underground formations. It can mark rock characteristics and help stratigraphic analysis. Hence, seismic data inversion for impedance is a key technology in oil and gas reservoir prediction. To invert impedance from seismic data, one can perform reflectivity series inversion first. Then, under a simple exponential integration transformation, the inverted reflectivity series can give the final inverted impedance. The quality of the inverted reflectivity series directly affects the quality of impedance. Sparse-spike inversion is the most common method to obtain reflectivity series with high resolution. It adopts a sparse regularization to impose sparsity on the inverted reflectivity series. However, the high resolution of sparse-spike-like reflectivity series is obtained at the cost of sacrificing small reflectivity. This is the inherent problem of sparse regularization. In fact, the reflectivity series from the actual impedance well log is not strictly sparse. It contains not only the sparse major large reflectivity, but also small reflectivity between major reflectivity. That is to say, the large reflectivity is sparse, but the small reflectivity is dense. To combat this issue, we adopt elastic-net regularization to replace sparse regularization in seismic impedance inversion. The elastic net is a hybrid regularization that combines sparse regularization and dense regularization. The proposed inversion method was performed on a synthetic seismic trace, which is created from an actual well log. Then, a real seismic data profile was used to test the practice application. The inversion results showed that it provides an effective new alternative method to invert impedance.