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

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.