Complex spectral decomposition via inversion strategies

Abstract

Spectral decomposition is a time-frequency analysis tool widely used in seismic data interpretation. Unlike conventional frequency analysis, such as the Fourier transform, spectral decomposition estimates the frequency content of a signal at any particular time. Thus, the frequency content is defined on a local, not global, scale. An alternative method for spectral decomposition is proposed in which the seismic signal is deconvolved with a dictionary of different frequency complex Ricker wavelets. By posing the underdetermined problem through a mixed 2 - 1 norm cost function, greater resolution is obtained in the time-frequency map as the frequency distribution is constrained to be sparse. Examples on synthetic data are presented to illustrate the proposed method for two different mixed 2 - 1 norm solving algorithms.