RR Algorithm for Robust Inversion of Seismic Data

Summary A robust metric of data misfit like Ll-norm is required for parameter estimation in sparse optimizations when the data are contaminated by erratic noise. Recently the iteratively re-weighted and refined least squares (IRRLS or RR for short) algorithm was introduced for efficient solution of geophysical inverse problems in the presence of additive Gaussian noise in the data. We extend the algorithm in two practically important directions to make it applicable to data with non-Gaussian noise and to make its regularization parameter tuning more efficient and automatic. A technique is thus proposed based on the secant method for root finding to concentrate on finding a solution to Ll-Ll problems that satisfies fitting to a target misfit. We further propose a simple and efficient scheme that tunes the regularization parameter without requiring the target bound. This method is of great importance for automatic inversion of field data. Numerical examples from non-stationary deconvolution and velocity-stack inversion show that the proposed algorithm is efficient, stable and robust.