LAUSR

A seismic trace corresponding to an anelastic layered earth model can be sparsely represented by a structured dictionary of properly attenuated wavelets, through a non-stationary sparse deconvolution. The sparseness of the coefficients (reflectivity series), however, considerably decreases when the wavelets are incorrectly attenuated due to an incorrect Q model. Mathematically, the wavelets, as the elements of the dictionary, are nonlinearly related to the Earth quality factor Q (the inverse of the attenuation coefficient). A parametric dictionary learning strategy enables interval-Q estimation and compensation by training the dictionary atoms from the input trace adaptively to provide a sparse representation of it. We assume a piecewise Q model by dividing the dictionary elements into several groups, each containing a number of wavelets whose temporal supports are close to each other and can be described by a single Q value. The dictionary is learnt iteratively where at each iteration only one group of t...