Simple kernel functions for TFR-based vibroseis seismic deconvolution

Time-frequency representations (TFRs) are useful tools for frequency-domain analysis of nonstationary signals. However, there is not a single TFR that can be considered optimum for all kinds of signals. This has motivated the appearance of a general optimization procedure trying to obtain a kernel or nucleus function specially matched to each of the signals to be analyzed. This paper proposes a set of kernel functions that solve the optimum TFR problem for the ease of seismic deconvolution using a vibroseis source. The postulated kernel functions are proved to be effective and simple to obtain and to use; one of them does not, use parameters of any kind, which makes it specially attractive for immediate practical use