Hybrid L1/L2 Norm IRLS Method with Application to Velocity-Stack Inversion

Least squares (l2 norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The l1 norm minimization gives more robust solutions than l2 norm solution does. Iteratively reweighted least squares (IRLS) method which is an efficient approximate solution of the l1 norm problem is widely used for robust inversion. I propose a simple way to implement IRLS method for a hybrid l1/l2 minimization problem that behaves as l2 fit for small residual and l1 fit for large residuals. The boundary between l1 and l2 is decided by a scale factor that is applied to data before and after inversion. Synthetic and real data examples in CMP data enhancing through inversion demonstrate the improvement of the hybrid l1/l2 norm method over least-squares method when there are outliers in the data.