Fractional Hilbert Transform And Its Application In Seismic Sedimentology

Seismic sedimentology is following the seismic stratigraphy and sequence stratigraphy occurs after a sedimentology of modern seismic technology and the emerging interdisciplinary combination is based on high-precision seismic data, outcrop of modern sedimentary environments and sedimentary environment model of joint feedback to identify the sedimentary units of the three-dimensional geometric shape, internal structure and the primary purpose of the deposition process methodology. Zeng Hongliu(doctor) who is Sedimentology founder of the Institute of Economic Research, University of Texas senior proposed 90°phase shift method, which enables layer and the corresponding logs. 90°phase shift technology allows the phase with the seismic stratigraphic significance, but the actual 90°phase shift which can not solve all problems.In this paper, we carried out research at any angle of this issue fractional phase shift of Hilbert transform. In the conventional Hilbert transform based on the Hilbert operator through research in the time domain and frequency domain in the form of derived time and frequency domain formula for the fractional Hilbert transform, and ultimately the fractional Hill Hilbert Transform, and realized the fractional Hilbert transform of the fast algorithm. Obtained fractional Hilbert transform the nature of the order obtained at the same time and wavelet-one correspondence between the early phase, and phase wavelet obtained the number zero and order one relationship.In Seismic Sedimentology, the phase axis is not sure reflection interface location, because phase axis is often complex wave superposition by vertical resolution of the effects. Which can not determine the formation of the approximate location in the seismic profile, layer and acoustic measurements Curve does not correspond well. Fractional Hilbert transform phase by any angle, to overcome the conventional 90° phase shift is zero defects phase to solve the problem of the phase phase shift at any angle. The polarity of phase axis has information of lithology, and the amplitude of phase axis has a stratigraphic concept. Allowing the formation in the seismic profile and corresponding logs. The key to seismic sedimentology one of the core --- 90°phase shift has been expanded.Time-domain algorithm for fractional Hilbert speed compared to the frequency domain algorithm is faster, and deal with the effects of time domain and frequency domain . Which can be found by the application in the XY region.Theory and practice show that phase shift at any angle of the fractional Hilbert transform supplement and expand 90°phase shift in the seismic sedimentology, so that seismic sedimentology is richer practicability in seismic exploration.