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Generalized Hilbert transform (GHT) has been widely and successfully used in signal processing and interpretation for many years. However, the order parameter in GHT can only be chosen in a certain range, and the GHT result is not stable with respect to the chosen order parameter, which usually leads to poor-stability and low-resolution outputs. To improve the stability of GHT and broaden its order parameter chosen range, and finally achieve high-efficiency and high-resolution results, we extend GHT by introducing the sign function, the two frequency integration parameters, and propose the Lp-order time–frequency spectra (LTFS). In LTFS, the sign function aims to broaden the chosen range of the order parameter into any positive numbers, and then leads to high-stability and high-resolution LTFS results; the two frequency integration parameters aim to optimize the computation efficiency and output resolution of LTFS. Synthetic one-dimensional (1D) channel data testing, synthetic two-dimensional (2D) seismic data, and actual three-dimensional (3D) seismic data examples demonstrate favorable capability of LTFS for edge detection.

Lp-Order Time–Frequency Spectra and Its Application in Edge Detection