Seismic reflectivity inversion by a sparsity and lateral continuity constrained gradient descent method

One of the crucial problems in seismic exploration is to invert the subsurface reflectivity from the surface recorded seismic data. However, the inversion process is ill-posed by nature. To tackle the ill-posed ness, we assume the reflectivity series is sparse in the time domain but continuous in the space domain, and encode such information in the form of sparse constraints within the trace and spatial smoothing constraints across the trace in the inverse problem. In particular, for the former we use a non monotone gradient descent method to solving the II-norm constrained minimization model, and for the latter we use structure-oriented filtering to enhance the coherence of seismic events across midpoints. Theoretical simulations are performed to verify the validity and feasibility of our method.