Nonminimum phase deconvolution in the log domain: A sparse inversion approach

Abstract

Being disturbed by the discrepancy between the Ricker wavelet and minimum phase wavelets, we wondered if a sparseness criterion could get us deconvolved data with the event polarity being more clearly evident. Five data sets found it does. The sparseness criterion we used is a hyperbolic penalty function. It ranged from [Formula: see text] at small residuals to [Formula: see text] at large residuals. The main pitfall was that introducing negative filter lags introduced a null space (obviously so for Gaussian data). The null space demanded a regularization. We found a formulation in the domain of the Fourier transform of a log spectrum, in which a Ricker-style regularization appeared. Curiously, this regularization eliminated the leg jumps. A quasi-Newton solver was faster than that of our earlier work, a combination of conjugate directions with a Newton solver.