The choice of t-f smoothing method is viewed as a significant procedure of Gabor deconvolution. Inspired by homomorphic deconvolution, this paper extends Gabor deconvolution into the log spectra, wherein the explicit linear form of nonstationary convolution model brings great facilities for studying its reverse process. More pertinently, we propose a hyperbolic smoothing method there, in which the linear analysis is iteratively employed to approach the factorization task. Since divisions are transformed to subtractions in log spectra, the usage of the pre-whitening factors in the iteration is avoided, thus reducing human intervention and boosting calculation accuracy. Moreover, a simple piecewise linearization is also introduced to enhance this technique's practical value. And our experiences on reef reservoir and carbonate reservoir show that nonstationary deconvolution based on this new hyperbolic smoothing can acquire higher resolution than ordinary hyperbolic smoothing, thus providing more detailed information and revealing more subtle geological phenomena, which enable better reservoir characterizations and definitions.


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