Enhanced Small Reflections Sparse-Spike Seismic Inversion with Iterative Hybrid Thresholding Algorithm

Seismic inversion is a process of imaging or predicting the spatial and physical properties of underground strata. The most commonly used one is sparse-spike seismic inversion with sparse regularization. There are many effective methods to solve sparse regularization, such as L0-norm, L1-norm, weighted L1-norm, etc. This paper studies the sparse-spike inversion with L0-norm. It is usually solved by the iterative hard thresholding algorithm (IHTA) or its faster variants. However, hard thresholding algorithms often lead to a sharp increase or numerical oscillation of the residual, which will affect the inversion results. In order to deal with this issue, this paper attempts the idea of the relaxed optimal thresholding algorithm (ROTA). In the solution process, due to the particularity of the sparse constraints in this convex relaxation model, this model can be considered as a L1-norm problem when dealt with the location of non-zero elements. We use a modified iterative soft thresholding algorithm (MISTA) to solve it. Hence, it forms a new algorithm called the iterative hybrid thresholding algorithm (IHyTA), which combines IHTA and MISTA. The synthetic and real seismic data tests show that, compared with IHTA, the results of IHyTA are more accurate with the same SNR. IHyTA improves the noise resistance.